Structured chaos in a devil's staircase of the Josephson junction.

PubMed

Shukrinov, Yu M; Botha, A E; Medvedeva, S Yu; Kolahchi, M R; Irie, A

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Structured chaos in a devil's staircase of the Josephson junction

NASA Astrophysics Data System (ADS)

Shukrinov, Yu. M.; Botha, A. E.; Medvedeva, S. Yu.; Kolahchi, M. R.; Irie, A.

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Structured chaos in a devil's staircase of the Josephson junction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukrinov, Yu. M.; Botha, A. E., E-mail: bothaae@unisa.ac.za; Medvedeva, S. Yu.

2014-09-01

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior.more » These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.« less

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

An Exploratory Study of the Butterfly Effect Using Agent-Based Modeling

NASA Technical Reports Server (NTRS)

Khasawneh, Mahmoud T.; Zhang, Jun; Shearer, Nevan E. N.; Rodriquez-Velasquez, Elkin; Bowling, Shannon R.

2010-01-01

This paper provides insights about the behavior of chaotic complex systems, and the sensitive dependence of the system on the initial starting conditions. How much does a small change in the initial conditions of a complex system affect it in the long term? Do complex systems exhibit what is called the "Butterfly Effect"? This paper uses an agent-based modeling approach to address these questions. An existing model from NetLogo library was extended in order to compare chaotic complex systems with near-identical initial conditions. Results show that small changes in initial starting conditions can have a huge impact on the behavior of chaotic complex systems. The term the "butterfly effect" is attributed to the work of Edward Lorenz [1]. It is used to describe the sensitive dependence of the behavior of chaotic complex systems on the initial conditions of these systems. The metaphor refers to the notion that a butterfly flapping its wings somewhere may cause extreme changes in the ecological system's behavior in the future, such as a hurricane.

Generating Random Numbers by Means of Nonlinear Dynamic Systems

ERIC Educational Resources Information Center

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-01-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the…

Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

NASA Astrophysics Data System (ADS)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.

Polynomiography and Chaos

NASA Astrophysics Data System (ADS)

Kalantari, Bahman

Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.

Chaotic inflationary universe and the anisotropy of the large-scale structure

NASA Technical Reports Server (NTRS)

Chibisov, G. V.; Shtanov, Yu. V.

1991-01-01

It has been realized that the inflationary universe is in fact chaotic, that globally it is strongly inhomogeneous, and that the inflation in the universe as a whole is eternal. In such a picture the region available to modern observations is just a tiny part of the universe, in which inflation finished about 10(exp 10) years ago. In spite of the great popularity of the chaotic inflationary universe models, it is usually taken for granted that their specific features (such as strong global inhomogeneity of the universe) can hardly lead to any observable consequences. The argument is that all that is seen is just a tiny part of the universe, a region about 10(exp 28) cm, and the typical scales of considerable inhomogeneities are much greater than this size. In contrast to this opinion, an attempt is made to show that such observable consequences can really exist. The phenomenon closely connected with the origin of structure (galaxies, clusters, etc.) in the observable region is discussed. The main idea considered is the vacuum fluctuations evolution on the inhomogeneous background.

A quasi-crisis

NASA Astrophysics Data System (ADS)

Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng; Zhang, Kai; Jiang, Yu-Mei; Wang, Xu-Ming; He, Da-Ren

2002-03-01

A system concatenated by two area-preserving maps may be addressed as "quasi- dissipative," since such a system can display dissipative behaviors^1. This is due to noninvertibility induced by discontinuity in the system function. In such a system, the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives the quasi-crisis has been investigated numerically. It reads: ∝ (p-p_c)^-ν , where is defined as the averaged length of quasi-transients. The scaling exponent ν=1.66 ± 0.04. The critical parameter value equals p_c=-1.0069799. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Liu, Bocheng; Hu, Hanping; Miao, Suoxia

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

NASA Astrophysics Data System (ADS)

Gros, J.-B.; Kuhl, U.; Legrand, O.; Mortessagne, F.

2016-03-01

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Chaotic behavior of renal sympathetic nerve activity: effect of baroreceptor denervation and cardiac failure.

PubMed

DiBona, G F; Jones, S Y; Sawin, L L

2000-09-01

Nonlinear dynamic analysis was used to examine the chaotic behavior of renal sympathetic nerve activity in conscious rats subjected to either complete baroreceptor denervation (sinoaortic and cardiac baroreceptor denervation) or induction of congestive heart failure (CHF). The peak interval sequence of synchronized renal sympathetic nerve discharge was extracted and used for analysis. In control rats, this yielded a system whose correlation dimension converged to a low value over the embedding dimension range of 10-15 and whose greatest Lyapunov exponent was positive. Complete baroreceptor denervation was associated with a decrease in the correlation dimension of the system (before 2.65 +/- 0.27, after 1.64 +/- 0.17; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.201 +/- 0.008 bits/data point before, 0.177 +/- 0.004 bits/data point after, P < 0.02). CHF, a state characterized by impaired sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, was associated with a similar decrease in the correlation dimension (control 3.41 +/- 0.23, CHF 2.62 +/- 0.26; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.205 +/- 0.048 bits/data point control, 0.136 +/- 0.033 bits/data point CHF, P < 0.02). These results indicate that removal of sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, occurring either physiologically or pathophysiologically, is associated with a decrease in the correlation dimensions of the system and a reduction in chaotic behavior.

A chaotic view of behavior change: a quantum leap for health promotion.

PubMed

Resnicow, Ken; Vaughan, Roger

2006-09-12

The study of health behavior change, including nutrition and physical activity behaviors, has been rooted in a cognitive-rational paradigm. Change is conceptualized as a linear, deterministic process where individuals weigh pros and cons, and at the point at which the benefits outweigh the cost change occurs. Consistent with this paradigm, the associated statistical models have almost exclusively assumed a linear relationship between psychosocial predictors and behavior. Such a perspective however, fails to account for non-linear, quantum influences on human thought and action. Consider why after years of false starts and failed attempts, a person succeeds at increasing their physical activity, eating healthier or losing weight. Or, why after years of success a person relapses. This paper discusses a competing view of health behavior change that was presented at the 2006 annual ISBNPA meeting in Boston. Rather than viewing behavior change from a linear perspective it can be viewed as a quantum event that can be understood through the lens of Chaos Theory and Complex Dynamic Systems. Key principles of Chaos Theory and Complex Dynamic Systems relevant to understanding health behavior change include: 1) Chaotic systems can be mathematically modeled but are nearly impossible to predict; 2) Chaotic systems are sensitive to initial conditions; 3) Complex Systems involve multiple component parts that interact in a nonlinear fashion; and 4) The results of Complex Systems are often greater than the sum of their parts. Accordingly, small changes in knowledge, attitude, efficacy, etc may dramatically alter motivation and behavioral outcomes. And the interaction of such variables can yield almost infinite potential patterns of motivation and behavior change. In the linear paradigm unaccounted for variance is generally relegated to the catch all "error" term, when in fact such "error" may represent the chaotic component of the process. The linear and chaotic paradigms are however, not mutually exclusive, as behavior change may include both chaotic and cognitive processes. Studies of addiction suggest that many decisions to change are quantum rather than planned events; motivation arrives as opposed to being planned. Moreover, changes made through quantum processes appear more enduring than those that involve more rational, planned processes. How such processes may apply to nutrition and physical activity behavior and related interventions merits examination.

Theory of turbulent thermal convection

NASA Astrophysics Data System (ADS)

Lohse, Detlef

2002-03-01

We review our universal theory for the scaling of the Nusselt number and the Reynolds number as functions of the Rayleigh number and the Prandtl number in turbulent thermal convection (Siegfried Grossmann and Detlef Lohse, J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001)). This theory is based on a decomposition of the energy dissipation and the thermal dissipation into a bulk and a boundary layer contribution. We will in particular focus on the behavior for large Prandtl numbers and on the scaling behavior of the Reynolds number for which new experimental results have been obtained recently. We will also address the chaotic switching of the large scale wind of turbulence.

Design and FPGA Implementation of a Universal Chaotic Signal Generator Based on the Verilog HDL Fixed-Point Algorithm and State Machine Control

NASA Astrophysics Data System (ADS)

Qiu, Mo; Yu, Simin; Wen, Yuqiong; Lü, Jinhu; He, Jianbin; Lin, Zhuosheng

In this paper, a novel design methodology and its FPGA hardware implementation for a universal chaotic signal generator is proposed via the Verilog HDL fixed-point algorithm and state machine control. According to continuous-time or discrete-time chaotic equations, a Verilog HDL fixed-point algorithm and its corresponding digital system are first designed. In the FPGA hardware platform, each operation step of Verilog HDL fixed-point algorithm is then controlled by a state machine. The generality of this method is that, for any given chaotic equation, it can be decomposed into four basic operation procedures, i.e. nonlinear function calculation, iterative sequence operation, iterative values right shifting and ceiling, and chaotic iterative sequences output, each of which corresponds to only a state via state machine control. Compared with the Verilog HDL floating-point algorithm, the Verilog HDL fixed-point algorithm can save the FPGA hardware resources and improve the operation efficiency. FPGA-based hardware experimental results validate the feasibility and reliability of the proposed approach.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

NASA Astrophysics Data System (ADS)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation.

PubMed

Ballard, Christopher C; Esty, C Clark; Egolf, David A

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Chaos control applied to cardiac rhythms represented by ECG signals

NASA Astrophysics Data System (ADS)

Borem Ferreira, Bianca; Amorim Savi, Marcelo; Souza de Paula, Aline

2014-10-01

The control of irregular or chaotic heartbeats is a key issue in cardiology. In this regard, chaos control techniques represent a good alternative since they suggest treatments different from those traditionally used. This paper deals with the application of the extended time-delayed feedback control method to stabilize pathological chaotic heart rhythms. Electrocardiogram (ECG) signals are employed to represent the cardiovascular behavior. A mathematical model is employed to generate ECG signals using three modified Van der Pol oscillators connected with time delay couplings. This model provides results that qualitatively capture the general behavior of the heart. Controlled ECG signals show the ability of the strategy either to control or to suppress the chaotic heart dynamics generating less-critical behaviors.

Chaotic dynamics and its analysis of Hindmarsh-Rose neurons by Shil’nikov approach

NASA Astrophysics Data System (ADS)

Wei, Wei; Zuo, Min

2015-08-01

In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh-Rose (HR) neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results. Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

The Influence of Road Bumps Characteristics on the Chaotic Vibration of a Nonlinear Full-Vehicle Model with Driver

NASA Astrophysics Data System (ADS)

Fakhraei, J.; Khanlo, H. M.; Ghayour, M.; Faramarzi, Kh.

In this paper, the chaotic behavior of a ground vehicle system with driver subjected to road disturbances is studied and the relationship between the nonlinear vibration of the vehicle and ride comfort is evaluated. The vehicle system is modeled as fully nonlinear with seven degrees of freedom and an additional degree of freedom for driver (8-DOF). The excitation force is the road irregularities that are assumed as road speed control bumps. The sinusoidal, consecutive half-sine and dented-rectangular waveforms are considered to simulate the road speed control bumps. The nonlinearities of the system are due to the nonlinear springs and dampers that are used in the suspension system and tires. The governing differential equations are extracted under Newton-Euler laws and solved via numerical methods. The chaotic behaviors were studied in more detail with special techniques such as bifurcation diagrams, phase plane portrait, Poincaré map and Lyapunov exponents. The ride comfort was evaluated as the RMS value of the vertical displacement of the vehicle body and driver. Firstly, the effect of amplitude (height) and frequency (vehicle’s speed) of these speed control bumps on chaotic vibrations of vehicle are studied. The obtained results show that various forms of vibrations, such as periodic, subharmonic and chaotic vibrations, can be detected in the system behavior with the change of the height and frequency of speed control bumps and present different types of strange attractors in the vehicle with and without driver. Then, the influence of nonlinear vibration on ride comfort and the relationship between chaotic vibrations of the vehicle and driving comfort are investigated. The results of analyzing the RMS diagrams reveal that the chaotic behaviors can directly affect the driving comfort and lead to the driver’s comfort being reduced. The obtained results can be used in the design of vehicle and road bumps pavement.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method.

PubMed

Wang, Yu; Li, Feng-Ming; Wang, Yi-Ze

2015-06-01

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

PubMed Central

Suzuki, Yoko; Lu, Mingyang; Ben-Jacob, Eshel; Onuchic, José N.

2016-01-01

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer. PMID:26876008

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yu; Wang, Yi-Ze; Li, Feng-Ming, E-mail: fmli@bjut.edu.cn

2015-06-15

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two bucklingmore » cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.« less

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

NASA Astrophysics Data System (ADS)

Suzuki, Yoko; Lu, Mingyang; Ben-Jacob, Eshel; Onuchic, José N.

2016-02-01

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.

Granular chaos and mixing: Whirled in a grain of sand.

PubMed

Shinbrot, Troy

2015-09-01

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Granular chaos and mixing: Whirled in a grain of sand

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shinbrot, Troy, E-mail: shinbrot@rutgers.edu

2015-09-15

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combinesmore » micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.« less

An introduction to chaotic and random time series analysis

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

NASA Astrophysics Data System (ADS)

Sun, Changchun; Chen, Zhongtang; Xu, Qicheng

2017-12-01

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

Chaotic Expansions of Elements of the Universal Enveloping Superalgebra Associated with a Z2-graded Quantum Stochastic Calculus

NASA Astrophysics Data System (ADS)

Eyre, T. M. W.

Given a polynomial function f of classical stochastic integrator processes whose differentials satisfy a closed Ito multiplication table, we can express the stochastic derivative of f as We establish an analogue of this formula in the form of a chaotic decomposition for Z2-graded theories of quantum stochastic calculus based on the natural coalgebra structure of the universal enveloping superalgebra.

Generating random numbers by means of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-07-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the angular displacements of chaotic motion, random binary numerical arrays can be generated. To check the randomness of generated numerical arrays, the NIST Special Publication 800-20 method was adopted. As a result, it was found that all the random arrays which were generated by the chaotic motion could pass the validity criteria and some of them were even better than the quality of pseudo-random numbers generated by a computer. Through the experiments, it is demonstrated that chaotic pendulum can be used as an efficient mechanical facility in generating random numbers, and can be applied in teaching random motion to the students.

Chaotic behavior of channeling particles.

PubMed

Chen, Ling; Kaloyeros, Alain E.; Wang, Guang-Hou

1994-03-01

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

Numerical explorations of R. M. Goodwin's business cycle model.

PubMed

Jakimowicz, Aleksander

2010-01-01

Goodwin's model, which was formulated in , still attracts economists' attention. The model possesses numerous interesting properties that have been discovered only recently due to the development of the chaos theory and the complexity theory. The first numerical explorations of the model were conducted in the early s by Strotz, McAnulty and Naines (1953). They discovered the coexistence of attractors that are well-known today, two properties of chaotic systems: the sensitive dependence on the initial conditions and the sensitive dependence on parameters. The occurrence of periodic and chaotic attractors is dependent on the value of parameters in a system. In case of certain parametric values fractal basin boundaries exist which results in enormous system sensitivity to external noise. If periodic attractors are placed in the neighborhood of the fractal basin boundaries, then even a low external noise can move the trajectory into the region in which the basin's structure is tangled. This leads to a kind of movement that resembles a chaotic movement on a strange attractor. In Goodwin's model, apart from typical chaotic behavior, there exists yet another kind of complex movements - transient chaotic behavior that is caused by the occurrence of invariant chaotic sets that are not attracting. Such sets are represented by chaotic saddles. Some of the latest observation methods of trajectories lying on invariant chaotic sets that are not attracting are straddle methods. This article provides examples of the basin boundary straddle trajectory and the saddle straddle trajectory. These cases were studied by Lorenz and Nusse (2002). I supplement the results they acquired with calculations of capacity dimension and correlation dimension.

Universality and chaotic dynamics in reactive scattering of ultracold KRb molecules with K atoms

NASA Astrophysics Data System (ADS)

Li, Ming; Makrides, Constantinos; Petrov, Alexander; Kotochigova, Svetlana; Croft, James F. E.; Balakrishnan, Naduvalath; Kendrick, Brian K.

2017-04-01

We study the benchmark reaction between the most-celebrated ultracold polar molecule, KRb, with an ultracold K atom. For the first time we map out an accurate ab initio ground potential energy surface of the K2Rb complex in full dimensionality and performed a numerically exact quantum-mechanical calculation of reaction dynamics based on coupled-channels approach in hyperspherical coordinates. An analysis of the adiabatic hyperspherical potentials reveals a chaotic distribution for the short-range complex that plays a key role in governing the reaction outcome. The equivalent distribution for a lighter collisional system with a smaller density of states (here the Li2Yb trimer) only shows random behavior. We find an extreme sensitivity of our chaotic system to a small perturbation associated with the weak non-additive three-body potential contribution that does not affect the total reaction rate coefficient but leads to a significant change in the rotational distribution in the product molecule. In both cases the distribution of these rates is random or Poissonian. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and PHY-1619788 (S.K.), ARO MURI Grant No. W911NF-12-1-0476 (N.B. & S.K.), and DOE LDRD Grant No. 20170221ER (B.K.).

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

NASA Astrophysics Data System (ADS)

Chavarette, Fábio Roberto; Balthazar, José Manoel; Felix, Jorge L. P.; Rafikov, Marat

2009-05-01

This paper analyzes the non-linear dynamics, with a chaotic behavior of a particular micro-electro-mechanical system. We used a technique of the optimal linear control for reducing the irregular (chaotic) oscillatory movement of the non-linear systems to a periodic orbit. We use the mathematical model of a (MEMS) proposed by Luo and Wang.

Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

NASA Astrophysics Data System (ADS)

Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You

1998-09-01

Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

A note on chaotic unimodal maps and applications.

PubMed

Zhou, C T; He, X T; Yu, M Y; Chew, L Y; Wang, X G

2006-09-01

Based on the word-lift technique of symbolic dynamics of one-dimensional unimodal maps, we investigate the relation between chaotic kneading sequences and linear maximum-length shift-register sequences. Theoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the set of the universal sequence of one-dimensional chaotic unimodal maps is given. By stabilizing unstable periodic orbits on superstable periodic orbits, we also develop techniques to control the generation of long binary sequences.

Nonlinear optimal control for the synchronization of chaotic and hyperchaotic finance systems

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Ademi, S.; Ghosh, T.

2017-11-01

It is possible to make specific finance systems get synchronized to other finance systems exhibiting chaotic and hyperchaotic dynamics, by applying nonlinear optimal (H-infinity) control. This signifies that chaotic behavior can be generated in finance systems by exerting a suitable control input. Actually, a lead financial system is considered which exhibits inherently chaotic dynamics. Moreover, a follower finance system is introduced having parameters in its model that inherently prohibit the appearance of chaotic dynamics. Through the application of a suitable nonlinear optimal (H-infinity) control input it is proven that the follower finance system can replicate the chaotic dynamics of the lead finance system. By applying Lyapunov analysis it is proven that asymptotically the follower finance system gets synchronized with the lead system and that the tracking error between the state variables of the two systems vanishes.

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics.

PubMed

Lecca, Paola; Mura, Ivan; Re, Angela; Barker, Gary C; Ihekwaba, Adaoha E C

2016-01-01

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

Proving Chaotic Behavior of CBC Mode of Operation

NASA Astrophysics Data System (ADS)

Abidi, Abdessalem; Wang, Qianxue; Bouallegue, Belgacem; Machhout, Mohsen; Guyeux, Christophe

2016-06-01

The cipher block chaining (CBC) mode of operation was invented by IBM (International Business Machine) in 1976. It presents a very popular way of encrypting that is used in various applications. In this paper, we have mathematically proven that, under some conditions, the CBC mode of operation can admit a chaotic behavior according to Devaney. Some cases will be properly studied in order to provide evidence for this idea.

Controlling chaos with localized heterogeneous forces in oscillator chains.

PubMed

Chacón, Ricardo

2006-10-01

The effects of decreasing the impulse transmitted by localized periodic pulses on the chaotic behavior of homogeneous chains of coupled nonlinear oscillators are studied. It is assumed that when the oscillators are driven synchronously, i.e., all driving pulses transmit the same impulse, the chains display chaotic dynamics. It is shown that decreasing the impulse transmitted by the pulses of the two free end oscillators results in regularization with the whole array exhibiting frequency synchronization, irrespective of the chain size. A maximum level of amplitude desynchrony as the pulses of the two end oscillators narrow is typically found, which is explained as the result of two competing universal mechanisms: desynchronization induced by localized heterogeneous pulses and oscillation death of the complete chain induced by drastic decreasing of the impulse transmitted by such localized pulses. These findings demonstrate that decreasing the impulse transmitted by localized external forces can suppress chaos and lead to frequency-locked states in networks of dissipative systems.

Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

NASA Astrophysics Data System (ADS)

Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

2017-12-01

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

Nonlinear analysis of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea

NASA Astrophysics Data System (ADS)

Rojo-Garibaldi, Berenice; Salas-de-León, David Alberto; Adela Monreal-Gómez, María; Sánchez-Santillán, Norma Leticia; Salas-Monreal, David

2018-04-01

Hurricanes are complex systems that carry large amounts of energy. Their impact often produces natural disasters involving the loss of human lives and materials, such as infrastructure, valued at billions of US dollars. However, not everything about hurricanes is negative, as hurricanes are the main source of rainwater for the regions where they develop. This study shows a nonlinear analysis of the time series of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea obtained from 1749 to 2012. The construction of the hurricane time series was carried out based on the hurricane database of the North Atlantic basin hurricane database (HURDAT) and the published historical information. The hurricane time series provides a unique historical record on information about ocean-atmosphere interactions. The Lyapunov exponent indicated that the system presented chaotic dynamics, and the spectral analysis and nonlinear analyses of the time series of the hurricanes showed chaotic edge behavior. One possible explanation for this chaotic edge is the individual chaotic behavior of hurricanes, either by category or individually regardless of their category and their behavior on a regular basis.

Chaos in nuclei: Theory and experiment

NASA Astrophysics Data System (ADS)

Muñoz, L.; Molina, R. A.; Gómez, J. M. G.

2018-05-01

During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.

Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

NASA Astrophysics Data System (ADS)

Li, Chuang; Min, Fuhong; Jin, Qiusen; Ma, Hanyuan

2017-12-01

An active charge-controlled memristive Chua's circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

NASA Technical Reports Server (NTRS)

Lee, Nam C.; Parks, George K.

1992-01-01

A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

Information's role in the estimation of chaotic signals

NASA Astrophysics Data System (ADS)

Drake, Daniel Fred

1998-11-01

Researchers have proposed several methods designed to recover chaotic signals from noise-corrupted observations. While the methods vary, their qualitative performance does not: in low levels of noise all methods effectively recover the underlying signal; in high levels of noise no method can recover the underlying signal to any meaningful degree of accuracy. Of the methods proposed to date, all represent sub-optimal estimators. So: Is the inability to recover the signal in high noise levels simply a consequence of estimator sub-optimality? Or is estimator failure actually a manifestation of some intrinsic property of chaos itself? These questions are answered by deriving an optimal estimator for a class of chaotic systems and noting that it, too, fails in high levels of noise. An exact, closed- form expression for the estimator is obtained for a class of chaotic systems whose signals are solutions to a set of linear (but noncausal) difference equations. The existence of this linear description circumvents the difficulties normally encountered when manipulating the nonlinear (but causal) expressions that govern. chaotic behavior. The reason why even the optimal estimator fails to recover underlying chaotic signals in high levels of noise has its roots in information theory. At such noise levels, the mutual information linking the corrupted observations to the underlying signal is essentially nil, reducing the estimator to a simple guessing strategy based solely on a priori statistics. Entropy, long the common bond between information theory and dynamical systems, is actually one aspect of a far more complete characterization of information sources: the rate distortion function. Determining the rate distortion function associated with the class of chaotic systems considered in this work provides bounds on estimator performance in high levels of noise. Finally, a slight modification of the linear description leads to a method of synthesizing on limited precision platforms ``pseudo-chaotic'' sequences that mimic true chaotic behavior to any finite degree of precision and duration. The use of such a technique in spread-spectrum communications is considered.

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems.

PubMed

Liu, Yue; Guan, Jian; Ma, Chunyang; Guo, Shuxu

2016-08-01

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a12a21 = 0, while the Chua system satisfies a12a21 > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.

Nonlinear modeling of chaotic time series: Theory and applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifyingmore » and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.« less

Modelling chaotic vibrations using NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1993-01-01

Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2016-07-01

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

Future missions studies: Combining Schatten's solar activity prediction model with a chaotic prediction model

NASA Technical Reports Server (NTRS)

Ashrafi, S.

1991-01-01

K. Schatten (1991) recently developed a method for combining his prediction model with our chaotic model. The philosophy behind this combined model and his method of combination is explained. Because the Schatten solar prediction model (KS) uses a dynamo to mimic solar dynamics, accurate prediction is limited to long-term solar behavior (10 to 20 years). The Chaotic prediction model (SA) uses the recently developed techniques of nonlinear dynamics to predict solar activity. It can be used to predict activity only up to the horizon. In theory, the chaotic prediction should be several orders of magnitude better than statistical predictions up to that horizon; beyond the horizon, chaotic predictions would theoretically be just as good as statistical predictions. Therefore, chaos theory puts a fundamental limit on predictability.

Chaotic universe model.

PubMed

Aydiner, Ekrem

2018-01-15

In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de  >-1, w dm  ≥ 0, w m  ≥ 0 and w r  ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

Firefly algorithm with chaos

NASA Astrophysics Data System (ADS)

Gandomi, A. H.; Yang, X.-S.; Talatahari, S.; Alavi, A. H.

2013-01-01

A recently developed metaheuristic optimization algorithm, firefly algorithm (FA), mimics the social behavior of fireflies based on the flashing and attraction characteristics of fireflies. In the present study, we will introduce chaos into FA so as to increase its global search mobility for robust global optimization. Detailed studies are carried out on benchmark problems with different chaotic maps. Here, 12 different chaotic maps are utilized to tune the attractive movement of the fireflies in the algorithm. The results show that some chaotic FAs can clearly outperform the standard FA.

Using chaotic artificial neural networks to model memory in the brain

NASA Astrophysics Data System (ADS)

Aram, Zainab; Jafari, Sajad; Ma, Jun; Sprott, Julien C.; Zendehrouh, Sareh; Pham, Viet-Thanh

2017-03-01

In the current study, a novel model for human memory is proposed based on the chaotic dynamics of artificial neural networks. This new model explains a biological fact about memory which is not yet explained by any other model: There are theories that the brain normally works in a chaotic mode, while during attention it shows ordered behavior. This model uses the periodic windows observed in a previously proposed model for the brain to store and then recollect the information.

Chimera states in coupled Kuramoto oscillators with inertia.

PubMed

Olmi, Simona

2015-12-01

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.

Interesting examples of supervised continuous variable systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joe; Ramadge, Peter

1990-01-01

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of the closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.

A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums

NASA Astrophysics Data System (ADS)

Dantsev, Danylo

In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.

Quantitative Universality for a Class of Weakly Chaotic Systems

NASA Astrophysics Data System (ADS)

Venegeroles, Roberto

2014-02-01

We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties, hitherto regarded independently in the literature, can be represented by a single characteristic function ϕ. A universal criterion for the choice of ϕ is obtained within the Feigenbaum's renormalization-group approach. We find a general expression for the dispersion rate ζ( t) of initially nearby trajectories and we show that the instability scenario for weakly chaotic systems is more general than that originally proposed by Gaspard and Wang (Proc. Natl. Acad. Sci. USA 85:4591, 1988). We also consider a spatially extended version of such class of maps, which leads to anomalous diffusion, and we show that the mean squared displacement satisfies σ 2( t)˜ ζ( t). To illustrate our results, some examples are discussed in detail.

Chaotic behavior in electro-rotation

NASA Astrophysics Data System (ADS)

Lemaire, E.; Lobry, L.

2002-11-01

We study the dynamics of an insulating cylinder in a weakly conducting liquid when submitted to a DC electric field. The cylinder is free to rotate along its long axis which is perpendicular to the applied field. Above a threshold value of the electric field, the cylinder rotates in either direction with constant angular velocity. This instability is known as Quincke rotation and can be easily understood by considering the polarization induced by the free charges accumulation on the cylinder surface. Here we present preliminary experimental results which exhibit a chaotic dynamics of the cylinder for higher electric fields: the velocity is no longer constant and the rotation direction changes randomly. By taking into account the finite Maxwell-Wagner polarization relaxation time, we show that this chaotic behavior can be described by the Lorenz equations.

Chaotic attractors with separated scrolls

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr

2015-07-15

This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This newmore » approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.« less

Synchronization between uncertain nonidentical networks with quantum chaotic behavior

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2016-11-01

Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.

Predicting chaos in memristive oscillator via harmonic balance method.

PubMed

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor

PubMed Central

Zhou, Ping; Ahmad, Bashir; Ren, Guodong; Wang, Chunni

2018-01-01

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities. PMID:29342178

Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor.

PubMed

Ma, Jun; Zhou, Ping; Ahmad, Bashir; Ren, Guodong; Wang, Chunni

2018-01-01

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities.

Effect of randomness in logistic maps

NASA Astrophysics Data System (ADS)

Khaleque, Abdul; Sen, Parongama

2015-01-01

We study a random logistic map xt+1 = atxt[1 - xt] where at are bounded (q1 ≤ at ≤ q2), random variables independently drawn from a distribution. xt does not show any regular behavior in time. We find that xt shows fully ergodic behavior when the maximum allowed value of at is 4. However , averaged over different realizations reaches a fixed point. For 1 ≤ at ≤ 4, the system shows nonchaotic behavior and the Lyapunov exponent is strongly dependent on the asymmetry of the distribution from which at is drawn. Chaotic behavior is seen to occur beyond a threshold value of q1(q2) when q2(q1) is varied. The most striking result is that the random map is chaotic even when q2 is less than the threshold value 3.5699⋯ at which chaos occurs in the nonrandom map. We also employ a different method in which a different set of random variables are used for the evolution of two initially identical x values, here the chaotic regime exists for all q1 ≠ q2 values.

Noise-driven switching and chaotic itinerancy among dynamic states in a three-mode intracavity second-harmonic generation laser operating on a Λ transition

NASA Astrophysics Data System (ADS)

Otsuka, Kenju; Ohtomo, Takayuki; Maniwa, Tsuyoshi; Kawasaki, Hazumi; Ko, Jing-Yuan

2003-09-01

We studied the antiphase self-pulsation in a globally coupled three-mode laser operating in different optical spectrum configurations. We observed locking of modal pulsation frequencies, quasiperiodicity, clustering behaviors, and chaos, resulting from the nonlinear interaction among modes. The robustness of [p:q:r] three-frequency locking states and quasiperiodic oscillations against residual noise has been examined by using joint time-frequency analysis of long-term experimental time series. Two sharply antithetical types of switching behaviors among different dynamic states were observed during temporal evolutions; noise-driven switching and self-induced switching, which manifests itself in chaotic itinerancy. The modal interplay behind observed behaviors was studied by using the statistical dynamic quantity of the information circulation. Well-organized information flows among modes, which correspond to the number of degeneracies of modal pulsation frequencies, were found to be established in accordance with the inherent antiphase dynamics. Observed locking behaviors, quasiperiodic motions, and chaotic itinerancy were reproduced by numerical simulation of the model equations.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, Fang, E-mail: yf210yf@163.com; Wang, Guangyi, E-mail: wanggyi@163.com; Wang, Xiaowei

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numericalmore » simulations.« less

Temperature crossover of decoherence rates in chaotic and regular bath dynamics.

PubMed

Sanz, A S; Elran, Y; Brumer, P

2012-03-01

The effect of chaotic bath dynamics on the decoherence of a quantum system is examined for the vibrational degrees of freedom of a diatomic molecule in a realistic, constant temperature collisional bath. As an example, the specific case of I(2) in liquid xenon is examined as a function of temperature, and the results compared with an integrable xenon bath. A crossover in behavior is found: The integrable bath induces more decoherence at low bath temperatures than does the chaotic bath, whereas the opposite is the case at the higher bath temperatures. These results, verifying a conjecture due to Wilkie, shed light on the differing views of the effect of chaotic dynamics on system decoherence.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Long period astronomical cycles from the Triassic to Jurassic bedded chert sequence (Inuyama, Japan); Geologic evidences for the chaotic behavior of solar planets

NASA Astrophysics Data System (ADS)

Ikeda, Masayuki; Tada, Ryuji

2013-04-01

Astronomical theory predicts that ~2 Myr eccentricity cycle have changed its periodicity and amplitude through time because of the chaotic behavior of solar planets, especially Earth-Mars secular resonance. Although the ~2 Myr eccentricity cycle has been occasionally recognized in geological records, their frequency transitions have never been reported. To explore the frequency evolution of ~2 Myr eccentricity cycle, we used the bedded chert sequence in Inuyama, Japan, of which rhythms were proven to be of astronomical origin, covering the ~30 Myr long spanning from the Triassic to Jurassic. The frequency modulation of ~2 Myr cycle between ~1.6 and ~1.8 Myr periodicity detected from wavelet analysis of chert bed thickness variation are the first geologic record of chaotic transition of Earth-Mars secular resonance. The frequency modulation of ~2 Myr cycle will provide new constraints for the orbital models. Additionally, ~8 Myr cycle detected as chert bed thickness variation and its amplitude modulation of ~2 Myr cycle may be related to the amplitude modulation of ~2 Myr eccentricity cycle through non-linear process(es) of Earth system dynamics, suggesting possible impact of the chaotic behavior of Solar planets on climate change.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

PubMed

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

NASA Astrophysics Data System (ADS)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Investigation of a Chaotic Double Pendulum in the Basic Level Physics Teaching Laboratory

ERIC Educational Resources Information Center

Vanko, Peter

2007-01-01

First-year physics students at the Technical University of Budapest carry out a wide range of measurements in the Basic Level Physics Teaching Laboratory. One of the most exciting experiments is the investigation of a chaotic double pendulum by a V-scope, a powerful three-dimensional motion tracking system. After a brief introduction to the…

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

NASA Astrophysics Data System (ADS)

Wen-Bo, Wang; Xiao-Dong, Zhang; Yuchan, Chang; Xiang-Li, Wang; Zhao, Wang; Xi, Chen; Lei, Zheng

2016-01-01

In this paper, a new method to reduce noises within chaotic signals based on ICA (independent component analysis) and EMD (empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions (IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor. Project supported by the National Science and Technology, China (Grant No. 2012BAJ15B04), the National Natural Science Foundation of China (Grant Nos. 41071270 and 61473213), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science, China (Grant No. Z201303), and the Hubei Key Laboratory Foundation of Transportation Internet of Things, Wuhan University of Technology, China (Grant No.2015III015-B02).

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yue; Guan, Jian; Ma, Chunyang

2016-08-15

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a{sub 12}a{sub 21} = 0, while the Chua system satisfies a{sub 12}a{sub 21} > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential usemore » in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.« less

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Zhiwei; Sun, Yong; University of the Chinese Academy of Sciences, Beijing 100049

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weakmore » coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.« less

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ellis, George F.R.; Platts, Emma; Weltman, Amanda

2016-04-01

We use the phase plane analysis technique of Madsen and Ellis [1] to consider a universe with a true cosmological constant as well as a cosmological 'constant' that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological constant. We present only a proof ofmore » principle, with no definite claim on the physical mechanism required for the present dark energy to decay.« less

Experiments of reconstructing discrete atmospheric dynamic models from data (I)

NASA Astrophysics Data System (ADS)

Lin, Zhenshan; Zhu, Yanyu; Deng, Ziwang

1995-03-01

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, x n + 1 = 1- μx {2/n}, could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

A Simple Secure Hash Function Scheme Using Multiple Chaotic Maps

NASA Astrophysics Data System (ADS)

Ahmad, Musheer; Khurana, Shruti; Singh, Sushmita; AlSharari, Hamed D.

2017-06-01

The chaotic maps posses high parameter sensitivity, random-like behavior and one-way computations, which favor the construction of cryptographic hash functions. In this paper, we propose to present a novel hash function scheme which uses multiple chaotic maps to generate efficient variable-sized hash functions. The message is divided into four parts, each part is processed by a different 1D chaotic map unit yielding intermediate hash code. The four codes are concatenated to two blocks, then each block is processed through 2D chaotic map unit separately. The final hash value is generated by combining the two partial hash codes. The simulation analyses such as distribution of hashes, statistical properties of confusion and diffusion, message and key sensitivity, collision resistance and flexibility are performed. The results reveal that the proposed anticipated hash scheme is simple, efficient and holds comparable capabilities when compared with some recent chaos-based hash algorithms.

Temporal chaos in Boussinesq magnetoconvection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bekki, Naoaki; Moriguchi, Hirofumi; Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495

2007-01-15

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famousmore » Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.« less

Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian

2018-06-01

In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it; INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaoticmore » but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.« less

Chaotic evolution of the long-period Milankovitch cycle during the early Mesozoic: independent evidences from the Newark lacustrine sequence (North America) and the pelagic bedded chert sequence (Japan)

NASA Astrophysics Data System (ADS)

Ikeda, M.; Olsen, P. E.; Tada, R.

2012-12-01

The correlation of Earth's orbital parameters with climatic variations has been used to generate astronomically calibrated geologic time scales of high accuracy. However, because of the chaotic behavior of the solar planets, the orbital models have a large uncertainty beyond several tens of million years in the past. This chaotic behavior also causes the long-period astronomical cycles (> 0.5 Myr periodicity) to modulate their frequency and amplitude. In other words, their modulation patterns could be potential constraints for the orbital models. Here we report the first geologic constraints on the timing of frequency transition and amplitude modulation of the ~ 2 Myr long eccentricity cycles during the early Mesozoic. We examined the lake level records of the early Mesozoic Newark lacustrine sequence in North America and the biogenic silica burial rate of the pelagic bedded chert sequence in the Inuyama area, Japan, which are proven to be reflect the astronomical cycle (Olsen, 1986; Olsen and Kent, 1996; Ikeda et al., 2010). The time scales of the two sequences were orbitally calibrated with the end-Triassic mass extinction interval as the age anchor, covering ~ 30 Myr and ~ 65 Myr, respectively (Olsen et al., 2011; Ikeda et al., 2010, in prep). We find that the frequency modulation of ~ 2 Myr cycle between 2.4 Myr to 1.6 Myr cycle have occurred at least the Middle to Late Triassic. In addition, the ~ 2 Myr cycle modulate its amplitude with ~ 10 Myr periodicity with in-phase relation between the two. Similar modulation patterns of ~ 2 Myr cycles from the two independent geologic records indicate convincing evidences for the chaotic behavior of the Solar planets. Because these modulation patterns are different from the results of the orbital models by Laskar et al. (2004, 2011), our records will provide the new and challenging constraints for the orbital models in terms of chaotic behavior of Solar planets.

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field ismore » chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.« less

Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models

NASA Astrophysics Data System (ADS)

Kuznetsov, Sergey P.

2015-05-01

Results are reviewed concerning the planar problem of a plate falling in a resisting medium studied with models based on ordinary differential equations for a small number of dynamical variables. A unified model is introduced to conduct a comparative analysis of the dynamical behaviors of models of Kozlov, Tanabe-Kaneko, Belmonte-Eisenberg-Moses and Andersen-Pesavento-Wang using common dimensionless variables and parameters. It is shown that the overall structure of the parameter spaces for the different models manifests certain similarities caused by the same inherent symmetry and by the universal nature of the phenomena involved in nonlinear dynamics (fixed points, limit cycles, attractors, and bifurcations).

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

NASA Technical Reports Server (NTRS)

Gonzalez, J. Jesus; Espinosa, Ismael E.; Fuentes, Alberto M.

1995-01-01

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.

Chaotic behavior of the coronary circulation.

PubMed

Trzeciakowski, Jerome; Chilian, William M

2008-05-01

The regulation of the coronary circulation is a complex paradigm in which many inputs that influence vasomotor tone have to be integrated to provide the coronary vasomotor adjustments to cardiac metabolism and to perfusion pressure. We hypothesized that the integration of many disparate signals that influence membrane potential of smooth muscle cells, calcium sensitivity of contractile filaments, receptor trafficking result in complex non-linear characteristics of coronary vasomotion. To test this hypothesis, we measured an index of vasomotion, flowmotion, the periodic fluctuations of flow that reflect dynamic changes in resistances in the microcirculation. Flowmotion was continuously measured in periods ranging from 15 to 40 min under baseline conditions, during antagonism of NO synthesis, and during combined purinergic and NOS antagonism in the beating heart of anesthetized open-chest dogs. Flowmotion was measured in arterioles ranging from 80 to 135 microm in diameter. The signals from the flowmotion measurements were used to derive quantitative indices of non-linear behavior: power spectra, chaotic attractors, correlation dimensions, and the sum of the Lyapunov exponents (Kolmogorov-Sinai entropy), which reflects the total chaos and unpredictability of flowmotion. Under basal conditions, the coronary circulation demonstrated chaotic non-linear behavior with a power spectra showing three principal frequencies in flowmotion. Blockade of nitric oxide synthase or antagonism of purinergic receptors did not affect the correlation dimensions, but significantly increased the Kolmogorov-Sinai entropy, altered the power spectra of flowmotion, and changed the nature of the chaotic attractor. These changes are consistent with the view that certain endogenous controls, nitric oxide and various purines (AMP, ADP, ATP, adenosine) make the coronary circulation more predictable, and that blockade of these controls makes the control of flow less predictable and more chaotic.

Chaos in high-dimensional dissipative dynamical systems

PubMed Central

Ispolatov, Iaroslav; Madhok, Vaibhav; Allende, Sebastian; Doebeli, Michael

2015-01-01

For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE’s with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10−5 − 10−4 for d = 3 to essentially one for d ~ 50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos. PMID:26224119

Slow dynamics and regularization phenomena in ensembles of chaotic neurons

NASA Astrophysics Data System (ADS)

Rabinovich, M. I.; Varona, P.; Torres, J. J.; Huerta, R.; Abarbanel, H. D. I.

1999-02-01

We have explored the role of calcium concentration dynamics in the generation of chaos and in the regularization of the bursting oscillations using a minimal neural circuit of two coupled model neurons. In regions of the control parameter space where the slowest component, namely the calcium concentration in the endoplasmic reticulum, weakly depends on the other variables, this model is analogous to three dimensional systems as found in [1] or [2]. These are minimal models that describe the fundamental characteristics of the chaotic spiking-bursting behavior observed in real neurons. We have investigated different regimes of cooperative behavior in large assemblies of such units using lattice of non-identical Hindmarsh-Rose neurons electrically coupled with parameters chosen randomly inside the chaotic region. We study the regularization mechanisms in large assemblies and the development of several spatio-temporal patterns as a function of the interconnectivity among nearest neighbors.

Chaotic structure of oil prices

NASA Astrophysics Data System (ADS)

Bildirici, Melike; Sonustun, Fulya Ozaksoy

2018-01-01

The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period.

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

Desktop chaotic systems: Intuition and visualization

NASA Technical Reports Server (NTRS)

Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.

1993-01-01

This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.

Transversal homoclinic orbits in a transiently chaotic neural network.

PubMed

Chen, Shyan-Shiou; Shih, Chih-Wen

2002-09-01

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images for the system. The investigation provides a theoretical confirmation on the scenario of transient chaos for the system. All the parameter conditions for the theory can be examined numerically. The numerical ranges for the parameters which yield chaotic dynamics and convergent dynamics provide significant information in the annealing process in solving combinatorial optimization problems using this transiently chaotic neural network. (c) 2002 American Institute of Physics.

Chaotic Homes and Children’s Disruptive Behavior

PubMed Central

Jaffee, Sara R.; Haworth, Claire M. A.; Davis, Oliver S. P.; Plomin, Robert

2012-01-01

Chaotic home lives are correlated with behavior problems in children. In the study reported here, we tested whether there was a cross-lagged relation between children’s experience of chaos and their disruptive behaviors (conduct problems and hyperactivity-inattention). Using genetically informative models, we then tested for the first time whether the influence of household chaos on disruptive behavior was environmentally mediated and whether genetic influences on children’s disruptive behaviors accounted for the heritability of household chaos. We measured children’s perceptions of household chaos and parents’ ratings of children’s disruptive behavior at ages 9 and 12 in a sample of 6,286 twin pairs from the Twins Early Development Study (TEDS). There was a phenotypic cross-lagged relation between children’s experiences of household chaos and their disruptive behavior. In genetically informative models, we found that the effect of household chaos on subsequent disruptive behavior was environmentally mediated. However, genetic influences on disruptive behavior did not explain why household chaos was heritable. PMID:22547656

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

PubMed Central

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

2016-01-01

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

DOE PAGES

Chen, Shuying; Yu, Liping; Ren, Jingli; ...

2016-07-20

Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, andmore » there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

PubMed

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

2016-07-20

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.

PubMed

Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik

2014-01-01

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Entanglement as a signature of quantum chaos.

PubMed

Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

2004-01-01

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation

NASA Astrophysics Data System (ADS)

Hailong, Zhang; Enrong, Wang; Fuhong, Min; Ning, Zhang

2016-03-01

The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc-Wen force-velocity (F-v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Combinatorial Optimization by Amoeba-Based Neurocomputer with Chaotic Dynamics

NASA Astrophysics Data System (ADS)

Aono, Masashi; Hirata, Yoshito; Hara, Masahiko; Aihara, Kazuyuki

We demonstrate a computing system based on an amoeba of a true slime mold Physarum capable of producing rich spatiotemporal oscillatory behavior. Our system operates as a neurocomputer because an optical feedback control in accordance with a recurrent neural network algorithm leads the amoeba's photosensitive branches to search for a stable configuration concurrently. We show our system's capability of solving the traveling salesman problem. Furthermore, we apply various types of nonlinear time series analysis to the amoeba's oscillatory behavior in the problem-solving process. The results suggest that an individual amoeba might be characterized as a set of coupled chaotic oscillators.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novaes, Marcel, E-mail: marcel.novaes@gmail.com

2015-10-15

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-06-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Design and implementation of grid multi-scroll fractional-order chaotic attractors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei; Wu, Ranchao

2016-08-15

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most.more » Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.« less

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-04-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

A chaotic-dynamical conceptual model to describe fluid flow and contaminant transport in a fractured vadose zone. 1997 progress report and presentations at the annual meeting, Ernest Orlando Lawrence Berkeley National Laboratory, December 3--4, 1997

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faybishenko, B.; Doughty, C.; Geller, J.

1998-07-01

Understanding subsurface flow and transport processes is critical for effective assessment, decision-making, and remediation activities for contaminated sites. However, for fluid flow and contaminant transport through fractured vadose zones, traditional hydrogeological approaches are often found to be inadequate. In this project, the authors examine flow and transport through a fractured vadose zone as a deterministic chaotic dynamical process, and develop a model of it in these terms. Initially, the authors examine separately the geometric model of fractured rock and the flow dynamics model needed to describe chaotic behavior. Ultimately they will put the geometry and flow dynamics together to developmore » a chaotic-dynamical model of flow and transport in a fractured vadose zone. They investigate water flow and contaminant transport on several scales, ranging from small-scale laboratory experiments in fracture replicas and fractured cores, to field experiments conducted in a single exposed fracture at a basalt outcrop, and finally to a ponded infiltration test using a pond of 7 by 8 m. In the field experiments, they measure the time-variation of water flux, moisture content, and hydraulic head at various locations, as well as the total inflow rate to the subsurface. Such variations reflect the changes in the geometry and physics of water flow that display chaotic behavior, which they try to reconstruct using the data obtained. In the analysis of experimental data, a chaotic model can be used to predict the long-term bounds on fluid flow and transport behavior, known as the attractor of the system, and to examine the limits of short-term predictability within these bounds. This approach is especially well suited to the need for short-term predictions to support remediation decisions and long-term bounding studies. View-graphs from ten presentations made at the annual meeting held December 3--4, 1997 are included in an appendix to this report.« less

Plasticity performance of Al 0.5 CoCrCuFeNi high-entropy alloys under nanoindentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Li-ping; Chen, Shu-ying; Ren, Jing-li

2017-04-01

The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy, Al0.5 CoCrCuFeNi, were analyzed for the nanoindentation performed at two temperatures. Critical behavior of serrations at room temperature and chaotic flows at 200 °C were detected. These results are attributed to the interaction among a large number of slip bands. For the nanoindentation at room temperature, recurrent partial events between slip bands introduce a hierarchy of length scales, leading to a critical state. For the nanoindentation at 200 °C, there is no spatial interference between two slip bands, which is corresponding to the evolution of separated trajectorymore » of chaotic behavior« less

Clustering stock market companies via chaotic map synchronization

NASA Astrophysics Data System (ADS)

Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pascazio, S.

2005-01-01

A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial time series to the coupling strengths between maps. The simulation of a chaotic map dynamics gives rise to a natural partition of the data, as companies belonging to the same industrial branch are often grouped together. The identification of clusters of companies of a given stock market index can be exploited in the portfolio optimization strategies.

Effect of collision duration on the chaotic dynamics of a ball bouncing on a vertically vibrating plate

NASA Astrophysics Data System (ADS)

Jiang, Z. H.; Liang, Z. J.; Wu, A. C.; Zheng, R. H.

2018-03-01

Experiments have been performed to study the chaotic dynamics of a ball bouncing on a vertically vibrating plate. The velocity dependence of collision duration and coefficient of restitution is determined, and phase portraits of chaotic structures for the flight time and the relative collision velocities are obtained. Numerical calculations are carried out to examine the effects of velocity-dependent collision duration on the ball dynamics. It is revealed that when the collision is instantaneous, sticking solutions are always observed, whereas when the collision duration is taken into account, sticking solutions are destroyed and thereby chaos behaviors are induced.

Highly dissipative Hénon map behavior in the four-level model of the CO 2 laser with modulated losses

NASA Astrophysics Data System (ADS)

Pando L., C. L.; Acosta, G. A. Luna; Meucci, R.; Ciofini, M.

1995-02-01

We show that the four-level model for the CO 2 laser with modulated losses behaves in a qualitatively similar way as the highly dissipative Hénon map. The ubiquity of elements of the universal sequence, their related symbolic dynamics, and the presence of reverse bifurcations of chaotic bands in the model are reminiscent of the logistic map which is the limit of the Hénon map when the Jacobian equals zero. The coexistence of attractors, its dynamics related to contraction of volumes in phase space and the associated return maps can be correlated with those of the highly dissipative Hénon map.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

2D CFT partition functions at late times

NASA Astrophysics Data System (ADS)

Dyer, Ethan; Gur-Ari, Guy

2017-08-01

We consider the late time behavior of the analytically continued partition function Z( β + it) Z( β - it) in holographic 2 d CFTs. This is a probe of information loss in such theories and in their holographic duals. We show that each Virasoro character decays in time, and so information is not restored at the level of individual characters. We identify a universal decaying contribution at late times, and conjecture that it describes the behavior of generic chaotic 2 d CFTs out to times that are exponentially large in the central charge. It was recently suggested that at sufficiently late times one expects a crossover to random matrix behavior. We estimate an upper bound on the crossover time, which suggests that the decay is followed by a parametrically long period of late time growth. Finally, we discuss gravitationally-motivated integrable theories and show how information is restored at late times by a series of characters. This hints at a possible bulk mechanism, where information is restored by an infinite sum over non-perturbative saddles.

Chaotic Motifs in Gene Regulatory Networks

PubMed Central

Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang

2012-01-01

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs. PMID:22792171

Masursky Crater

NASA Technical Reports Server (NTRS)

2003-01-01

[figure removed for brevity, see original site]

Released 9 June 2003

The large, tilted blocks in this THEMIS visible image are chaotic terrain in Masursky Crater. Chaotic terrain is thought to occur when subsurface water is suddenly released to the surface, and the resulting loss of ground support causes the surface material to slump and break into blocks. Most of the chaotic terrain on Mars is seen in the vicinity of the large catastrophic outflow channels. Many of the outflow channels actually have chaotic terrain as their source. This chaotic terrain is the source of a small channel that connects to the much larger Tiu Valles.

Image information: VIS instrument. Latitude 12, Longitude 327.6 East (32.4 West). 19 meter/pixel resolution.

Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

A quasi-intermittency

NASA Astrophysics Data System (ADS)

He, Da-Ren; Wang, Xu-Ming; Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng

2002-03-01

A kind of discontinuous and noninvertible area-preserving maps can display behaviors as a dissipative one, so it may be addressed as a "quasi-dissipative system"^1. In a quasi-dissipative system the disappearance of some elliptic periodic orbits and the elliptic islands around them via a collision with the discontinuous border of the system function can be observed. A chaotic quasi-attractor dominates behavior of the system after the disappearance of the elliptic periodic orbit and a sequence of transition elliptic periodic orbits. When the chaotic quasi-attractor just appears, the chaotic time sequence shows a random intersperse between laminar and turbulence phases. All these are very similar to the properties of type V intermittency happened in a dissipative system. So, we may call the phenomenon as a "type V quasi-intermittency". However, there can be only some remnants of the last disappeared transition elliptic island instead of its "ghost", therefore type V quasi-intermittency does not obey the characteristic scaling laws of type V intermittency. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model.

PubMed

Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei

2017-11-17

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.

Chaos of energetic positron orbits in a dipole magnetic field and its potential application to a new injection scheme

NASA Astrophysics Data System (ADS)

Saitoh, H.; Yoshida, Z.; Yano, Y.; Nishiura, M.; Kawazura, Y.; Horn-Stanja, J.; Pedersen, T. Sunn

2016-10-01

We study the behavior of high-energy positrons emitted from a radioactive source in a magnetospheric dipole field configuration. Because the conservation of the first and second adiabatic invariants is easily destroyed in a strongly inhomogeneous dipole field for high-energy charged particles, the positron orbits are nonintegrable, resulting in chaotic motions. In the geometry of a typical magnetospheric levitated dipole experiment, it is shown that a considerable ratio of positrons from a 22Na source, located at the edge of the confinement region, has chaotic long orbit lengths before annihilation. These particles make multiple toroidal circulations and form a hollow toroidal positron cloud. Experiments with a small 22Na source in the Ring Trap 1 (RT-1) device demonstrated the existence of such long-lived positrons in a dipole field. Such a chaotic behavior of high-energy particles is potentially applicable to the formation of a dense toroidal positron cloud in the strong-field region of the dipole field in future studies.

Epileptic Seizure Prediction Using a New Similarity Index for Chaotic Signals

NASA Astrophysics Data System (ADS)

Niknazar, Hamid; Nasrabadi, Ali Motie

Epileptic seizures are generated by abnormal activity of neurons. The prediction of epileptic seizures is an important issue in the field of neurology, since it may improve the quality of life of patients suffering from drug resistant epilepsy. In this study a new similarity index based on symbolic dynamic techniques which can be used for extracting behavior of chaotic time series is presented. Using Freiburg EEG dataset, it is found that the method is able to detect the behavioral changes of the neural activity prior to epileptic seizures, so it can be used for prediction of epileptic seizure. A sensitivity of 63.75% with 0.33 false positive rate (FPR) in all 21 patients and sensitivity of 96.66% with 0.33 FPR in eight patients were achieved using the proposed method. Moreover, the method was evaluated by applying on Logistic and Tent map with different parameters to demonstrate its robustness and ability in determining similarity between two time series with the same chaotic characterization.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Chaos in the sunspot cycle - Analysis and prediction

NASA Technical Reports Server (NTRS)

Mundt, Michael D.; Maguire, W. Bruce, II; Chase, Robert R. P.

1991-01-01

The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

An investigation of chaotic Kolmogorov flows

NASA Technical Reports Server (NTRS)

Platt, N.; Sirovich, L.; Fitzmaurice, N.

1990-01-01

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.

PubMed

Papasavvas, Christoforos A; Wang, Yujiang; Trevelyan, Andrew J; Kaiser, Marcus

2015-09-01

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

Fulai, Wang

2012-12-01

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Chaotic examination

NASA Astrophysics Data System (ADS)

Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri

2018-01-01

In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.

Parametric number covariance in quantum chaotic spectra.

PubMed

Vinayak; Kumar, Sandeep; Pandey, Akhilesh

2016-03-01

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

FAST TRACK COMMUNICATION: Quantum anomalies and linear response theory

NASA Astrophysics Data System (ADS)

Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen, Doron

2010-08-01

The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ɛ2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time tɛ, and a self-generated (intrinsic) dephasing process leads to nonlinear dependence of D on ɛ2.

A full computation-relevant topological dynamics classification of elementary cellular automata.

PubMed

Schüle, Martin; Stoop, Ruedi

2012-12-01

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos."

Quantum-classical correspondence in the vicinity of periodic orbits

NASA Astrophysics Data System (ADS)

Kumari, Meenu; Ghose, Shohini

2018-05-01

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

NASA Astrophysics Data System (ADS)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Chaotic evolution of arms races

NASA Astrophysics Data System (ADS)

Tomochi, Masaki; Kono, Mitsuo

1998-12-01

A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

NASA Astrophysics Data System (ADS)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

Gross-Pitaevski map as a chaotic dynamical system.

PubMed

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

Developing Scenarios: Linking Environmental Scanning and Strategic Planning.

ERIC Educational Resources Information Center

Whiteley, Meredith A.; And Others

1990-01-01

The multiple scenario analysis technique for organizational planning used by multinational corporations is adaptable for colleges and universities. Arizona State University launched a futures-based planning project using the Delphi technique and cross-impact analysis to produce three alternative scenarios (stable, turbulent, and chaotic) to expand…

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

Characterization of normality of chaotic systems including prediction and detection of anomalies

NASA Astrophysics Data System (ADS)

Engler, Joseph John

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

Coexisting multiple attractors and riddled basins of a memristive system.

PubMed

Wang, Guangyi; Yuan, Fang; Chen, Guanrong; Zhang, Yu

2018-01-01

In this paper, a new memristor-based chaotic system is designed, analyzed, and implemented. Multistability, multiple attractors, and complex riddled basins are observed from the system, which are investigated along with other dynamical behaviors such as equilibrium points and their stabilities, symmetrical bifurcation diagrams, and sustained chaotic states. With different sets of system parameters, the system can also generate various multi-scroll attractors. Finally, the system is realized by experimental circuits.

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, L. H.; Xiang, Y. Y.; Dun, G. T.

The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaoticmore » attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.« less

Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

NASA Astrophysics Data System (ADS)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

Incrementalism and Strategic Change: A University's Experience

ERIC Educational Resources Information Center

Arnaboldi, Michela; Azzone, Giovanni

2005-01-01

Purpose: The processual interpretation of strategic change has been often applied to private companies searching for a logic behind their apparent chaotic transformation. The purpose of this paper is to report on an experience in a public organisation, an Italian university, where this perspective is exceptionally reflected, entailing a refining…

Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: Multiple states and routes to chaos

NASA Astrophysics Data System (ADS)

Verjus, Romuald; Guillou, Sylvain; Ezersky, Alexander; Angilella, Jean-Régis

2016-12-01

The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (ReT) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., "Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state," Phys. Fluids 15, 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

Hyperpolarization-Activated Current Induces Period-Doubling Cascades and Chaos in a Cold Thermoreceptor Model

PubMed Central

Xu, Kesheng; Maidana, Jean P.; Caviedes, Mauricio; Quero, Daniel; Aguirre, Pablo; Orio, Patricio

2017-01-01

In this article, we describe and analyze the chaotic behavior of a conductance-based neuronal bursting model. This is a model with a reduced number of variables, yet it retains biophysical plausibility. Inspired by the activity of cold thermoreceptors, the model contains a persistent Sodium current, a Calcium-activated Potassium current and a hyperpolarization-activated current (Ih) that drive a slow subthreshold oscillation. Driven by this oscillation, a fast subsystem (fast Sodium and Potassium currents) fires action potentials in a periodic fashion. Depending on the parameters, this model can generate a variety of firing patterns that includes bursting, regular tonic and polymodal firing. Here we show that the transitions between different firing patterns are often accompanied by a range of chaotic firing, as suggested by an irregular, non-periodic firing pattern. To confirm this, we measure the maximum Lyapunov exponent of the voltage trajectories, and the Lyapunov exponent and Lempel-Ziv's complexity of the ISI time series. The four-variable slow system (without spiking) also generates chaotic behavior, and bifurcation analysis shows that this is often originated by period doubling cascades. Either with or without spikes, chaos is no longer generated when the Ih is removed from the system. As the model is biologically plausible with biophysically meaningful parameters, we propose it as a useful tool to understand chaotic dynamics in neurons. PMID:28344550

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

A financial market model with two discontinuities: Bifurcation structures in the chaotic domain

NASA Astrophysics Data System (ADS)

Panchuk, Anastasiia; Sushko, Iryna; Westerhoff, Frank

2018-05-01

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

Emergence of chimeras through induced multistability

NASA Astrophysics Data System (ADS)

Ujjwal, Sangeeta Rani; Punetha, Nirmal; Prasad, Awadhesh; Ramaswamy, Ramakrishna

2017-03-01

Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators—with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)—inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.

A reanalysis of "Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons".

PubMed

Engelken, Rainer; Farkhooi, Farzad; Hansel, David; van Vreeswijk, Carl; Wolf, Fred

2016-01-01

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.

Exploration of the Chaotic Behaviour in a Buck-Boost Converter Depending on the Converter and Load Elements

NASA Astrophysics Data System (ADS)

Demirbaş, Şevki; Fidanboy, Hikmet; Kurt, Erol

2016-08-01

In this paper, detailed analyses of the chaotic behavior observed in a buck-boost converter are presented. Although this basic converter system is already known world-wide for the purpose of dc-dc conversion of the output of renewable energy systems, it indicates certain chaotic regimes where both the output amplitude and frequency change randomly. This chaotic regime can yield an unstable output over the resistive or resistive/inductive electrical loads. This study presents a detailed map for the regular and chaotic regions in terms of material parameters, such as converter capacitance C, resistive load R, and inductive load L. Thus, the stable area of operation for efficient and renewable electricity production will be ascertained for the studied converter system. We emphasize that the material parameters C, R, and L play important roles in generating energy from the solar cell; indeed, the stability increases with higher values of the converter capacitor and load inductance, whereas it decreases according to the resistive load. A number of periodic windows have been observed and the output frequency gives a broad-band spectrum of up to 50 kHz.

Detecting chaos in irregularly sampled time series.

PubMed

Kulp, C W

2013-09-01

Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.

Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

PubMed

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

From globally coupled maps to complex-systems biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaneko, Kunihiko, E-mail: kaneko@complex.c.u-tokyo.ac.jp

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Presence of 1/f noise in the temporal structure of psychoacoustic parameters of natural and urban sounds.

PubMed

Yang, Ming; De Coensel, Bert; Kang, Jian

2015-08-01

1/f noise or pink noise, which has been shown to be universal in nature, has also been observed in the temporal envelope of music, speech, and environmental sound. Moreover, the slope of the spectral density of the temporal envelope of music has been shown to correlate well to its pleasing, dull, or chaotic character. In this paper, the temporal structure of a number of instantaneous psychoacoustic parameters of environmental sound is examined in order to investigate whether a 1/f temporal structure appears in various types of sound that are generally preferred by people in everyday life. The results show, to some extent, that different categories of environmental sounds have different temporal structure characteristics. Only a number of urban sounds considered and birdsong, generally, exhibit 1/f behavior on short to medium duration time scales, i.e., from 0.1 s to 10 s, in instantaneous loudness and sharpness, whereas a more chaotic variation is found in birdsong at longer time scales, i.e., of 10 s-200 s. The other sound categories considered exhibit random or monotonic variations in the different time scales. In general, this study shows that a 1/f temporal structure is not necessarily present in environmental sounds that are commonly perceived as pleasant.

A Weyl-Dirac cosmological model with DM and DE

NASA Astrophysics Data System (ADS)

Israelit, Mark

2011-03-01

In the Weyl-Dirac (W-D) framework a spatially closed cosmological model is considered. It is assumed that the space-time of the universe has a chaotic Weylian microstructure but is described on a large scale by Riemannian geometry. Locally fields of the Weyl connection vector act as creators of massive bosons having spin 1. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe. At the beginning the universe is a spherically symmetric geometric entity without matter. Primary matter is created by Dirac’s gauge function very close to the beginning. In the early epoch, when the temperature of the universe achieves its maximum, chaotically oriented Weyl vector fields being localized in micro-cells create weylons. In the dust dominated period Dirac’s gauge function is giving rise to dark energy, the latter causing the cosmic acceleration at present. This oscillatory universe has an initial radius identical to the Plank length = 1.616 exp (-33) cm, at present the cosmic scale factor is 3.21 exp (28) cm, while its maximum value is 8.54 exp (28) cm. All forms of matter are created by geometrically based functions of the W-D theory.

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model

PubMed Central

Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus

2016-01-01

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Chaotic electron transport in semiconductor devices

NASA Astrophysics Data System (ADS)

Scannell, William Christian

The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q, that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of DF values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high DF values are shown to de-correlate at smaller increments of field than the FCF with lower DF values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated.

Fermi acceleration in time-dependent billiards: theory of the velocity diffusion in conformally breathing fully chaotic billiards

NASA Astrophysics Data System (ADS)

Batistić, Benjamin; Robnik, Marko

2011-09-01

We study aspects of the Fermi acceleration (the unbounded growth of the energy) in a certain class of time-dependent 2D billiards. Specifically, we look at the conformally breathing billiards (periodic oscillation of the boundary which preserves the shape of the billiard at all times), which are fully chaotic as static (frozen) billiards, and we show that for large velocities around v0 and for not too long times, we observe just normal diffusion of the velocity as a function of the physical (continuous) time, around v0. However, the diffusion is not homogeneous, as the diffusion constant D depends on v0 as a power law D∝1/v30. Taking this into account, we show that to the leading order the average velocity v(n) as a function of the number of collisions n obeys a power law v∝n1/6 thus, the Fermi acceleration exponent is β = 1/6, which is in excellent agreement with the numerical calculations of the fully chaotic oval billiard, the Sinai billiard and the cardioid billiard. The error of the velocity estimates is of the order 1/v2. Thus, the higher the velocity, the better our analytic approximation. Moreover, we derive the underlying universal equation of the velocity dynamics of the time-dependent conformally breathing billiards, correct up to and including the order 1/v in the regime of the large velocity of the particle v. This universal equation does not depend on the dynamical properties of the system (integrability, ergodicity, chaoticity). We present the results of the numerical simulations for three billiards in complete agreement with the theory. We believe that this is a first step towards theoretical understanding of the power law growth and the Fermi acceleration exponents in 2D billiards, although our theory is so far specialized to the conformally breathing fully chaotic billiards.

Memcapacitor model and its application in chaotic oscillator with memristor.

PubMed

Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

2017-01-01

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps

NASA Astrophysics Data System (ADS)

Bukh, Andrei V.; Slepnev, Andrei V.; Anishchenko, Vadim S.; Vadivasova, Tatiana E.

2018-05-01

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

NASA Astrophysics Data System (ADS)

Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella

2017-03-01

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

Predictors of Behavioral Regulation in Kindergarten: Household Chaos, Parenting, and Early Executive Functions

ERIC Educational Resources Information Center

Vernon-Feagans, Lynne; Garrett-Peters, Patricia; Willoughby, Michael

2016-01-01

Behavioral regulation is an important school readiness skill that has been linked to early executive function (EF) and later success in learning and school achievement. Although poverty and related risks, as well as negative parenting, have been associated with poorer EF and behavioral regulation, chaotic home environments may also play a role in…

Nonlinear behavior of the tarka flute's distinctive sounds.

PubMed

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Nonlinear behavior of the tarka flute's distinctive sounds

NASA Astrophysics Data System (ADS)

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

PubMed

Sharma, Vijay

2009-09-10

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

PubMed Central

Sharma, Vijay

2009-01-01

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts. PMID:19812706

Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force

NASA Astrophysics Data System (ADS)

Ando, Hiroyasu; Suetani, Hiromichi; Kurths, Jürgen; Aihara, Kazuyuki

2012-07-01

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1:1 phase locking between a single spike and one period of the force and 1:l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.

A local chaotic quasi-attractor in a kicked rotator

NASA Astrophysics Data System (ADS)

Jiang, Yu-Mei; Lu, Yun-Qing; Zhao, Jin-Gang; Wang, Xu-Ming; Chen, He-Sheng; He, Da-Ren

2002-03-01

Recently, Hu et al. reported a diffusion in a special kind of stochastic web observed in a kicked rotator described by a discontinuous but invertible two-dimensional area-preserving map^1. We modified the function form of the system so that the period of the kicking force becomes different in two parts of the space, and the conservative map becomes both discontinuous and noninvertible. It is found that when the ratio between both periods becomes smaller or larger than (but near to) 1, the chaotic diffusion in the web transfers to chaotic transients, which are attracted to the elliptic islands those existed inside the holes of the web earlier when the ratio equals 1. As soon as reaching the islands, the iteration follows the conservative laws exactly. Therefore we address these elliptic islands as "regular quasi-attractor"^2. When the ratio increases further and becomes far from 1, all the elliptic islands disappear and a local chaotic quasi-attractor appears instead. It attracts the iterations starting from most initial points in the phase space. This behavior may be considered as a kind of "confinement" of chaotic motion of a particle. ^1B. Hu et al., Phys.Rev.Lett.,82(1999)4224. ^2J. Wang et al., Phys.Rev.E, 64(2001)026202.

Effect of Parametric Dichotomic Markov Noise on the Properties of Chaotic Transitions in Dynamical Systems

NASA Astrophysics Data System (ADS)

Gac, J. M.; Żebrowski, J. J.

A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.

Reconfigurable dynamic all-optical chaotic logic operations in an optically injected VCSEL

NASA Astrophysics Data System (ADS)

Zhong, Dong-Zhou; Xu, Ge-Liang; Luo, Wei; Xiao, Zhen-Zhen

2017-12-01

Not Available Project supported by the National Natural Science Foundation of China (Grant No. 61475120) and the Innovative Projects in Guangdong Colleges and Universities, China (Grant No. 2015KTSCX146).

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

NASA Astrophysics Data System (ADS)

Subramanian, Natarajan; Kellogg, Louise H.; Turcotte, Donald L.

2009-09-01

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421-432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376-380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^{-1/2} . However, it is observed that stretching becomes exponential log S˜ t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^{-1/2} . This behavior is consistent with a random multiplicative stretching process.

Working Towards Führer: A Chaotic View

NASA Astrophysics Data System (ADS)

Cakar, Ulas

Leadership is a concept that has been discussed since the beginning of history. Even though there have been many theories in the field accepting leadership's role in bringing order, chaotic aspects of leadership are generally neglected. This chapter aims to examine the leadership beyond an orderly interpretation of universe. For this purpose, Third Reich period and leadership during this period will be examined. Ian Kershaw's "Working Towards Führer" concept provides a unique understanding of leadership concept. It goes beyond the dualist depiction of Third Reich, it does not state Adolf Hitler as an all powerful dictator, or a weak one. Rather, he expresses that due to the conditions in the Third Reich, Adolf Hitler was both of this. This complex situation can be understood deeper when it is examined through the lens of chaos theory. This study contributes to the field by being the first in using chaos theory for examining "Working Towards Führer" concept and its development. Seemingly orderly nature of synchronization process and its vortex will be shown. Adolf Hitler's storm spot position in the chaotic system and its dynamics are explained. War's entropic power and its effect on the downfall of the system is crucial in understanding this unique chaotic system. The chaotic pattern of "Working Towards Führer" offers an opportunity to analyze the complexities of the leadership concept.

Supply based on demand dynamical model

NASA Astrophysics Data System (ADS)

Levi, Asaf; Sabuco, Juan; Sanjuán, Miguel A. F.

2018-04-01

We propose and numerically analyze a simple dynamical model that describes the firm behaviors under uncertainty of demand. Iterating this simple model and varying some parameter values, we observe a wide variety of market dynamics such as equilibria, periodic, and chaotic behaviors. Interestingly, the model is also able to reproduce market collapses.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Fast, Parallel and Secure Cryptography Algorithm Using Lorenz's Attractor

NASA Astrophysics Data System (ADS)

Marco, Anderson Gonçalves; Martinez, Alexandre Souto; Bruno, Odemir Martinez

A novel cryptography method based on the Lorenz's attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography applications. An internet page has been set up, which enables the readers to test the algorithm and also to try to break into the cipher.

Synchronization of networked chaotic oscillators under external periodic driving.

PubMed

Yang, Wenchao; Lin, Weijie; Wang, Xingang; Huang, Liang

2015-03-01

The dynamical responses of a complex system to external perturbations are of both fundamental interest and practical significance. Here, by the model of networked chaotic oscillators, we investigate how the synchronization behavior of a complex network is influenced by an externally added periodic driving. Interestingly, it is found that by a slight change of the properties of the external driving, e.g., the frequency or phase lag between its intrinsic oscillation and external driving, the network synchronizability could be significantly modified. We demonstrate this phenomenon by different network models and, based on the method of master stability function, give an analysis on the underlying mechanisms. Our studies highlight the importance of external perturbations on the collective behaviors of complex networks, and also provide an alternate approach for controlling network synchronization.

Quantum Tunneling and Chaos in Classical Scale Walkers

NASA Astrophysics Data System (ADS)

Su, Jenny; Dijksman, Joshua; Ward, Jeremy; Behringer, Robert

2014-03-01

We study the behavior of `walkers' small droplets bouncing on a fluid layer vibrated at amplitudes just below the onset of Faraday instability. It was shown recently that despite their macroscopic size, the droplet dynamics are stochastic in nature and reminiscent of the dual particle-wave dynamics in the realm of quantum mechanics (Couder PRL 2006). We use these walkers to study how chaos, which is macroscopically unpredictable, will manifest in a quantum setting. Pecora showed in 2011 that tunneling for particles that have a chaotic ground state is different from tunneling for particles with a regular ground state (PRE 2011). In the experiment we gather data that illustrates the particle trajectory and tunneling behavior as particles transition across the barrier in the double well system with both integrable and chaotic shapes.

Controlling chaotic behavior in CO2 and other lasers

NASA Astrophysics Data System (ADS)

1993-06-01

Additional substantial experimental progress has been made, in the third month of the project, in setting up equipment and testing for producing chaotic behavior with a CO2 laser. The project goal is to synchronize and control chaos in CO2 and other lasers, and thereby increase the power in ensembles of coupled laser sources. Numerous investigations into the chaos regime have been made, a second CO2 laser has been brought on stream, and work is progressing in the fourth month toward coupling the two lasers and control of the first laser. It is also intended to submit at least two papers to the Second Experimental Chaos Conference which is supported by the Office of Naval Research. Abstracts to those two papers are attached. Last month's report discussed the experimental investigation of nonlinear dynamics of CO2 lasers which involved a new technique of inducing chaos. In this new technique, an acoustically modulated feedback of the laser light was used and led to chaotic dynamics at a very low modulation frequency of 375 Hz. Since then, new results have been obtained by an Electro-Optical Modulation (EOM) technique. In the new setup, the electro-optical modulator is placed in an external cavity outside the laser.

Long-Range Correlations in Stride Intervals May Emerge from Non-Chaotic Walking Dynamics

PubMed Central

Ahn, Jooeun; Hogan, Neville

2013-01-01

Stride intervals of normal human walking exhibit long-range temporal correlations. Similar to the fractal-like behaviors observed in brain and heart activity, long-range correlations in walking have commonly been interpreted to result from chaotic dynamics and be a signature of health. Several mathematical models have reproduced this behavior by assuming a dominant role of neural central pattern generators (CPGs) and/or nonlinear biomechanics to evoke chaos. In this study, we show that a simple walking model without a CPG or biomechanics capable of chaos can reproduce long-range correlations. Stride intervals of the model revealed long-range correlations observed in human walking when the model had moderate orbital stability, which enabled the current stride to affect a future stride even after many steps. This provides a clear counterexample to the common hypothesis that a CPG and/or chaotic dynamics is required to explain the long-range correlations in healthy human walking. Instead, our results suggest that the long-range correlation may result from a combination of noise that is ubiquitous in biological systems and orbital stability that is essential in general rhythmic movements. PMID:24086274

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less

Dynamics of delay-coupled FitzHugh-Nagumo neural rings.

PubMed

Mao, Xiaochen; Sun, Jianqiao; Li, Shaofan

2018-01-01

This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.

Dynamics of delay-coupled FitzHugh-Nagumo neural rings

NASA Astrophysics Data System (ADS)

Mao, Xiaochen; Sun, Jianqiao; Li, Shaofan

2018-01-01

This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.

A vast amount of various invariant tori in the Nosé-Hoover oscillator.

PubMed

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

Discrete dynamical laser equation for the critical onset of bistability, entanglement and disappearance

NASA Astrophysics Data System (ADS)

Abdul, M.; Farooq, U.; Akbar, Jehan; Saif, F.

2018-06-01

We transform the semi-classical laser equation for single mode homogeneously broadened lasers to a one-dimensional nonlinear map by using the discrete dynamical approach. The obtained mapping, referred to as laser logistic mapping (LLM), characteristically exhibits convergent, cyclic and chaotic behavior depending on the control parameter. Thus, the so obtained LLM explains stable, bistable, multi-stable, and chaotic solutions for output field intensity. The onset of bistability takes place at a critical value of the effective gain coefficient. The obtained analytical results are confirmed through numerical calculations.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

NASA Astrophysics Data System (ADS)

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lei; Department of Mathematics and Physics, Hefei University, Hefei 230601; Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn

2015-12-15

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator.

A case study in bifurcation theory

NASA Astrophysics Data System (ADS)

Khmou, Youssef

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

Experimental chaotic quantification in bistable vortex induced vibration systems

NASA Astrophysics Data System (ADS)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear out the regularity of periodic responses. For this purpose, a surrogate data test is used in order to check the hypotheses for the presence of chaotic behavior. The analyses from the experimental results support the hypothesis from simulation that chaotic response is likely occur on the real system.

Solar system dynamics

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

The rotational dynamics of irregularly shaped satellites and the origin of Kirkwood Gaps are discussed. The chaotic tumbling of Hyperion and the anomalously low eccentricity of Deimos are examined. The Digital Orrery is used to explore the phase space of the ellipic restricted three body problem near the principal commensurabilities (2/1, 5/2, 3/1, and 3/2). The results for the 3/1 commensurability are in close agreement with those found earlier with the algebraic mapping method. Large chaotic zones are associated with the 3/1, 2/1 and 5/2 resonances, where there are gaps in the distribution of asteroids. The region near the 3/2 resonance, where the Hilda group of asteroids is located, is largely devoid of chaotic behavior. Thus, there is a qualitative agreement between the character of the motion and the distribution of asteroids.

How to control chaotic behaviour and population size with proportional feedback

NASA Astrophysics Data System (ADS)

Liz, Eduardo

2010-01-01

We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior, leading the system to a stable equilibrium. In this Letter, we make a rigorous analysis of the proportional feedback method under certain conditions fulfilled by a wide family of maps. We show that it is possible to stabilize the chaotic dynamics towards a globally stable positive equilibrium, that can be chosen among a broad range of possible values. In particular, the size of the population can be enhanced by control in form of population reduction. This paradoxical phenomenon is known as the hydra effect, and it has important implications in the design of strategies in such areas as fishing, pest management, and conservation biology.

Universality in volume-law entanglement of scrambled pure quantum states.

PubMed

Nakagawa, Yuya O; Watanabe, Masataka; Fujita, Hiroyuki; Sugiura, Sho

2018-04-24

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. The thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and mandate a correction to this simple volume law. The elucidation of the size dependence of the entanglement entropy is thus essentially important in linking quantum physics with thermodynamics. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing equilibrium. We numerically find that our formula applies universally to any sufficiently scrambled pure state representing thermal equilibrium, i.e., energy eigenstates of non-integrable models and states after quantum quenches. Our formula is exploited as diagnostics for chaotic systems; it can distinguish integrable models from non-integrable models and many-body localization phases from chaotic phases.

Chaotic Terrain

NASA Technical Reports Server (NTRS)

2003-01-01

[figure removed for brevity, see original site]

Released 4 June 2003

Chaotic terrain on Mars is thought to form when there is a sudden removal of subsurface water or ice, causing the surface material to slump and break into blocks. The chaotic terrain in this THEMIS visible image is confined to a crater just south of Elysium Planitia. It is common to see chaotic terrain in the vicinity of the catastrophic outflow channels on Mars, but the terrain in this image is on the opposite side of the planet from these channels, making it somewhat of an oddity.

Image information: VIS instrument. Latitude -5.9, Longitude 108.1 East (251.9 West). 19 meter/pixel resolution.

Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

Efficient and universal quantum key distribution based on chaos and middleware

NASA Astrophysics Data System (ADS)

Jiang, Dong; Chen, Yuanyuan; Gu, Xuemei; Xie, Ling; Chen, Lijun

2017-01-01

Quantum key distribution (QKD) promises unconditionally secure communications, however, the low bit rate of QKD cannot meet the requirements of high-speed applications. Despite the many solutions that have been proposed in recent years, they are neither efficient to generate the secret keys nor compatible with other QKD systems. This paper, based on chaotic cryptography and middleware technology, proposes an efficient and universal QKD protocol that can be directly deployed on top of any existing QKD system without modifying the underlying QKD protocol and optical platform. It initially takes the bit string generated by the QKD system as input, periodically updates the chaotic system, and efficiently outputs the bit sequences. Theoretical analysis and simulation results demonstrate that our protocol can efficiently increase the bit rate of the QKD system as well as securely generate bit sequences with perfect statistical properties. Compared with the existing methods, our protocol is more efficient and universal, it can be rapidly deployed on the QKD system to increase the bit rate when the QKD system becomes the bottleneck of its communication system.

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnes, Rory; Deitrick, Russell; Quinn, Thomas R.

2015-03-10

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs aftermore » several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.« less

Chaotic behaviors of operational amplifiers.

PubMed

Yim, Geo-Su; Ryu, Jung-Wan; Park, Young-Jai; Rim, Sunghwan; Lee, Soo-Young; Kye, Won-Ho; Kim, Chil-Min

2004-04-01

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability.

PubMed

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-01-01

By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived in this paper. The system state equations are composed of nine terms including only one constant term. Depending on the different values of the constant term, this new proposed system has a line of equilibrium points or no equilibrium points. Compared with other similar chaotic systems, the newly presented system owns more abundant and complicated dynamic properties. What interests us is the observation that if the value of the constant term of the system is nonzero, it has no equilibria, and therefore, the Shil'nikov theorem is not suitable to verify the existence of chaos for the lack of heteroclinic or homoclinic trajectory. However, one-wing, two-wing, three-wing, and four-wing hidden attractors can be obtained from this new system. In addition, various coexisting hidden attractors are obtained and the complex transient transition behaviors are also observed. More interestingly, the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises. The rich and complex hidden dynamic characteristics of this system are investigated by phase portraits, bifurcation diagrams, Lyapunov exponents, and so on. Finally, the new system is implemented by an electronic circuit. A very good agreement is observed between the experimental results and the numerical simulations of the same system on the Matlab platform.

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-01-01

By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived in this paper. The system state equations are composed of nine terms including only one constant term. Depending on the different values of the constant term, this new proposed system has a line of equilibrium points or no equilibrium points. Compared with other similar chaotic systems, the newly presented system owns more abundant and complicated dynamic properties. What interests us is the observation that if the value of the constant term of the system is nonzero, it has no equilibria, and therefore, the Shil'nikov theorem is not suitable to verify the existence of chaos for the lack of heteroclinic or homoclinic trajectory. However, one-wing, two-wing, three-wing, and four-wing hidden attractors can be obtained from this new system. In addition, various coexisting hidden attractors are obtained and the complex transient transition behaviors are also observed. More interestingly, the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises. The rich and complex hidden dynamic characteristics of this system are investigated by phase portraits, bifurcation diagrams, Lyapunov exponents, and so on. Finally, the new system is implemented by an electronic circuit. A very good agreement is observed between the experimental results and the numerical simulations of the same system on the Matlab platform.

Solar System Chaos and its climatic and biogeochemical consequences

NASA Astrophysics Data System (ADS)

Ikeda, M.; Tada, R.; Ozaki, K.; Olsen, P. E.

2017-12-01

Insolation changes caused by changes in Earth's orbital parameters are the main driver of climatic variations, whose pace has been used for astronomically-calibrated geologic time scales of high accuracy to understand Earth system dynamics. However, the astrophysical models beyond several tens of million years ago have large uncertainty due to chaotic behavior of the Solar System, and its impact on amplitude modulation of multi-Myr-scale orbital variations and consequent climate changes has become the subject of debate. Here we show the geologic constraints on the past chaotic behavior of orbital cycles from early Mesozoic monsoon-related records; the 30-Myr-long lake level records of the lacustrine sequence in Newark-Hartford basins (North America) and 70-Myr-long biogenic silica (BSi) burial flux record of pelagic deep-sea chert sequence in Inuyama area (Japan). BSi burial flux of chert could be considered as proportional to the dissolved Si (DSi) input from chemical weathering on timescales longer than the residence time of DSi ( 100 kyr), because chert could represent a major sink for oceanic dissolved silica (Ikeda et al., 2017).These geologic records show multi-Myr cycles with similar frequency modulations of eccentricity solution of astronomical model La2010d (Laskar et al., 2011) compared with other astronomical solutions, but not exactly same. Our geologic records provide convincing evidence for the past chaotic dynamical behaviour of the Solar System and new and challenging additional constraints for astrophysical models. In addition, we find that ˜10 Myr cycle detected in monsoon proxies and their amplitude modulation of ˜2 Myr cycle may be related to the amplitude modulation of ˜2 Myr eccentricity cycle through non-linear process(es) of Earth system dynamics, suggesting possible impact of the chaotic behavior of Solar planets on climate change. Further impact of multi-Myr orbital cycles on global biogeochemical cycles will be discussed.

THE ASTEROID BELT AS A RELIC FROM A CHAOTIC EARLY SOLAR SYSTEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Izidoro, André; Raymond, Sean N.; Pierens, Arnaud

The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ∼10{sup −3} Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may havemore » been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.« less

Study of some chaotic inflationary models in f(R) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nawazish, Iqra

2018-04-01

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in f(R) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of f(R) gravity and construct the graphical analysis of tensor-scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

Is the Filinov integral conditioning technique useful in semiclassical initial value representation methods?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spanner, Michael; Batista, Victor S.; Brumer, Paul

2005-02-22

The utility of the Filinov integral conditioning technique, as implemented in semiclassical initial value representation (SC-IVR) methods, is analyzed for a number of regular and chaotic systems. For nonchaotic systems of low dimensionality, the Filinov technique is found to be quite ineffective at accelerating convergence of semiclassical calculations since, contrary to the conventional wisdom, the semiclassical integrands usually do not exhibit significant phase oscillations in regions of large integrand amplitude. In the case of chaotic dynamics, it is found that the regular component is accurately represented by the SC-IVR, even when using the Filinov integral conditioning technique, but that quantummore » manifestations of chaotic behavior was easily overdamped by the filtering technique. Finally, it is shown that the level of approximation introduced by the Filinov filter is, in general, comparable to the simpler ad hoc truncation procedure introduced by Kay [J. Chem. Phys. 101, 2250 (1994)].« less

Study on a new chaotic bitwise dynamical system and its FPGA implementation

NASA Astrophysics Data System (ADS)

Wang, Qian-Xue; Yu, Si-Min; Guyeux, C.; Bahi, J.; Fang, Xiao-Le

2015-06-01

In this paper, the structure of a new chaotic bitwise dynamical system (CBDS) is described. Compared to our previous research work, it uses various random bitwise operations instead of only one. The chaotic behavior of CBDS is mathematically proven according to the Devaney's definition, and its statistical properties are verified both for uniformity and by a comprehensive, reputed and stringent battery of tests called TestU01. Furthermore, a systematic methodology developing the parallel computations is proposed for FPGA platform-based realization of this CBDS. Experiments finally validate the proposed systematic methodology. Project supported by China Postdoctoral Science Foundation (Grant No. 2014M552175), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Chinese Education Ministry, the National Natural Science Foundation of China (Grant No. 61172023), and the Specialized Research Foundation of Doctoral Subjects of Chinese Education Ministry (Grant No. 20114420110003).

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

NASA Astrophysics Data System (ADS)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

Double-well chimeras in 2D lattice of chaotic bistable elements

NASA Astrophysics Data System (ADS)

Shepelev, I. A.; Bukh, A. V.; Vadivasova, T. E.; Anishchenko, V. S.; Zakharova, A.

2018-01-01

We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition ;coherence - incoherence; for varying coupling strength for a fixed interaction radius. For the 2D ensemble we show the appearance of amplitude and phase chimera states previously reported for 1D ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel type of chimera state, double-well chimera, which occurs due to the interplay of the bistability of the local dynamics and the 2D ensemble structure. Additionally, we find double-well chimera behavior for steady states which we call double-well chimera death. A distinguishing feature of chimera patterns observed in the lattice is that they mainly combine clusters of different chimera types: phase, amplitude and double-well chimeras.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

NASA Astrophysics Data System (ADS)

Lai, Qiang; Akgul, Akif; Zhao, Xiao-Wen; Pei, Huiqin

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Strategic approaches at the corridor and network level to minimize disruption from the renewal process.

DOT National Transportation Integrated Search

2014-01-01

Program managers within state departments of transportation (DOTs) and metropolitan planning organizations (MPOs) are charged with distilling a chaotic universe of identified renewal needs into a logically sequenced program of manageable projects ove...

Qualitative and quantitative behaviour of planetary systems; Proceedings of the 3rd Alexander von Humboldt Colloquium on Celestial Mechanics, Ramsau, Austria, Mar. 29-Apr. 4, 1992

NASA Astrophysics Data System (ADS)

Dvorak, R.; Henrard, J.

1993-06-01

Topics addressed include planetary theories, the Sitnikov problem, asteroids, resonance, general dynamical systems, and chaos and stability. Particular attention is given to recent progress in the theory and application of symplectic integrators, a computer-aided analysis of the Sitnikov problem, the chaotic behavior of trajectories for the asteroidal resonances, and the resonant motion in the restricted three-body problem. Also discussed are the second order long-period motion of Hyperion, meteorites from the asteroid 6 Hebe, and least squares parameter estimation in chaotic differential equations.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Open problems in active chaotic flows: Competition between chaos and order in granular materials.

PubMed

Ottino, J. M.; Khakhar, D. V.

2002-06-01

There are many systems where interaction among the elementary building blocks-no matter how well understood-does not even give a glimpse of the behavior of the global system itself. Characteristic for these systems is the ability to display structure without any external organizing principle being applied. They self-organize as a consequence of synthesis and collective phenomena and the behavior cannot be understood in terms of the systems' constitutive elements alone. A simple example is flowing granular materials, i.e., systems composed of particles or grains. How the grains interact with each other is reasonably well understood; as to how particles move, the governing law is Newton's second law. There are no surprises at this level. However, when the particles are many and the material is vibrated or tumbled, surprising behavior emerges. Systems self-organize in complex patterns that cannot be deduced from the behavior of the particles alone. Self-organization is often the result of competing effects; flowing granular matter displays both mixing and segregation. Small differences in either size or density lead to flow-induced segregation and order; similar to fluids, noncohesive granular materials can display chaotic mixing and disorder. Competition gives rise to a wealth of experimental outcomes. Equilibrium structures, obtained experimentally in quasi-two-dimensional systems, display organization in the presence of disorder, and are captured by a continuum flow model incorporating collisional diffusion and density-driven segregation. Several open issues remain to be addressed. These include analysis of segregating chaotic systems from a dynamical systems viewpoint, and understanding three-dimensional systems and wet granular systems (slurries). General aspects of the competition between chaos-enhanced mixing and properties-induced de-mixing go beyond granular materials and may offer a paradigm for other kinds of physical systems. (c) 2002 American Institute of Physics.

Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis

NASA Astrophysics Data System (ADS)

Ogunjo, Samuel T.; Adediji, Adekunle T.; Dada, Joseph B.

2017-01-01

The use of solar energy for power generation and other uses is on the increase. This demand necessitate a better understanding of the underlying dynamics for better prediction. Nonlinear dynamics and its associated tools readily lend itself for such analysis. In this paper, nonlinearity in solar radiation data is tested using recurrence plot (RP) and recurrence quantification analysis (RQA) in a tropical station. The data used was obtained from an ongoing campaign at the Federal University of Technology, Akure, Southwestern Nigeria using an Integrated Sensor Suite (Vantage2 Pro). Half hourly and daily values were tested for each month of the year. Both were found to be nonlinear. The dry months of the year exhibit higher chaoticity compared to the wet months of the year. The daily average values were found to be mildly chaotic. Using RQA, features due to external effects such as harmattan and intertropical discontinuity (ITD) on solar radiation data were uniquely identified.

Pathways to Problem Behaviors: Chaotic Homes, Parent and Child Effortful Control, and Parenting

ERIC Educational Resources Information Center

Valiente, Carlos; Lemery-Chalfant, Kathryn; Reiser, Mark

2007-01-01

Guided by Belsky's and Eisenberg, Cumberland, and Spinrad's heuristic models, we tested a process model with hypothesized paths from parents' effortful control (EC) and family chaos to indices of parenting to children's EC, and finally children's externalizing problem behavior. Parents reported on all constructs and children (N = 188; M age = 9.55…

Traffic flow theory and chaotic behavior

DOT National Transportation Integrated Search

1989-03-01

Many commonly occurring natural systems are modeled with mathematical experessions and exhibit a certain stability. The inherent stability of these equations allows them to serve as the basis for engineering predictions. More complex models, such as ...

Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system

NASA Astrophysics Data System (ADS)

Woillez, E.; Bouchet, F.

2017-11-01

Over timescales much longer than an orbital period, the solar system exhibits large-scale chaotic behavior and can thus be viewed as a stochastic dynamical system. The aim of the present paper is to compare different sources of stochasticity in the solar system. More precisely we studied the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects of asteroids on planets is similar to a white noise process, when those effects are considered on a timescale much larger than the correlation time τϕ ≃ 104 yr of asteroid trajectories. We computed the timescale τe after which the effects of the stochastic evolution of the asteroids lead to a loss of information for the initial conditions of the perturbed Laplace-Lagrange secular dynamics. The order of magnitude of this timescale is precisely determined by theoretical argument, and we find that τe ≃ 104 Myr. Although comparable to the full main-sequence lifetime of the sun, this timescale is considerably longer than the Lyapunov time τI ≃ 10 Myr of the solar system without asteroids. This shows that the external sources of chaos arise as a small perturbation in the stochastic secular behavior of the solar system, rather due to intrinsic chaos.

Chaotic Transport in Circumterrestrial Orbits

NASA Astrophysics Data System (ADS)

Rosengren, Aaron Jay

2018-04-01

The slow deformation of circumterrestrial orbits in the medium region, subject to lunisolar secular resonances, is well approximated by a Hamiltonian system with 2.5 degrees of freedom. This dynamical model is referred to in the astrophysical and celestial dynamics communities as the quadrupolar, secular, hierarchical three-body problem, and, in the non-autonomous case, gives rise to the classical Kozai-Lidov mechanism. In the time-dependent model, brought about in our case by the Moon's perturbed motion, the action variables of the system may experience chaotic variations and large drifts due to the possible overlap of nearby resonances. Using variational chaos indicators, we compute high-resolution portraits of the action space, revealing the existence of tori and structures filling chaotic regions. Our refined and elaborate calculations allow us to isolate precise initial conditions near specific areas of interest and to study their asymptotic behavior in time. We highlight in particular how the drift in phase space is mediated by the complement of the numerically detected KAM tori. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, like the small body remnants of Solar system formation, they have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

Gauge Fields in Homogeneous and Inhomogeneous Cosmologies

NASA Astrophysics Data System (ADS)

Darian, Bahman K.

Despite its formidable appearance, the study of classical Yang-Mills (YM) fields on homogeneous cosmologies is amenable to a formal treatment. This dissertation is a report on a systematic approach to the general construction of invariant YM fields on homogeneous cosmologies undertaken for the first time in this context. This construction is subsequently followed by the investigation of the behavior of YM field variables for the most simple of self-gravitating YM fields. Particularly interesting was a dynamical system analysis and the discovery of chaotic signature in the axially symmetric Bianchi I-YM cosmology. Homogeneous YM fields are well studied and are known to have chaotic properties. The chaotic behavior of YM field variables in homogeneous cosmologies might eventually lead to an invariant definition of chaos in (general) relativistic cosmological models. By choosing the gauge fields to be Abelian, the construction and the field equations presented so far reduce to that of electromagnetic field in homogeneous cosmologies. A perturbative analysis of gravitationally interacting electromagnetic and scalar fields in inhomogeneous cosmologies is performed via the Hamilton-Jacobi formulation of general relativity. An essential feature of this analysis is the spatial gradient expansion of the generating functional (Hamilton principal function) to solve the Hamiltonian constraint. Perturbations of a spatially flat Friedman-Robertson-Walker cosmology with an exponential potential for the scalar field are presented.

Randomly chosen chaotic maps can give rise to nearly ordered behavior

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł; Islam, Md. Shafiqul

2005-10-01

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226-5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72], the resulting composed map has a periodic orbit which is stable.

ASTEROIDS: Living in the Kingdom of Chaos

NASA Astrophysics Data System (ADS)

Morbidelli, A.

2000-10-01

The existence of chaotic regions in the main asteroid belt, related with the lowest-order mean-motion and secular resonances, has long been known. However, only in the last decade have semi-analytic theories allowed a proper understanding of the chaotic behavior observed in numerical simulations which accurately incorporate the entire planetary system. The most spectacular result has been the discovery that the asteroids in some of these resonance may collide with the Sun on typical time scales of a few million year, their eccentricities being pumped to unity during their chaotic evolution. But the asteroid belt is not simply divided into violent chaotic zones and regular regions. It has been shown that the belt is criss-crossed by a large number of high-order mean-motion resonances with Jupiter or Mars, as well as by `three-body resonances' with Jupiter and Saturn. All these weak resonances cause the slow chaotic drift of the `proper' eccentricities and inclinations. The traces left by this evolution are visible, for example, in the structure of the Eos and Themis asteroid families. Weak chaos may also explain the anomalous dispersion of the eccentricities and inclinations observed in the Flora ``clan." Moreover, due to slow increases in their eccentricities, many asteroids start to cross the orbit of Mars, over a wide range of semimajor axes. The improved knowledge of the asteroid belt's chaotic structure provides, for the first time, an opportunity to build detailed quantitative models of the origin and the orbital distribution of Near-Earth Asteroids and meteorites. In turn, these models seem to imply that the semimajor axes of main-belt asteroids must also slowly evolve with time. For asteroids larger than about 20 km this is due mainly to encounters with Ceres, Pallas, and Vesta, while for smaller bodies the so-called Yarkovsky effect should dominate. Everything moves chaotically in the asteroid belt.

Cyclic mixmaster universes

NASA Astrophysics Data System (ADS)

Barrow, John D.; Ganguly, Chandrima

2017-04-01

We investigate the behavior of bouncing Bianchi type IX "mixmaster" universes in general relativity. This generalizes all previous studies of the cyclic behavior of closed spatially homogeneous universes with and without an entropy increase. We determine the behavior of models containing radiation by analytic and numerical integration and show that an increase of radiation entropy leads to an increasing cycle size and duration. We introduce a null energy condition violating ghost field to create a smooth, nonsingular bounce of finite size at the end of each cycle and compute the evolution through many cycles with and without an entropy increase injected at the start of each cycle. In the presence of increasing entropy, we find that the cycles grow larger and longer and the dynamics approach flatness, as in the isotropic case. However, successive cycles become increasingly anisotropic at the expansion maxima which is dominated by the general-relativistic effects of anisotropic 3-curvature. When the dynamics are significantly anisotropic, the 3-curvature is negative. However, it becomes positive after continued expansion drives the dynamics close enough to isotropy for the curvature to become positive and for gravitational collapse to ensue. In the presence of a positive cosmological constant, radiation, and a ghost field, we show that, for a very wide range of cosmological constant values, the growing oscillations always cease and the dynamics subsequently approach those of the isotropic de Sitter universe at late times. This model is not included in the scope of earlier cosmic no-hair theorems because the 3-curvature can be positive. In the case of a negative cosmological constant, radiation, and an ultrastiff field (to create nonsingular bounces), we show that a sequence of chaotic oscillations also occurs, with sensitive dependence on initial conditions. In all cases, we follow the oscillatory evolution of the scale factors, the shear, and the 3-curvature from cycle to cycle.

Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.

2015-07-01

We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

Plastic dynamics of the Al0.5CoCrCuFeNi high entropy alloy at cryogenic temperatures: Jerky flow, stair-like fluctuation, scaling behavior, and non-chaotic state

NASA Astrophysics Data System (ADS)

Guo, Xiaoxiang; Xie, Xie; Ren, Jingli; Laktionova, Marina; Tabachnikova, Elena; Yu, Liping; Cheung, Wing-Sum; Dahmen, Karin A.; Liaw, Peter K.

2017-12-01

This study investigates the plastic behavior of the Al0.5CoCrCuFeNi high-entropy alloy at cryogenic temperatures. The samples are uniaxially compressed at 4.2 K, 7.5 K, and 9 K. A jerky evolution of stress and stair-like fluctuation of strain are observed during plastic deformation. A scaling relationship is detected between the released elastic energy and strain-jump sizes. Furthermore, the dynamical evolution of serrations is characterized by the largest Lyapunov exponent. The largest Lyapunov exponents of the serrations at the three temperatures are all negative, which indicates that the dynamical regime is non-chaotic. This trend reflects an ordered slip process, and this ordered slip process exhibits a more disordered slip process, as the temperature decreases from 9 K to 4.2 K or 7.5 K.

Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling.

PubMed

Yao, Chenggui; Zhan, Meng; Shuai, Jianwei; Ma, Jun; Kurths, Jürgen

2017-12-01

It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure. This lack of sensitivity was numerically tested in several typical regular networks, such as different locally and globally coupled ones as well as in several complex networks, such as small-world and scale-free networks. Furthermore, we find that the emergence of a synchronous periodic state induced by time delay is of key importance for the complete synchronization.

Getting Things Sorted With Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team

2014-11-01

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of Lagrangian Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.

External Source of Infection and Nutritional Efficiency Control Chaos in a Predator-Prey Model with Disease in the Predator

NASA Astrophysics Data System (ADS)

Pada Das, Krishna; Roy, Prodip; Ghosh, Subhabrata; Maiti, Somnath

This paper deals with an eco-epidemiological approach with disease circulating through the predator species. Disease circulation in the predator species can be possible by contact as well as by external sources. Here, we try to discuss the role of external source of infection along with nutritional value on system dynamics. To establish our findings, we have worked out the local and global stability analysis of the equilibrium points with Hopf bifurcation analysis associated with interior equilibrium point. The ecological consequence by ecological basic reproduction number as well as the disease basic reproduction number or basic reproductive ratio are obtained and we have analyzed the community structure of the particular system with the help of ecological and disease basic reproduction numbers. Further we pay attention to the chaotic dynamics which is produced by disease circulating in predator species by contact. Our numerical simulations reveal that eco-epidemiological system without external source of infection induced chaotic dynamics for increasing force of infection due to contact, whereas in the presence of external source of infection, it exhibits stable solution. It is also observed that nutritional value can prevent chaotic dynamics. We conclude that chaotic dynamics can be controlled by the external source of infection as well as nutritional value. We apply basic tools of nonlinear dynamics such as Poincare section and maximum Lyapunov exponent to investigate chaotic behavior of the system.

Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems.

PubMed

Riser, Roman; Osipov, Vladimir Al; Kanzieper, Eugene

2017-05-19

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.

Transient chaos in the Lorenz-type map with periodic forcing.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Crash test for the Copenhagen problem.

PubMed

Nagler, Jan

2004-06-01

The Copenhagen problem is a simple model in celestial mechanics. It serves to investigate the behavior of a small body under the gravitational influence of two equally heavy primary bodies. We present a partition of orbits into classes of various kinds of regular motion, chaotic motion, escape and crash. Collisions of the small body onto one of the primaries turn out to be unexpectedly frequent, and their probability displays a scale-free dependence on the size of the primaries. The analysis reveals a high degree of complexity so that long term prediction may become a formidable task. Moreover, we link the results to chaotic scattering theory and the theory of leaking Hamiltonian systems.

Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system

NASA Astrophysics Data System (ADS)

Manal, Messadi; Adel, Mellit; Karim, Kemih; Malek, Ghanes

2015-01-01

This paper investigates how to address the chaos problem in a permanent magnet synchronous generator (PMSG) in a wind turbine system. Predictive control approach is proposed to suppress chaotic behavior and make operating stable; the advantage of this method is that it can only be applied to one state of the wind turbine system. The use of the genetic algorithms to estimate the optimal parameter values of the wind turbine leads to maximization of the power generation. Moreover, some simulation results are included to visualize the effectiveness and robustness of the proposed method. Project supported by the CMEP-TASSILI Project (Grant No. 14MDU920).

RP and RQA Analysis for Floating Potential Fluctuations in a DC Magnetron Sputtering Plasma

NASA Astrophysics Data System (ADS)

Sabavath, Gopikishan; Banerjee, I.; Mahapatra, S. K.

2016-04-01

The nonlinear dynamics of a direct current magnetron sputtering plasma is visualized using recurrence plot (RP) technique. RP comprises the recurrence quantification analysis (RQA) which is an efficient method to observe critical regime transitions in dynamics. Further, RQA provides insight information about the system’s behavior. We observed the floating potential fluctuations of the plasma as a function of discharge voltage by using Langmuir probe. The system exhibits quasi-periodic-chaotic-quasi-periodic-chaotic transitions. These transitions are quantified from determinism, Lmax, and entropy of RQA. Statistical investigations like kurtosis and skewness also studied for these transitions which are in well agreement with RQA results.

Transient chaos in the Lorenz-type map with periodic forcing

NASA Astrophysics Data System (ADS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Experimental evidence of chaotic mixing at pore scale in 3D porous media

NASA Astrophysics Data System (ADS)

Heyman, J.; Turuban, R.; Jimenez Martinez, J.; Lester, D. R.; Meheust, Y.; Le Borgne, T.

2017-12-01

Mixing of dissolved chemical species in porous media plays a central role in many natural and industrial processes, such as contaminant transport and degradation in soils, oxygen and nitrates delivery in river beds, clogging in geothermal systems, CO2 sequestration. In particular, incomplete mixing at the pore scale may strongly affect the spatio-temporal distribution of reaction rates in soils and rocks, questioning the validity of diffusion-reaction models at the Darcy scale. Recent theoretical [1] and numerical [2] studies of flow in idealized porous media have suggested that fluid mixing may be chaotic at pore scale, hence pointing to a whole new set of models for mixing and reaction in porous media. However, so far this remained to be confirmed experimentally. Here we present experimental evidence of the chaotic nature of transverse mixing at the pore scale in three-dimensional porous media. We designed a novel experimental setup allowing high resolution pore scale imaging of the structure of a tracer plume in porous media columns consisting of 7, 10 and 20 mm glass bead packings. We conjointly used refractive index matching techniques, laser induced fluorescence and a moving laser-sheet to reconstruct the shape of a steady tracer plume as it gets deformed by the porous media flow. In this talk, we focus on the transverse behavior of mixing, that is, on the plane orthogonal to the main flow direction, in the limit of high Péclet numbers (diffusion is negligible). Moving away from the injection point, the plume cross-section turns quickly into complex, interlaced, lamellar structures. These structures elongated at an exponential rate, characteristic of a chaotic system, that can be characterized by an average Lyapunov exponent. We finally discuss the origin of this chaotic behavior and its most significant consequences for upscaling mixing and reactive transport in porous media. Reference:[1] D. R. Lester, G. Metcafle, M. G. Trefry, Physical Review Letters, 111, 174101 (2013) [2] R. Turuban, D. R. Lester, T. Le Borgne, and Y. Méheust (2017), under review.

Chaotic behavior in the locomotion of Amoeba proteus.

PubMed

Miyoshi, H; Kagawa, Y; Tsuchiya, Y

2001-01-01

The locomotion of Amoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area of A. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion of A. proteus is subjected only to 3-4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior of A. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

Insights on chaotic dynamics: mixing experiments between natural silicate melts from Vulcano island (Aeolian Islands, Italy)

NASA Astrophysics Data System (ADS)

Rossi, Stefano; Morgavi, Daniele; Vetere, Francesco; Petrelli, Maurizio; Perugini, Diego

2017-04-01

keywords: Magma mixing, chaotic dynamics, time series experiments Magma mixing is a petrologic phenomenon which is recognized as potential trigger of highly explosive eruptions and its evidence is commonly observable in natural rocks. Here we tried to replicate the dynamic conditions of mixing performing a set of chaotic mixing experiments between shoshonitic and rhyolitic magmas from Vulcano island. Vulcano is the southernmost island of the Aeolian Archipelago (Aeolian Islands, Italy); it is completely built by volcanic rocks with variable degree of evolution ranging from basalt to rhyolite (e.g. Keller 1980; Ellam et al. 1988; De Astis 1995; De Astis et al. 2013) and its magmatic activity dates back to about 120 ky. Last eruption occurred in 1888-1890. The chaotic mixing experiments were performed by using the new ChaOtic Magma Mixing Apparatus (COMMA), held at the Department of Physics and Geology, University of Perugia. This new experimental device allows to track the evolution of the mixing process and the associated modulation of chemical composition between different magmas. Experiments were performed at 1200°C and atmospheric pressure with a viscosity ratio higher than three orders of magnitude. The experimental protocol was chosen to ensure the occurrence of chaotic dynamics in the system and the run duration was progressively increased (e.g. 10.5 h, 21 h, 42 h). The products of each experiment are crystal-free glasses in which the variation of major elements was investigated along different profiles using electron microprobe (EMPA) at Institute für Mineralogie, Leibniz Universität of Hannover (Germany). The efficiency of the mixing process is estimated by calculating the decrease of concentration variance in time and it is shown that the variance of major elements exponentially decays. Our results confirm and quantify how different chemical elements homogenize in the melt at differing rates. It is also observable that the mixing structures generated during the mixing experiments are topologically identical to those observed in natural mixed volcanic rocks.

Uncovering low dimensional macroscopic chaotic dynamics of large finite size complex systems

NASA Astrophysics Data System (ADS)

Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward

2017-08-01

In the last decade, it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the macroscopic dynamics of other similar systems also have a low dimensional description in the infinite N limit has, however, remained elusive. In this paper, we show how techniques originally designed to analyze noisy experimental chaotic time series can be used to identify effective low dimensional macroscopic descriptions from simulations with a finite number of elements. We illustrate and verify the effectiveness of our approach by applying it to the dynamics of an ensemble of globally coupled Landau-Stuart oscillators for which we demonstrate low dimensional macroscopic chaotic behavior with an effective 4-dimensional description. By using this description, we show that one can calculate dynamical invariants such as Lyapunov exponents and attractor dimensions. One could also use the reconstruction to generate short-term predictions of the macroscopic dynamics.

Synchronizability of nonidentical weakly dissipative systems

NASA Astrophysics Data System (ADS)

Sendiña-Nadal, Irene; Letellier, Christophe

2017-10-01

Synchronization is a very generic process commonly observed in a large variety of dynamical systems which, however, has been rarely addressed in systems with low dissipation. Using the Rössler, the Lorenz 84, and the Sprott A systems as paradigmatic examples of strongly, weakly, and non-dissipative chaotic systems, respectively, we show that a parameter or frequency mismatch between two coupled such systems does not affect the synchronizability and the underlying structure of the joint attractor in the same way. By computing the Shannon entropy associated with the corresponding recurrence plots, we were able to characterize how two coupled nonidentical chaotic oscillators organize their dynamics in different dissipation regimes. While for strongly dissipative systems, the resulting dynamics exhibits a Shannon entropy value compatible with the one having an average parameter mismatch, for weak dissipation synchronization dynamics corresponds to a more complex behavior with higher values of the Shannon entropy. In comparison, conservative dynamics leads to a less rich picture, providing either similar chaotic dynamics or oversimplified periodic ones.

Influence of external extrusion on stability of hydrogen molecule and its chaotic behavior

NASA Astrophysics Data System (ADS)

Jarosik, M. W.; SzczÈ©śniak, R.; Durajski, A. P.; Kalaga, J. K.; Leoński, W.

2018-01-01

We have determined the stability conditions of the hydrogen molecule under the influence of an external force of harmonic-type explicitly dependent on the amplitude (A) and frequency (Ω). The ground state of the molecule has been determined in the framework of the Born-Oppenheimer approximation, whereas the energy of the electronic subsystem has been calculated using the Hubbard model including all two-site electron interactions. The diagram of RT0(A ,Ω) , where RT0 denotes the distance between protons after the fixed initial time T0, allowed us to visualize the area of the instability with the complicated structure. We have shown that the vibrations of the hydrogen molecule have a chaotic nature for some points of the instability region. In addition to the amplitude and frequency of the extrusion, the control parameter of the stability of the molecule is the external force associated with pressure. The increase in its value causes the disappearance of the area of the instability and chaotic vibrations.

Scale invariance in chaotic time series: Classical and quantum examples

NASA Astrophysics Data System (ADS)

Landa, Emmanuel; Morales, Irving O.; Stránský, Pavel; Fossion, Rubén; Velázquez, Victor; López Vieyra, J. C.; Frank, Alejandro

Important aspects of chaotic behavior appear in systems of low dimension, as illustrated by the Map Module 1. It is indeed a remarkable fact that all systems tha make a transition from order to disorder display common properties, irrespective of their exacta functional form. We discuss evidence for 1/f power spectra in the chaotic time series associated in classical and quantum examples, the one-dimensional map module 1 and the spectrum of 48Ca. A Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of the energy fluctuations in the spectrum of 48Ca obtained with a large realistic shell model calculation (ANTOINE code) and with a random shell model (TBRE) calculation also in the time series obtained with the map mod 1. We compare the scale invariant properties of the 48Ca nuclear spectrum sith similar analyses applied to the RMT ensambles GOE and GDE. A comparison with the corresponding power spectra is made in both cases. The possible consequences of the results are discussed.

Characterization of chaotic dynamics in the human menstrual cycle

NASA Astrophysics Data System (ADS)

Derry, Gregory; Derry, Paula

2010-03-01

The human menstrual cycle exhibits much unexplained variability, which is typically dismissed as random variation. Given the many delayed nonlinear feedbacks in the reproductive endocrine system, however, the menstrual cycle might well be a nonlinear dynamical system in a chaotic trajectory, and that this instead accounts for the observed variability. Here, we test this hypothesis by performing a time series analysis on data for 7438 menstrual cycles from 38 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Using phase space reconstruction techniques with a maximum embedding dimension of 6, we find appropriate scaling behavior in the correlation sums for this data, indicating low dimensional deterministic dynamics. A correlation dimension of 2.6 is measured in this scaling regime, and this result is confirmed by recalculation using the Takens estimator. These results may be interpreted as offering an approximation to the fractal dimension of a strange attractor governing the chaotic dynamics of the menstrual cycle.

Towards a unified study of extreme events using universality concepts and transdisciplinary analysis methods

NASA Astrophysics Data System (ADS)

Balasis, George; Donner, Reik V.; Donges, Jonathan F.; Radebach, Alexander; Eftaxias, Konstantinos; Kurths, Jürgen

2013-04-01

The dynamics of many complex systems is characterized by the same universal principles. In particular, systems which are otherwise quite different in nature show striking similarities in their behavior near tipping points (bifurcations, phase transitions, sudden regime shifts) and associated extreme events. Such critical phenomena are frequently found in diverse fields such as climate, seismology, or financial markets. Notably, the observed similarities include a high degree of organization, persistent behavior, and accelerated energy release, which are common to (among others) phenomena related to geomagnetic variability of the terrestrial magnetosphere (intense magnetic storms), seismic activity (electromagnetic emissions prior to earthquakes), solar-terrestrial physics (solar flares), neurophysiology (epileptic seizures), and socioeconomic systems (stock market crashes). It is an open question whether the spatial and temporal complexity associated with extreme events arises from the system's structural organization (geometry) or from the chaotic behavior inherent to the nonlinear equations governing the dynamics of these phenomena. On the one hand, the presence of scaling laws associated with earthquakes and geomagnetic disturbances suggests understanding these events as generalized phase transitions similar to nucleation and critical phenomena in thermal and magnetic systems. On the other hand, because of the structural organization of the systems (e.g., as complex networks) the associated spatial geometry and/or topology of interactions plays a fundamental role in the emergence of extreme events. Here, a few aspects of the interplay between geometry and dynamics (critical phase transitions) that could result in the emergence of extreme events, which is an open problem, will be discussed.

A challenge to chaotic itinerancy from brain dynamics

NASA Astrophysics Data System (ADS)

Kay, Leslie M.

2003-09-01

Brain hermeneutics and chaotic itinerancy proposed by Tsuda are attractive characterizations of perceptual dynamics in the mammalian olfactory system. This theory proposes that perception occurs at the interface between itinerant neural representation and interaction with the environment. Quantifiable application of these dynamics has been hampered by the lack of definable history and action processes which characterize the changes induced by behavioral state, attention, and learning. Local field potentials measured from several brain areas were used to characterize dynamic activity patterns for their use as representations of history and action processes. The signals were recorded from olfactory areas (olfactory bulb, OB, and pyriform cortex) and hippocampal areas (entorhinal cortex and dentate gyrus, DG) in the brains of rats. During odor-guided behavior the system shows dynamics at three temporal scales. Short time-scale changes are system-wide and can occur in the space of a single sniff. They are predictable, associated with learned shifts in behavioral state and occur periodically on the scale of the intertrial interval. These changes occupy the theta (2-12 Hz), beta (15-30 Hz), and gamma (40-100 Hz) frequency bands within and between all areas. Medium time-scale changes occur relatively unpredictably, manifesting in these data as alterations in connection strength between the OB and DG. These changes are strongly correlated with performance in associated trial blocks (5-10 min) and may be due to fluctuations in attention, mood, or amount of reward received. Long time-scale changes are likely related to learning or decline due to aging or disease. These may be modeled as slow monotonic processes that occur within or across days or even weeks or years. The folding of different time scales is proposed as a mechanism for chaotic itinerancy, represented by dynamic processes instead of static connection strengths. Thus, the individual maintains continuity of experience within the stability of fast periodic and slow monotonic processes, while medium scale events alter experience and performance dramatically but temporarily. These processes together with as yet to be determined action effects from motor system feedback are proposed as an instantiation of brain hermeneutics and chaotic itinerancy.

A nonlinear delayed model for the immune response in the presence of viral mutation

NASA Astrophysics Data System (ADS)

Messias, D.; Gleria, Iram; Albuquerque, S. S.; Canabarro, Askery; Stanley, H. E.

2018-02-01

We consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains a wild-type virus and a mutant. We consider the finite response time of the immune system and find sustained oscillatory behavior as well as chaotic behavior triggered by the presence of delays. We present a numeric analysis and some analytical results.

Single particle and collective behavior of electrons in a diamagnetic Kepler trap

NASA Astrophysics Data System (ADS)

Godino, Joseph L.

2001-10-01

The Diamagnetic Kepler Trap (DKT) is a potential energy well that arises from a static Coulomb potential in a superimposed uniform magnetic field. Our goal is to study the single particle and collective behavior of electrons in a DKT. We have three principal reasons for doing so. First, trajectories of a single electron in a DKT can exhibit chaotic motion. The transition from regular to chaotic motion is theoretically interesting and we want to understand how this occurs. Second, we want to understand the behavior of a system of electrons in a laboratory realization of a DKT. In this situation, we have a many particle system of electrons and ions that move under the influence of external potentials in a neutral background gas. Under these conditions, trapped electrons exhibit collective modes of oscillation. Finally, by understanding the behavior of the trapped electrons we believe that we may be able to develop the DKT into an ion beam source. Due to the complexity of the DKT, we break our investigation into three parts. First, we conduct a theoretical and computational study of the motion of a single electron in a DKT. To enhance our understanding, we develop a simple model of the DKT that retains the significant properties of the exact system while permitting us to go further with our theoretical analysis. We develop a solution to the model equations of motion, which provide us with additional insight into the behavior of trajectories near the chaotic transition. Second, we characterize the behavior of trapped electrons in our experimental DKT. We present a set of measurements showing the collective oscillations. In addition, when we operate the DKT at magnetic fields greater than 100 gauss, we observe a columnar plasma beam emerging from the trap that we also characterize. Finally, we simulate the dynamics of the electrons and ions in a DKT. Here we include their interactions with the neutral background gas, boundary effects and space charge. We use the information obtained from our simulations to enhance our knowledge of the electrons in the experimental system.

Chaotic Excitation and Tidal Damping in the GJ 876 System

NASA Astrophysics Data System (ADS)

Puranam, Abhijit; Batygin, Konstantin

2018-04-01

The M-dwarf GJ 876 is the closest known star to harbor a multi-planetary system. With three outer planets locked in a chaotic Laplace-type resonance and an appreciably eccentric short-period super-Earth, this system represents a unique exposition of extrasolar planetary dynamics. A key question that concerns the long-term evolution of this system, and the fate of close-in planets in general, is how the significant eccentricity of the inner-most planet is maintained against tidal circularization on timescales comparable to the age of the universe. Here, we employ stochastic secular perturbation theory and N-body simulations to show that the orbit of the inner-most planet is shaped by a delicate balance between extrinsic chaotic forcing and tidal dissipation. As such, the planet’s orbital eccentricity represents an indirect measure of its tidal quality factor. Based on the system’s present-day architecture, we estimate that the extrasolar super-Earth GJ 876 d has a tidal Q ∼ 104–105, a value characteristic of solar system gas giants.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

Universality of modulation length and time exponents.

PubMed

Chakrabarty, Saurish; Dobrosavljević, Vladimir; Seidel, Alexander; Nussinov, Zohar

2012-10-01

We study systems with a crossover parameter λ, such as the temperature T, which has a threshold value λ(*) across which the correlation function changes from exhibiting fixed wavelength (or time period) modulations to continuously varying modulation lengths (or times). We introduce a hitherto unknown exponent ν(L) characterizing the universal nature of this crossover and compute its value in general instances. This exponent, similar to standard correlation length exponents, is obtained from motion of the poles of the momentum (or frequency) space correlation functions in the complex k-plane (or ω-plane) as the parameter λ is varied. Near the crossover (i.e., for λ→λ(*)), the characteristic modulation wave vector K(R) in the variable modulation length "phase" is related to that in the fixed modulation length "phase" q via |K(R)-q|[proportionality]|T-T(*)|(νL). We find, in general, that ν(L)=1/2. In some special instances, ν(L) may attain other rational values. We extend this result to general problems in which the eigenvalue of an operator or a pole characterizing general response functions may attain a constant real (or imaginary) part beyond a particular threshold value λ(*). We discuss extensions of this result to multiple other arenas. These include the axial next-nearest-neighbor Ising (ANNNI) model. By extending our considerations, we comment on relations pertaining not only to the modulation lengths (or times), but also to the standard correlation lengths (or times). We introduce the notion of a Josephson time scale. We comment on the presence of aperiodic "chaotic" modulations in "soft-spin" and other systems. These relate to glass-type features. We discuss applications to Fermi systems, with particular application to metal to band insulator transitions, change of Fermi surface topology, divergent effective masses, Dirac systems, and topological insulators. Both regular periodic and glassy (and spatially chaotic behavior) may be found in strongly correlated electronic systems.

Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Linde, Andrei

2015-02-23

I describe the first model of chaotic inflation in supergravity, which was proposed by Goncharov and the present author in 1983. The inflaton potential of this model has a plateau-type behavior V{sub 0}(1−(8/3) e{sup −√6|ϕ|}) at large values of the inflaton field. This model predicts n{sub s}=1−(2/N)≈0.967 and r=(4/(3N{sup 2}))≈4×10{sup −4}, in good agreement with the Planck data. I propose a slight generalization of this model, which allows to describe not only inflation but also dark energy and supersymmetry breaking.

Chaotic behavior of a spin-glass model on a Cayley tree

NASA Astrophysics Data System (ADS)

da Costa, F. A.; de Araújo, J. M.; Salinas, S. R.

2015-06-01

We investigate the phase diagram of a spin-1 Ising spin-glass model on a Cayley tree. According to early work of Thompson and collaborators, this problem can be formulated in terms of a set of nonlinear discrete recursion relations along the branches of the tree. Physically relevant solutions correspond to the attractors of these mapping equations. In the limit of infinite coordination of the tree, and for some choices of the model parameters, we make contact with findings for the phase diagram of more recently investigated versions of the Blume-Emery-Griffiths spin-glass model. In addition to the anticipated phases, we numerically characterize the existence of modulated and chaotic structures.

Chaotic one-dimensional domains induced by periodic potentials in normal-dispersion fiber lasers

NASA Astrophysics Data System (ADS)

Urzagasti, Deterlino; Vargas, Bryan A.; Quispe-Flores, Luzmila A.

2017-10-01

We investigate numerically the effects of external time-periodic potentials on time-localized perturbations to the amplitude of electromagnetic waves propagating in normal-dispersion fiber lasers which are described by the complex Ginzburg-Landau equation. Two main effects were found: The formation of domains enclosed by two maxima of the external periodic field and the generation of a chaotic behavior of these domains in the region of relatively high amplitudes and low frequencies of the external fields. Maps and bifurcation diagrams of the largest Lyapunov exponent and moments, such as energy and momentum, are also provided for different values of the amplitude and frequency of such external potentials.

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

PubMed Central

da Cunha, C. R.; Mineharu, M.; Matsunaga, M.; Matsumoto, N.; Chuang, C.; Ochiai, Y.; Kim, G.-H.; Watanabe, K.; Taniguchi, T.; Ferry, D. K.; Aoki, N.

2016-01-01

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene. PMID:27609184

Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior.

PubMed

da Cunha, C R; Mineharu, M; Matsunaga, M; Matsumoto, N; Chuang, C; Ochiai, Y; Kim, G-H; Watanabe, K; Taniguchi, T; Ferry, D K; Aoki, N

2016-09-09

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

Analysis of chaotic saddles in a nonlinear vibro-impact system

NASA Astrophysics Data System (ADS)

Feng, Jinqian

2017-07-01

In this paper, a computational investigation of chaotic saddles in a nonlinear vibro-impact system is presented. For a classical Duffing vibro-impact oscillator, we employ the bisection procedure and an improved stagger-and-step method to present evidence of visual chaotic saddles on the fractal basin boundary and in the internal basin, respectively. The results show that the period saddles play an important role in the evolution of chaotic saddle. The dynamics mechanics of three types of bifurcation such as saddle-node bifurcation, chaotic saddle crisis bifurcation and interior chaotic crisis bifurcation are discussed. The results reveal that the period saddle created at saddle-node bifurcation is responsible for the switch of the internal chaotic saddle to the boundary chaotic saddle. At chaotic saddle crisis bifurcation, a large chaotic saddle can divide into two different chaotic saddle connected by a period saddle. The intersection points between stable and unstable manifolds of this period saddle supply access for chaotic orbits from one chaotic saddle to another and eventually induce the coupling of these two chaotic saddle. Interior chaotic crisis bifurcation is associated with the intersection of stable and unstable manifolds of the period saddle connecting two chaotic invariant sets. In addition, the gaps in chaotic saddle is responsible for the fractal structure.

A novel high-resolution chaotic lidar with optical injection to chaotic laser diode

NASA Astrophysics Data System (ADS)

Wang, Yun-cai; Wang, An-bang

2008-03-01

A novel chaotic lidar with high resolution is proposed and studied theoretically. In chaotic lidar system, the chaotic laser emitted from chaotic laser diode is split into two beams: the probe and the reference light. The ranging is achieved by correlating the reference waveform with the delayed probe waveform backscattered from the target. In chaotic lidar systems presented previously, the chaotic signal source is laser diode with optical feedback or with optical injection by another one. The ranging resolution is limited by the bandwidth of chaotic laser which determined by the configuration of chaotic signal source. We proposed a novel chaotic lidar which ranging resolution is enhanced significantly by external optical injected chaotic laser diode. With the bandwidth-enhanced chaotic laser, the range resolution of the chaotic lidar system with optical injection is roughly two times compared with that of without optical injection. The resolution increases with injection strength increasing in a certain frequency detuning range.

Chaos-order transition in foraging behavior of ants.

PubMed

Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian; Schellnhuber, Hans Joachim

2014-06-10

The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants' physical abilities, and ants' knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal.

Chaos–order transition in foraging behavior of ants

PubMed Central

Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Yang, Yixian; Schellnhuber, Hans Joachim

2014-01-01

The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants’ physical abilities, and ants’ knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal. PMID:24912159

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derrida, B.; Meir, R.

We consider the evolution of configurations in a layered feed-forward neural network. Exact expressions for the evolution of the distance between two configurations are obtained in the thermodynamic limit. Our results show that the distance between two arbitrarily close configurations always increases, implying chaotic behavior, even in the phase of good retrieval.

Flutter Analysis of the Thermal Protection Layer on the NASA HIAD

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2013-01-01

A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated.

Chaotic behavior of three interacting vortices in a confined Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kyriakopoulos, Nikos; Koukouloyannis, Vassilis; Skokos, Charalampos

2014-06-01

Motivated by recent experimental works, we investigate a system of vortex dynamics in an atomic Bose-Einstein condensate (BEC), consisting of three vortices, two of which have the same charge. These vortices are modeled as a system of point particles which possesses a Hamiltonian structure. This tripole system constitutes a prototypical model of vortices in BECs exhibiting chaos. By using the angular momentum integral of motion, we reduce the study of the system to the investigation of a two degree of freedom Hamiltonian model and acquire quantitative results about its chaotic behavior. Our investigation tool is the construction of scan mapsmore » by using the Smaller ALignment Index as a chaos indicator. Applying this approach to a large number of initial conditions, we manage to accurately and efficiently measure the extent of chaos in the model and its dependence on physically important parameters like the energy and the angular momentum of the system.« less

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Universality of quantum information in chaotic CFTs

NASA Astrophysics Data System (ADS)

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong

2018-03-01

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

NASA Astrophysics Data System (ADS)

Tajaddodianfar, Farid; Hairi Yazdi, Mohammad Reza; Pishkenari, Hossein Nejat

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.

Nonlinear analysis of dynamic signature

NASA Astrophysics Data System (ADS)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Foraging at the Edge of Chaos: Internal Clock versus External Forcing

NASA Astrophysics Data System (ADS)

Nicolis, S. C.; Fernández, J.; Pérez-Penichet, C.; Noda, C.; Tejera, F.; Ramos, O.; Sumpter, D. J. T.; Altshuler, E.

2013-06-01

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from “autocatalytic” mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hailong; Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042; Zhang, Ning

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phasemore » trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.« less

Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop.

PubMed

Morosi, J; Berti, N; Akrout, A; Picozzi, A; Guasoni, M; Fatome, J

2018-01-22

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Mahmoud, Gamal M.

Dynamical systems described by real and complex variables are currently one of the most popular areas of scientific research. These systems play an important role in several fields of physics, engineering, and computer sciences, for example, laser systems, control (or chaos suppression), secure communications, and information science. Dynamical basic properties, chaos (hyperchaos) synchronization, chaos control, and generating hyperchaotic behavior of these systems are briefly summarized. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. They are also used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, where the electric field and the atomic polarization amplitudes are both complex. Clearly, if the variables of the system are complex the equations involve twice as many variables and control parameters, thus making it that much harder for a hostile agent to intercept and decipher the coded message. Chaotic and hyperchaotic complex systems are stated as examples. Finally there are many open problems in the study of chaotic and hyperchaotic complex nonlinear dynamical systems, which need further investigations. Some of these open problems are given.

Gravitational dynamos and the low-frequency geomagnetic secular variation.

PubMed

Olson, P

2007-12-18

Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions.

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1996-01-01

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Gravitational dynamos and the low-frequency geomagnetic secular variation

PubMed Central

Olson, P.

2007-01-01

Self-sustaining numerical dynamos are used to infer the sources of low-frequency secular variation of the geomagnetic field. Gravitational dynamo models powered by compositional convection in an electrically conducting, rotating fluid shell exhibit several regimes of magnetic field behavior with an increasing Rayleigh number of the convection, including nearly steady dipoles, chaotic nonreversing dipoles, and chaotic reversing dipoles. The time average dipole strength and dipolarity of the magnetic field decrease, whereas the dipole variability, average dipole tilt angle, and frequency of polarity reversals increase with Rayleigh number. Chaotic gravitational dynamos have large-amplitude dipole secular variation with maximum power at frequencies corresponding to a few cycles per million years on Earth. Their external magnetic field structure, dipole statistics, low-frequency power spectra, and polarity reversal frequency are comparable to the geomagnetic field. The magnetic variability is driven by the Lorentz force and is characterized by an inverse correlation between dynamo magnetic and kinetic energy fluctuations. A constant energy dissipation theory accounts for this inverse energy correlation, which is shown to produce conditions favorable for dipole drift, polarity reversals, and excursions. PMID:18048345

Critical edge between frozen extinction and chaotic life

NASA Astrophysics Data System (ADS)

Monetti, Roberto A.; Albano, Ezequiel V.

1995-12-01

The cellular automata ``game of life'' (GL) proposed by J. Conway simulates the dynamic evolution of a society of living organisms. It has been extensively studied in order to understand the emergence of complexity and diversity from a set of local rules. More recently, the capability of GL to self-oranize into a critical state has opened an interesting debate. In this work we adopt a different approach: by introducing stochastic rules in the GL it is found that ``life'' exhibits a very rich critical behavior. Discontinuous (first-order) irreversible phase transitions (IPT's) between an extinct phase and a steady state supporting life are found. A precise location of the critical edge is achieved by means of an epidemic analysis, which also allows us to determine dynamic critical exponents. Furthermore, by means of a damage spreading study we conclude that the living phase is chaotic. The edge of the frozen-chaotic transition coincides with that of the IPT's life extinction. Close to the edge, fractal spreading of the damage is observed; however, deep inside the living phase such spreading becomes homogeneous. (c) 1995 The American Physical Society

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Shaohua

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaosmore » of PMSM and show the effectiveness and robustness of the proposed method.« less

Chaotic behavior of light-assisted physical aging in arsenoselenide glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shpotyuk, O., E-mail: shpotyuk@novas.lviv.ua; Institute of Physics of Jan Dlugosz University, 13/15, al. Armii Krajowej, Czestochowa 42201; Balitska, V.

2014-12-15

The theory of strange attractors is shown to be adequately applicable for analyzing the kinetics of light-assisted physical aging revealed in structural relaxation of Se-rich As-Se glasses below glass transition. Kinetics of enthalpy losses is used to determine the phase space reconstruction parameters. Observed chaotic behaviour (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, false nearest neighbours, etc.) reconstructed via the TISEAN program package is treated within a microstructure model describing multistage aging behaviour in arsenoselenide glasses. This simulation testifies that photoexposure acts as an initiating factor onlymore » at the beginning stage of physical aging, thus facilitating further atomic shrinkage of a glassy backbone.« less

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

NASA Astrophysics Data System (ADS)

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

2018-03-01

We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes–Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain.

PubMed

Luo, Shaohua

2014-09-01

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaos of PMSM and show the effectiveness and robustness of the proposed method.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

Qualitative dynamical analysis of chaotic plasma perturbations model

NASA Astrophysics Data System (ADS)

Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

2018-06-01

In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

Teaching Deterministic Chaos through Music.

ERIC Educational Resources Information Center

Chacon, R.; And Others

1992-01-01

Presents music education as a setting for teaching nonlinear dynamics and chaotic behavior connected with fixed-point and limit-cycle attractors. The aim is not music composition but a first approach to an interdisciplinary tool suitable for a single-session class, at either the secondary or undergraduate level, for the introduction of these…

Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.

ERIC Educational Resources Information Center

Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis

This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Turning Classroom Failure into Student Success: The Value of Integrating Resiliency Building Activities in the Academic Classroom

ERIC Educational Resources Information Center

Berg, Patricia; Pietrasz, Carol

2017-01-01

Millennials are a unique generational cohort populating the classroom, leaving university professors with the challenge of appropriately preparing them for the chaotic workforce. One challenge is their lower levels of resiliency. When faced with setbacks, Millennials tend to give up instead of bouncing back. This lack of resiliency is negatively…

Incoherent by Design: What You Should Know about Differences between Undergraduate and Graduate Training of Elementary Teachers

ERIC Educational Resources Information Center

Greenberg, Julie; Dugan, Natalie

2015-01-01

This brief quantifies the fundamentally chaotic nature of elementary teacher preparation for initial certification, which is by far the most popular choice of individuals who consider teaching. In order to understand the different approaches taken by programs housed on the same university campus, researchers examined 13 institutions that offer…

Warm inflationary model in loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herrera, Ramon

A warm inflationary universe model in loop quantum cosmology is studied. In general we discuss the condition of inflation in this framework. By using a chaotic potential, V({phi}){proportional_to}{phi}{sup 2}, we develop a model where the dissipation coefficient {Gamma}={Gamma}{sub 0}=constant. We use recent astronomical observations for constraining the parameters appearing in our model.

Chaos modeling applied to environmental dynamics from in situ and satellite observational time series

NASA Astrophysics Data System (ADS)

Mangiarotti, S.

2016-12-01

The idea that a low-dimensional system can be simultaneously deterministic and unpredictable at long term was clearly understood by Henri Poincaré at the end of the 19thcentury [1]. It is however several decades later that a system providing a straightforward illustration of such behavior was obtained by Lorenz in 1963 [2]. Such type of behavior is now called chaotic. The idea that dynamics can be chaotic deeply modifies our knowledge of the world and has important incidences for modeling, analyzing and characterizing real world behaviors. Important developments were performed since the 1980's for modeling chaos directly from observational data [3-6]. Until the early 2000s, chaotic systems of Ordinary Differential Equations were retrieved exclusively for theoretical systems or for lab experimentations. The first global model obtained under real world conditions was for the population cycles of Canadian Lynx [7] in 2006. Thanks to further developments [6], numerous other global models were recently obtained for several natural and environmental real systems, directly from observational data. In the present talk, the global modeling technique will be first introduced. Then, several of the chaotic global models obtained from in situ and satellite environmental data will be presented. The following domains will be considered: cereal crops cycles in semi-arid regions [8], karstic sources discharge under various climatic conditions, snow surface cycles [9], the historical Bombay plague epidemic that broke out in 1896 and its coupling to rats epizootics [10], and the recent epidemic of Ebola virus disease in West Africa (2014-2016). [1] Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste (Gauthier-Vilard, Paris, 1899), Tome III. [2] E.N. Lorenz, J. Atmos. Sci., 20,130-141 (1963). [3] J. P. Crutchfield and B. S. McNamara, Complex Syst. 1, 417-452 (1987). [4] G. Gouesbet and C. Letellier, Phys. Rev. E 49, 4955-4972 (1994). [5] C. Letellier et al., Chaos 19(2), 023103 (2009). [6] S. Mangiarotti et al., Phys. Rev. E 86(4), 046205 (2012). [7] J. Maquet et al., J. Math. Biol. 55(1), 21-39 (2007). [8] S. Mangiarotti et al., Chaos, 24, 023130 (2014). [9] S. Mangiarotti, Habilitation to Direct Research Thesis, Université de Toulouse 3(2014). [10] S. Mangiarotti, Chaos, Solitons and Fractals, 81A, 184-196 (2015).

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaojun; School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001; Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuousmore » change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.« less

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Breaking chaotic secure communication using a spectrogram

NASA Astrophysics Data System (ADS)

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

1998-10-01

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Universality and chaoticity in ultracold K+KRb chemical reactions

DOE PAGES

Croft, J. F. E.; Makrides, C.; Li, M.; ...

2017-07-19

A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysismore » of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.« less

Stochastic dynamics and combinatorial optimization

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Wang, Kang L.

2017-11-01

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.

Psychotic Depression and Suicidal Behavior.

PubMed

Fredriksen, Kristin J; Schoeyen, Helle K; Johannessen, Jan O; Walby, Fredrik A; Davidson, Larry; Schaufel, Margrethe A

2017-01-01

This study investigated how severely depressed individuals experienced the relationship between psychotic symptoms and suicidal ideation and behavior. Semi-structured qualitative interviews were conducted with a purposive sample of nine inpatients from a psychiatric university hospital between September 2012 and May 2013 fulfilling diagnostic criteria for a psychotic depressive episode as part of a unipolar or bipolar disorder. Analysis was conducted using systematic text condensation. Participants experienced (1) being directed to perform impulsive potentially fatal actions, (2) feeling hounded to death, (3) becoming trapped in an inescapable darkness, and (4) being left bereft of mental control. They described how impulsivity directed by delusions and hallucinations resulted in unpredictable actions with only moments from decision to conduct. Suicide was seen as an escape not only from life problems but also from psychotic experiences and intense anxiety. Participants reported being in a chaotic state, unable to think rationally or anticipate the consequences of their actions. Their ability to identify and communicate psychotic symptoms and suicidal ideation and behavior was compromised, leaving them to struggle alone with these terrifying experiences. Suicide risk assessments based on verbal reports from individuals with psychotic depression may not always be valid due to potential impulsivity and underreporting of suicidal ideation. It may be important for clinicians to explore the delusional content of such patients' experiences to assess the possibility of suicide as a result of shame, guilt, remorse, or altruistic intentions to save others from harm.

Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Hilborn, Robert C.

2004-04-01

The butterfly effect has become a popular metaphor for sensitive dependence on initial conditions—the hallmark of chaotic behavior. I describe how, where, and when this term was conceived in the 1970s. Surprisingly, the butterfly metaphor was predated by more than 70 years by the grasshopper effect.

Nonlinear Dynamical Analysis of Fibrillation

NASA Astrophysics Data System (ADS)

Kerin, John A.; Sporrer, Justin M.; Egolf, David A.

2013-03-01

The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.

The spatial dynamics of ecosystem engineers.

PubMed

Franco, Caroline; Fontanari, José F

2017-10-01

The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics of organisms that must modify their habitats in order to survive, the so-called ecosystem engineers, requires the explicit incorporation of abiotic interactions in the models. Here we study a model of ecosystem engineers that is discrete both in space and time, and where the engineers and their habitats are arranged in patches fixed to the sites of regular lattices. The growth of the engineer population is modeled by Ricker equation with a density-dependent carrying capacity that is given by the number of modified habitats. A diffusive dispersal stage ensures that a fraction of the engineers move from their birth patches to neighboring patches. We find that dispersal influences the metapopulation dynamics only in the case that the local or single-patch dynamics exhibit chaotic behavior. In that case, it can suppress the chaotic behavior and avoid extinctions in the regime of large intrinsic growth rate of the population. Copyright © 2017 Elsevier Inc. All rights reserved.

Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria

NASA Astrophysics Data System (ADS)

Bao, Han; Wang, Ning; Bao, Bocheng; Chen, Mo; Jin, Peipei; Wang, Guangyi

2018-04-01

Memristor-based nonlinear dynamical system easily presents the initial condition-dependent dynamical phenomenon of extreme multistability, i.e., coexisting infinitely many attractors, which has been received much attention in recent years. By introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting memristor-based chaotic system with hypogenetic jerk equation and circuit forms is proposed. The most striking feature is that this system has four line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. Stability of these line equilibria are analyzed, and coexisting infinitely many attractors' behaviors with the variations of the initial conditions are investigated by bifurcation diagrams, Lyapunov exponent spectra, attraction basins, and phased portraits, upon which the forming mechanism of extreme multistablity in the memristor-based hypogenetic jerk system is explored. Specially, unusual transition behavior of long term transient period with steady chaos, completely different from the phenomenon of transient chaos, can be also found for some initial conditions. Moreover, a hardware circuit is design and fabricated and its experimental results effectively verify the truth of extreme multistablity.

Nonlinear time-series analysis of current signal in cathodic contact glow discharge electrolysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allagui, Anis, E-mail: aallagui@sharjah.ac.ae; Abdelkareem, Mohammad Ali; Rojas, Andrea Espinel

In the standard two-electrode configuration employed in electrolytic process, when the control dc voltage is brought to a critical value, the system undergoes a transition from conventional electrolysis to contact glow discharge electrolysis (CGDE), which has also been referred to as liquid-submerged micro-plasma, glow discharge plasma electrolysis, electrode effect, electrolytic plasma, etc. The light-emitting process is associated with the development of an irregular and erratic current time-series which has been arbitrarily labelled as “random,” and thus dissuaded further research in this direction. Here, we examine the current time-series signals measured in cathodic CGDE configuration in a concentrated KOH solution atmore » different dc bias voltages greater than the critical voltage. We show that the signals are, in fact, not random according to the NIST SP. 800-22 test suite definition. We also demonstrate that post-processing low-pass filtered sequences requires less time than the native as-measured sequences, suggesting a superposition of low frequency chaotic fluctuations and high frequency behaviors (which may be produced by more than one possible source of entropy). Using an array of nonlinear time-series analyses for dynamical systems, i.e., the computation of largest Lyapunov exponents and correlation dimensions, and re-construction of phase portraits, we found that low-pass filtered datasets undergo a transition from quasi-periodic to chaotic to quasi-hyper-chaotic behavior, and back again to chaos when the voltage controlling-parameter is increased. The high frequency part of the signals is discussed in terms of highly nonlinear turbulent motion developed around the working electrode.« less

Hybrid electronic/optical synchronized chaos communication system.

PubMed

Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

2009-04-27

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

Regimes of stability and scaling relations for the removal time in the asteroid belt: a simple kinetic model and numerical tests

NASA Astrophysics Data System (ADS)

Cubrovic, Mihailo

2005-02-01

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.

Phase locking route behind complex periodic windows in a forced oscillator

NASA Astrophysics Data System (ADS)

Jan, Hengtai; Tsai, Kuo-Ting; Kuo, Li-wei

2013-09-01

Chaotic systems have complex reactions against an external driving force; even in cases with low-dimension oscillators, the routes to synchronization are diverse. We proposed a stroboscope-based method for analyzing driven chaotic systems in their phase space. According to two statistic quantities generated from time series, we could realize the system state and the driving behavior simultaneously. We demonstrated our method in a driven bi-stable system, which showed complex period windows under a proper driving force. With increasing periodic driving force, a route from interior periodic oscillation to phase synchronization through the chaos state could be found. Periodic windows could also be identified and the circumstances under which they occurred distinguished. Statistical results were supported by conditional Lyapunov exponent analysis to show the power in analyzing the unknown time series.

A review of human factors challenges of complex adaptive systems: discovering and understanding chaos in human performance.

PubMed

Karwowski, Waldemar

2012-12-01

In this paper, the author explores a need for a greater understanding of the true nature of human-system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. Human performance, more often than not, constitutes complex adaptive phenomena with emergent properties that exhibit nonlinear dynamical (chaotic) behaviors. The complexity challenges in the design and management of contemporary work systems, including service systems, are explored. Examples of selected applications of the concepts of nonlinear dynamics to the study of human physical performance are provided. Understanding and applications of the concepts of theory of complex adaptive and dynamical systems should significantly improve the effectiveness of human-centered design efforts of a large system of systems. Performance of many contemporary work systems and environments may be sensitive to the initial conditions and may exhibit dynamic nonlinear properties and chaotic system behaviors. Human-centered design of emergent human-system interactions requires application of the theories of nonlinear dynamics and complex adaptive system. The success of future human-systems integration efforts requires the fusion of paradigms, knowledge, design principles, and methodologies of human factors and ergonomics with those of the science of complex adaptive systems as well as modern systems engineering.

Intermittency of intermittencies

NASA Astrophysics Data System (ADS)

Hramov, Alexander E.; Koronovskii, Alexey A.; Moskalenko, Olga I.; Zhuravlev, Maxim O.; Ponomarenko, Vladimir I.; Prokhorov, Mikhail D.

2013-09-01

A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.

Dynamical singularities of glassy systems in a quantum quench.

PubMed

Obuchi, Tomoyuki; Takahashi, Kazutaka

2012-11-01

We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a freezing transition at some critical time. The behavior is understood by the partition-function zeros in the complex temperature plane. We discuss the properties of the freezing phase as a dynamical chaotic phase, which are contrasted to those of the spin-glass phase in the static system.

A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system.

PubMed

Zaher, Ashraf A

2008-03-01

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.

A novel procedure for the identification of chaos in complex biological systems

NASA Astrophysics Data System (ADS)

Bazeia, D.; Pereira, M. B. P. N.; Brito, A. V.; Oliveira, B. F. De; Ramos, J. G. G. S.

2017-03-01

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.

Prediction of the reference evapotranspiration using a chaotic approach.

PubMed

Wang, Wei-guang; Zou, Shan; Luo, Zhao-hui; Zhang, Wei; Chen, Dan; Kong, Jun

2014-01-01

Evapotranspiration is one of the most important hydrological variables in the context of water resources management. An attempt was made to understand and predict the dynamics of reference evapotranspiration from a nonlinear dynamical perspective in this study. The reference evapotranspiration data was calculated using the FAO Penman-Monteith equation with the observed daily meteorological data for the period 1966-2005 at four meteorological stations (i.e., Baotou, Zhangbei, Kaifeng, and Shaoguan) representing a wide range of climatic conditions of China. The correlation dimension method was employed to investigate the chaotic behavior of the reference evapotranspiration series. The existence of chaos in the reference evapotranspiration series at the four different locations was proved by the finite and low correlation dimension. A local approximation approach was employed to forecast the daily reference evapotranspiration series. Low root mean square error (RSME) and mean absolute error (MAE) (for all locations lower than 0.31 and 0.24, resp.), high correlation coefficient (CC), and modified coefficient of efficiency (for all locations larger than 0.97 and 0.8, resp.) indicate that the predicted reference evapotranspiration agrees well with the observed one. The encouraging results indicate the suitableness of chaotic approach for understanding and predicting the dynamics of the reference evapotranspiration.

Children’s looking preference for biological motion may be related to an affinity for mathematical chaos

PubMed Central

Haworth, Joshua L.; Kyvelidou, Anastasia; Fisher, Wayne; Stergiou, Nicholas

2015-01-01

Recognition of biological motion is pervasive in early child development. Further, viewing the movement behavior of others is a primary component of a child’s acquisition of complex, robust movement repertoires, through imitation and real-time coordinated action. We theorize that inherent to biological movements are particular qualities of mathematical chaos and complexity. We further posit that this character affords the rich and complex inter-dynamics throughout early motor development. Specifically, we explored whether children’s preference for biological motion may be related to an affinity for mathematical chaos. Cross recurrence quantification analysis (cRQA) was used to investigate the coordination of gaze and posture with various temporal structures (periodic, chaotic, and aperiodic) of the motion of an oscillating visual stimulus. Children appear to competently perceive and respond to chaotic motion, both in rate (cRQA-percent determinism) and duration (cRQA-maxline) of coordination. We interpret this to indicate that children not only recognize chaotic motion structures, but also have a preference for coordination with them. Further, stratification of our sample (by age) uncovers the suggestion that this preference may become refined with age. PMID:25852600

High-Speed Imaging of Dusty Plasma Instabilities

NASA Astrophysics Data System (ADS)

Tawidian, H.; Couëdel, L.; Mikikian, M.; Lecas, T.; Boufendi, L.; Vallée, O.

2011-11-01

Dust particles in a plasma acquire negative charges by capturing electrons. If the dust particle density is high, a huge loss of free electrons can trigger unstable behaviors in the plasma. Several types of plasma behaviors are analyzed thanks to a high-speed camera like dust particle growth instabilities (DPGI) and a new phenomenon called plasma spheroids. These small plasma spheroids are about a few mm, have a slightly enhanced luminosity, and are observed in the vicinity of the electrodes. Different behaviors are identified for these spheroids like a rotational motion, or a chaotic regime (fast appearance and disappearance).

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-06-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.

2007-01-01

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Development and Survival: A Study of Children at Risk Living in Adverse Psychosocial Milieu.

ERIC Educational Resources Information Center

Wahlsten, Viveka Sundelin

1994-01-01

This 4-year longitudinal study followed 12 infants or young children (6 boys and 6 girls) in 7 high-risk Swedish families (including drug abuse, chaotic family structure, antisocial behavior, and child care problems). Three girls developed mainly constructive (moderating) strategies; the other children demonstrated more or less destructive,…

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Chaos and crises in a model for cooperative hunting: a symbolic dynamics approach.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2009-12-01

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C(0)) and (K,sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K(c) decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Second Annual Research Center for Optical Physics (RCOP) Forum

NASA Technical Reports Server (NTRS)

Allario, Frank (Editor); Temple, Doyle (Editor)

1995-01-01

The Research Center for Optical Physics (RCOP) held its Second Annual Forum on September 23-24, 1994. The forum consisted of two days of technical sessions with invited talks, submitted talks, and a student poster session. Participants in the technical sessions included students and researchers from CCNY/CUNY, Fisk University, Georgia Institute of Technology, Hampton University, University of Maryland, the Univeristy of Michigan, NASA Langley Research Center, North Caroline A and T University, Steven's Institute of Technology, and NAWC-Warminster. Topics included chaotic lasers, pumped optical filters, nonlinear responses in polythiophene and thiophene based thin films, crystal growth and spectroscopy, laser-induced photochromic centers, raman scattering in phorphyrin, superradiance, doped fluoride crystals, luminescence of terbium in silicate glass, and radiative and nonradiative transitions in rare-earth ions.

Partially chaotic orbits in a perturbed cubic force model

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2017-11-01

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincaré maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus

NASA Astrophysics Data System (ADS)

Ito, Takanori; Ito, Kikukatsu

2005-11-01

Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 °C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the “Zazen attractor.” Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.

Coherent motion of chaotic attractors

NASA Astrophysics Data System (ADS)

Louodop, Patrick; Saha, Suman; Tchitnga, Robert; Muruganandam, Paulsamy; Dana, Syamal K.; Cerdeira, Hilda A.

2017-10-01

We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.

Synchronization of strange non-chaotic attractors via unidirectional coupling of quasiperiodically-forced systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Daniel Sweetlin, M.; Arulgnanam, A.

2016-07-01

In this paper, we present a numerical investigation on the robust synchronization phenomenon observed in a unidirectionally-coupled quasiperiodically-forced simple nonlinear electronic circuit system exhibiting strange non-chaotic attractors (SNAs) in its dynamics. The SNA obtained in the simple quasiperiodic system is characterized for its SNA behavior. Then, we studied the nature of the synchronized state in unidirectionally coupled SNAs by using the Master-Slave approach. The stability of the synchronized state is studied through the master stability functions (MSF) obtained for coupling different state variables of the drive and response system. The property of robust synchronization is analyzed for one type of coupling of the state variables through phase portraits, conditional lyapunov exponents and the Kaplan-Yorke dimension. The phenomenon of complete synchronization of SNAs via a unidirectional coupling scheme is reported for the first time.

State-space prediction model for chaotic time series

NASA Astrophysics Data System (ADS)

Alparslan, A. K.; Sayar, M.; Atilgan, A. R.

1998-08-01

A simple method for predicting the continuation of scalar chaotic time series ahead in time is proposed. The false nearest neighbors technique in connection with the time-delayed embedding is employed so as to reconstruct the state space. A local forecasting model based upon the time evolution of the topological neighboring in the reconstructed phase space is suggested. A moving root-mean-square error is utilized in order to monitor the error along the prediction horizon. The model is tested for the convection amplitude of the Lorenz model. The results indicate that for approximately 100 cycles of the training data, the prediction follows the actual continuation very closely about six cycles. The proposed model, like other state-space forecasting models, captures the long-term behavior of the system due to the use of spatial neighbors in the state space.

Chaotic obliquity and the nature of the Martian climate

NASA Technical Reports Server (NTRS)

Jakosky, Bruce M.; Henderson, Bradley G.; Mellon, Michael T.

1995-01-01

Recent calculations of the Martian obliquity suggests that it varies chaotically on timescales longer than about 10(exp 7) years and varies between about 0 and 60 deg. We examine the seasonal water behavior at obliquities between 40 and 60 deg. Up to several tens of centimeters of water may sublime from the polar caps each year, and possibly move to the equator, where it is more stable. The CO2 frost and CO2-H2O clathrate hydrate are stable in thepolar deposits below a few tens of meters depth, so that the polar cap could contain a significant CO2 reservoir. If CO2 is present, it could be left over from the early history of Mars; also, it could be released into the atmosphere during periods of high obliquity, causing occasional periods of more-clement climate.

Characterizing Strength of Chaotic Dynamics and Numerical Simulation Relevant to Modified Taylor-Couette Flow with Hourglass Geometry

NASA Astrophysics Data System (ADS)

Hou, Yu; Kowalski, Adam; Schroder, Kjell; Halmstad, Andrew; Olsen, Thomas; Wiener, Richard

2006-05-01

We characterize the strength of chaos in two different regimes of Modified Taylor-Couette flow with Hourglass Geometry: the formation of Taylor Vortices with laminar flow and with turbulent flow. We measure the strength of chaos by calculating the correlation dimension and the Kaplan-Yorke dimension based upon the Lyapunov Exponents of each system. We determine the reliability of our calculations by considering data from a chaotic electronic circuit. In order to predict the behavior of the Modified Taylor-Couette flow system, we employ simulations based upon an idealized Reaction-Diffusion model with a third order non-linearity in the reaction rate. Variation of reaction rate with length corresponds to variation of the effective Reynolds Number along the Taylor-Couette apparatus. We present preliminary results and compare to experimental data.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.

PubMed

Gotoda, Hiroshi; Nikimoto, Hiroyuki; Miyano, Takaya; Tachibana, Shigeru

2011-03-01

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

The fast kinematic magnetic dynamo and the dissipationless limit

NASA Technical Reports Server (NTRS)

Finn, John M.; Ott, Edward

1990-01-01

The evolution of the magnetic field in models that incorporate chaotic field line stretching, field cancellation, and finite magnetic Reynolds number is examined analytically and numerically. Although the models used here are highly idealized, it is claimed that they display and illustrate typical behavior relevant to fast magnetic dynamic behavior. It is shown, in particular, that consideration of magnetic flux through a finite fixed surface provides a simple and effective way of deducing fast dynamo behavior from the zero resistivity equation. Certain aspects of the fast dynamo problem can thus be reduced to a study of nonlinear dynamic properties of the underlying flow.

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

PubMed

Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

2005-01-01

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

Periodicity and chaos from switched flow systems - Contrasting examples of discretely controlled continuous systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joseph; Ramadge, Peter J.

1993-01-01

We analyze two examples of the discrete control of a continuous variable system. These examples exhibit what may be regarded as the two extremes of complexity of the closed-loop behavior: one is eventually periodic, the other is chaotic. Our examples are derived from sampled deterministic flow models. These are of interest in their own right but have also been used as models for certain aspects of manufacturing systems. In each case, we give a precise characterization of the closed-loop behavior.

Behavior dynamics: One perspective

PubMed Central

Marr, M. Jackson

1992-01-01

Behavior dynamics is a field devoted to analytic descriptions of behavior change. A principal source of both models and methods for these descriptions is found in physics. This approach is an extension of a long conceptual association between behavior analysis and physics. A theme common to both is the role of molar versus molecular events in description and prediction. Similarities and differences in how these events are treated are discussed. Two examples are presented that illustrate possible correspondence between mechanical and behavioral systems. The first demonstrates the use of a mechanical model to describe the molar properties of behavior under changing reinforcement conditions. The second, dealing with some features of concurrent schedules, focuses on the possible utility of nonlinear dynamical systems to the description of both molar and molecular behavioral events as the outcome of a deterministic, but chaotic, process. PMID:16812655

Proceedings of the Antenna Applications Symposium (1993). Volume 2,

DTIC Science & Technology

1994-02-01

Fig. 2). Even though Pwill can be computed accurately (Pial = PBWG - Pm), its field distribution and its chaotic behavior inside the lossy BWG is...34s""I+(n-1)M1)] (4) where M1 = K / N1. Since eq. (4) can be used to obtain the actual field, the time comsuming computation of matix [Y] need only be

Traveling waves and chaos in thermosolutal convection

NASA Technical Reports Server (NTRS)

Deane, A. E.; Toomre, J.; Knobloch, E.

1987-01-01

Numerical experiments on two-dimensional thermosolutal convection reveal oscillations in the form of traveling, standing, modulated, and chaotic waves. Transitions between these wave forms and steady convection are investigated and compared with theory. Such rich nonlinear behavior is possible in fluid layers of wide horizontal extent, and provides an explanation for waves observed in recent laboratory experiments with binary fluid mixtures.

Jet Engine Noise Reduction

DTIC Science & Technology

2009-04-01

greatest attention. 4 Excessive noise can cause temporary or permanent hearing loss or tinnitus , a constant ringing in the ear. In addition...industry effort focused on a ten-fold improvement in turbine engine affordable capability by the year 2017. This is following the model of the...exhibit a mix of chaotic and deterministic behavior . Although the governing equations describing fluid flows, the Navier Stokes equations, are based

Investigation of Dynamic Algorithms for Pattern Recognition Identified in Cerebral Cortex

DTIC Science & Technology

1991-12-02

oscillatory and possibly chaotic activity forin the actual cortical substrate of the diverse sensory, motor, and cognitive operations now studied in...September Neural Information Processing Systems - Natural and Synthetic, Denver, Colo., November 1989 U.C. San Diego, Cognitive Science Dept...Baird. Biologically applied neural networks may foster the co-evolution of neurobiology and cognitive psychology. Brain and Behavioral Sciences, 37

Chaos as a psychological construct: historical roots, principal findings, and current growth directions.

PubMed

Guastello, Stephen J

2009-07-01

The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.

Optimization of the resources management in fighting wildfires.

PubMed

Martin-Fernández, Susana; Martínez-Falero, Eugenio; Pérez-González, J Manuel

2002-09-01

Wildfires lead to important economic, social, and environmental losses, especially in areas of Mediterranean climate where they are of a high intensity and frequency. Over the past 30 years there has been a dramatic surge in the development and use of fire spread models. However, given the chaotic nature of environmental systems, it is very difficult to develop real-time fire-extinguishing models. This article proposes a method of optimizing the performance of wildfire fighting resources such that losses are kept to a minimum. The optimization procedure includes discrete simulation algorithms and Bayesian optimization methods for discrete and continuous problems (simulated annealing and Bayesian global optimization). Fast calculus algorithms are applied to provide optimization outcomes in short periods of time such that the predictions of the model and the real behavior of the fire, combat resources, and meteorological conditions are similar. In addition, adaptive algorithms take into account the chaotic behavior of wildfire so that the system can be updated with data corresponding to the real situation to obtain a new optimum solution. The application of this method to the Northwest Forest of Madrid (Spain) is also described. This application allowed us to check that it is a helpful tool in the decision-making process.

Dynamic analysis and electronic circuit implementation of a novel 3D autonomous system without linear terms

NASA Astrophysics Data System (ADS)

Kengne, J.; Jafari, S.; Njitacke, Z. T.; Yousefi Azar Khanian, M.; Cheukem, A.

2017-11-01

Mathematical models (ODEs) describing the dynamics of almost all continuous time chaotic nonlinear systems (e.g. Lorenz, Rossler, Chua, or Chen system) involve at least a nonlinear term in addition to linear terms. In this contribution, a novel (and singular) 3D autonomous chaotic system without linear terms is introduced. This system has an especial feature of having two twin strange attractors: one ordinary and one symmetric strange attractor when the time is reversed. The complex behavior of the model is investigated in terms of equilibria and stability, bifurcation diagrams, Lyapunov exponent plots, time series and Poincaré sections. Some interesting phenomena are found including for instance, period-doubling bifurcation, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits) and chaos while monitoring the system parameters. Compared to the (unique) case previously reported by Xu and Wang (2014) [31], the system considered in this work displays a more 'elegant' mathematical expression and experiences richer dynamical behaviors. A suitable electronic circuit (i.e. the analog simulator) is designed and used for the investigations. Pspice based simulation results show a very good agreement with the theoretical analysis.

Optimization of the Resources Management in Fighting Wildfires

NASA Astrophysics Data System (ADS)

Martin-Fernández, Susana; Martínez-Falero, Eugenio; Pérez-González, J. Manuel

2002-09-01

Wildfires lead to important economic, social, and environmental losses, especially in areas of Mediterranean climate where they are of a high intensity and frequency. Over the past 30 years there has been a dramatic surge in the development and use of fire spread models. However, given the chaotic nature of environmental systems, it is very difficult to develop real-time fire-extinguishing models. This article proposes a method of optimizing the performance of wildfire fighting resources such that losses are kept to a minimum. The optimization procedure includes discrete simulation algorithms and Bayesian optimization methods for discrete and continuous problems (simulated annealing and Bayesian global optimization). Fast calculus algorithms are applied to provide optimization outcomes in short periods of time such that the predictions of the model and the real behavior of the fire, combat resources, and meteorological conditions are similar. In addition, adaptive algorithms take into account the chaotic behavior of wildfire so that the system can be updated with data corresponding to the real situation to obtain a new optimum solution. The application of this method to the Northwest Forest of Madrid (Spain) is also described. This application allowed us to check that it is a helpful tool in the decision-making process.

Statistical characterization of discrete conservative systems: The web map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-10-01

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.

Video encryption using chaotic masks in joint transform correlator

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; Frasca, Mattia; OświÈ©cimka, Paweł; Faes, Luca; DroŻdŻ, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity.

PubMed

Minati, Ludovico; Frasca, Mattia; Oświȩcimka, Paweł; Faes, Luca; Drożdż, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Chaotic component obscured by strong periodicity in voice production system

NASA Astrophysics Data System (ADS)

Tao, Chao; Jiang, Jack J.

2008-06-01

The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity.

Chaotic component obscured by strong periodicity in voice production system

PubMed Central

Tao, Chao; Jiang, Jack J.

2010-01-01

The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity. PMID:18643315

Prediction of the Reference Evapotranspiration Using a Chaotic Approach

PubMed Central

Wang, Wei-guang; Zou, Shan; Luo, Zhao-hui; Zhang, Wei; Kong, Jun

2014-01-01

Evapotranspiration is one of the most important hydrological variables in the context of water resources management. An attempt was made to understand and predict the dynamics of reference evapotranspiration from a nonlinear dynamical perspective in this study. The reference evapotranspiration data was calculated using the FAO Penman-Monteith equation with the observed daily meteorological data for the period 1966–2005 at four meteorological stations (i.e., Baotou, Zhangbei, Kaifeng, and Shaoguan) representing a wide range of climatic conditions of China. The correlation dimension method was employed to investigate the chaotic behavior of the reference evapotranspiration series. The existence of chaos in the reference evapotranspiration series at the four different locations was proved by the finite and low correlation dimension. A local approximation approach was employed to forecast the daily reference evapotranspiration series. Low root mean square error (RSME) and mean absolute error (MAE) (for all locations lower than 0.31 and 0.24, resp.), high correlation coefficient (CC), and modified coefficient of efficiency (for all locations larger than 0.97 and 0.8, resp.) indicate that the predicted reference evapotranspiration agrees well with the observed one. The encouraging results indicate the suitableness of chaotic approach for understanding and predicting the dynamics of the reference evapotranspiration. PMID:25133221

DOE Office of Scientific and Technical Information (OSTI.GOV)

Modeste Nguimdo, Romain, E-mail: Romain.Nguimdo@vub.ac.be; Tchitnga, Robert; Woafo, Paul

We numerically investigate the possibility of using a coupling to increase the complexity in simplest chaotic two-component electronic circuits operating at high frequency. We subsequently show that complex behaviors generated in such coupled systems, together with the post-processing are suitable for generating bit-streams which pass all the NIST tests for randomness. The electronic circuit is built up by unidirectionally coupling three two-component (one active and one passive) oscillators in a ring configuration through resistances. It turns out that, with such a coupling, high chaotic signals can be obtained. By extracting points at fixed interval of 10 ns (corresponding to a bitmore » rate of 100 Mb/s) on such chaotic signals, each point being simultaneously converted in 16-bits (or 8-bits), we find that the binary sequence constructed by including the 10(or 2) least significant bits pass statistical tests of randomness, meaning that bit-streams with random properties can be achieved with an overall bit rate up to 10×100 Mb/s =1Gbit/s (or 2×100 Mb/s =200 Megabit/s). Moreover, by varying the bias voltages, we also investigate the parameter range for which more complex signals can be obtained. Besides being simple to implement, the two-component electronic circuit setup is very cheap as compared to optical and electro-optical systems.« less

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

NASA Astrophysics Data System (ADS)

Gu, Hua-Guang; Chen, Sheng-Gen; Li, Yu-Ye

2015-05-01

We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength. Project supported by the National Natural Science Foundation of China (Grant Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127).

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Hierarchical collapse of regular islands via dissipation

NASA Astrophysics Data System (ADS)

Jousseph, C. A. C.; Abdulack, S. A.; Manchein, C.; Beims, M. W.

2018-03-01

In this work we investigate how regular islands localized in a mixed phase-space of generic area-preserving Hamiltonian systems are affected by a small amount of dissipation. Mainly we search for a universality (hierarchy) in the convergence of higher-order resonances and their periods when dissipation increases. One very simple scenario is already known: when subjected to small dissipation, stable periodic points become sinks attracting almost all the surrounding orbits, destroying all invariant curves which divide the phase-space in chaotic and regular domains. However, performing numerical experiments with the paradigmatic Chirikov-Taylor standard mapping we show that this presumably simple scenario can be rather complicated. The first, not trivial, scenario is what happens to chaotic trajectories, since they can be attracted by the sinks or by chaotic attractors, in cases when they exist. We show that this depends very much on how basins of attraction are formed as dissipation increases. In addition, we demonstrate that higher-order resonances are usually first affected by small dissipation when compared to lower-order resonances from the conservative case. Nevertheless, this is not a generic behaviour. We show that a local hierarchical collapse of resonances, as dissipation increases, is related to the area of the islands from the conservative case surrounding the periodic orbits. All observed resonance destructions occur via the bifurcation phenomena and are quantified here by determining the largest finite-time Lyapunov exponent.

Stability analysis of an implicitly defined labor market model

NASA Astrophysics Data System (ADS)

Mendes, Diana A.; Mendes, Vivaldo M.

2008-06-01

Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1-10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.

From Fault-Diagnosis and Performance Recovery of a Controlled System to Chaotic Secure Communication

NASA Astrophysics Data System (ADS)

Hsu, Wen-Teng; Tsai, Jason Sheng-Hong; Guo, Fang-Cheng; Guo, Shu-Mei; Shieh, Leang-San

Chaotic systems are often applied to encryption on secure communication, but they may not provide high-degree security. In order to improve the security of communication, chaotic systems may need to add other secure signals, but this may cause the system to diverge. In this paper, we redesign a communication scheme that could create secure communication with additional secure signals, and the proposed scheme could keep system convergence. First, we introduce the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker for the sampled-data linear time-varying system with unanticipated decay factors in actuators/system states. Besides, robustness, convergence in the mean, and tracking ability are given in this paper. A residual generation scheme and a mechanism for auto-tuning switched gain is also presented, so that the introduced methodology is applicable for the fault detection and diagnosis (FDD) for actuator and state faults to yield a high tracking performance recovery. The evolutionary programming-based adaptive observer is then applied to the problem of secure communication. Whenever the tracker induces a large control input which might not conform to the input constraint of some physical systems, the proposed modified linear quadratic optimal tracker (LQT) can effectively restrict the control input within the specified constraint interval, under the acceptable tracking performance. The effectiveness of the proposed design methodology is illustrated through tracking control simulation examples.

External modes in quantum dot light emitting diode with filtered optical feedback

NASA Astrophysics Data System (ADS)

Al Husseini, Hussein B.; Al Naimee, Kais A.; Al-Khursan, Amin H.; Khedir, Ali. H.

2016-06-01

This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations, MMOs). The results agree with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse case in conventional optical feedback to a coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.

Maternal Executive Function, Harsh Parenting, and Child Conduct Problems

PubMed Central

Deater-Deckard, Kirby; Wang, Zhe; Chen, Nan; Bell, Martha Ann

2012-01-01

Background Maternal executive function and household regulation both are critical aspects of optimal childrearing, but their interplay is not understood. We tested the hypotheses that 1) the link between challenging child conduct problems and harsh parenting would be strongest for mothers with poorer executive function and weakest among those with better executive function, and 2) this mechanism would be further moderated by the degree of household chaos. Methods The socioeconomically diverse sample included 147 mothers of 3-to-7 year old children. Mothers completed questionnaires and a laboratory assessment of executive function. Results Consistent with hypotheses, harsh parenting was linked with child conduct problems only among mothers with poorer executive function. This effect was particularly strong in calm, predictable environments, but was not evident in chaotic environments. Conclusion Maternal executive function is critical to minimizing harsh parenting in the context of challenging child behavior, but this self-regulation process may not operate well in chaotic environments. PMID:22764829

Self-organization of complex networks as a dynamical system

NASA Astrophysics Data System (ADS)

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

NASA Astrophysics Data System (ADS)

Zhou, Ling; Wang, Chunhua; Zhang, Xin; Yao, Wei

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter b. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

Bouncing ball problem: stability of the periodic modes.

PubMed

Barroso, Joaquim J; Carneiro, Marcus V; Macau, Elbert E N

2009-02-01

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

Effects of periodic forcing in chaotic scattering

NASA Astrophysics Data System (ADS)

Blesa, Fernando; Seoane, Jesús M.; Barrio, Roberto; Sanjuán, Miguel A. F.

2014-04-01

The effects of a periodic forcing on chaotic scattering are relevant in certain situations of physical interest. We investigate the effects of the forcing amplitude and the external frequency in both the survival probability of the particles in the scattering region and the exit basins associated to phase space. We have found an exponential decay law for the survival probability of the particles in the scattering region. A resonant-like behavior is uncovered where the critical values of the frequencies ω ≃1 and ω ≃2 permit the particles to escape faster than for other different values. On the other hand, the computation of the exit basins in phase space reveals the existence of Wada basins depending of the frequency values. We provide some heuristic arguments that are in good agreement with the numerical results. Our results are expected to be relevant for physical phenomena such as the effect of companion galaxies, among others.

Complex dynamics of a delayed discrete neural network of two nonidentical neurons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yuanlong; Huang, Tingwen; Huang, Yu, E-mail: stshyu@mail.sysu.edu.cn

2014-03-15

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zoumore » [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.« less

Complex dynamics of a delayed discrete neural network of two nonidentical neurons.

PubMed

Chen, Yuanlong; Huang, Tingwen; Huang, Yu

2014-03-01

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.

External modes in quantum dot light emitting diode with filtered optical feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Al Husseini, Hussein B.; Department of Physics, College of Science, University of Baghdad, Al Jadiriyah, Baghdad; Al Naimee, Kais A.

2016-06-14

This research reports a theoretical investigation on the role of filtered optical feedback (FOF) in the quantum dot light emitting diode (QD-LED). The underlying dynamics is affected by a sidle node, which returns to an elliptical shape when the wetting layer (WL) is neglected. Both filter width and time delay change the appearance of different dynamics (chaotic and mixed mode oscillations, MMOs). The results agree with the experimental observations. Here, the fixed point analysis for QDs was done for the first time. For QD-LED with FOF, the system transits from the coherence collapse case in conventional optical feedback to amore » coherent case with a filtered mode in FOF. It was found that the WL washes out the modes which is an unexpected result. This may attributed to the longer capture time of WL compared with that between QD states. Thus, WL reduces the chaotic behavior.« less

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Complexity and network dynamics in physiological adaptation: an integrated view.

PubMed

Baffy, György; Loscalzo, Joseph

2014-05-28

Living organisms constantly interact with their surroundings and sustain internal stability against perturbations. This dynamic process follows three fundamental strategies (restore, explore, and abandon) articulated in historical concepts of physiological adaptation such as homeostasis, allostasis, and the general adaptation syndrome. These strategies correspond to elementary forms of behavior (ordered, chaotic, and static) in complex adaptive systems and invite a network-based analysis of the operational characteristics, allowing us to propose an integrated framework of physiological adaptation from a complex network perspective. Applicability of this concept is illustrated by analyzing molecular and cellular mechanisms of adaptation in response to the pervasive challenge of obesity, a chronic condition resulting from sustained nutrient excess that prompts chaotic exploration for system stability associated with tradeoffs and a risk of adverse outcomes such as diabetes, cardiovascular disease, and cancer. Deconstruction of this complexity holds the promise of gaining novel insights into physiological adaptation in health and disease. Published by Elsevier Inc.

Self-organization of complex networks as a dynamical system.

PubMed

Aoki, Takaaki; Yawata, Koichiro; Aoyagi, Toshio

2015-01-01

To understand the dynamics of real-world networks, we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers. Our numerical studies reveal that, under suitable conditions, the co-evolving dynamics lead to the emergence of stationary power-law distributions of the resource and link weights, while the resource quantity at each node ceaselessly changes with time. We analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability, with numerous fixed points, limit cycles, and chaotic states. The chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises. We conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real-world networks.

Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier

NASA Astrophysics Data System (ADS)

Geurts, Bernard J.; Wiegel, Frederik W.; Creswick, Richard J.

1990-05-01

The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.

Multistability in Chua's circuit with two stable node-foci

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, B. C.; Wang, N.; Xu, Q.

2016-04-15

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponentmore » spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.« less

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2018-02-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2017-12-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

On the onset of secondary flow and unsteady solutions through a loosely coiled rectangular duct for large aspect ratio

NASA Astrophysics Data System (ADS)

Shaha, Poly Rani; Rudro, Sajal Kanti; Poddar, Nayan Kumar; Mondal, Rabindra Nath

2016-07-01

The study of flows through coiled ducts and channels has attracted considerable attention not only because of their ample applications in Chemical, Mechanical, Civil, Nuclear and Biomechanical engineering but also because of their ample applications in other areas, such as blood flow in the veins and arteries of human and other animals. In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a loosely coiled rectangular duct of large aspect ratio. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number, Dn, for two types of curvatures of the duct. The main concern of the present study is to find out effects of curvature as well as formation of secondary vortices on unsteady solutions whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn is increased. Time evolution calculations as well as their phase spaces are performed with a view to study the non-linear behavior of the unsteady solutions, and it is found that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn's and oscillates periodically or non-periodically (chaotic) between two- and twelve-vortex solutions, if Dn is increased. It is also found that the chaotic solution is weak for small Dn's but strong as Dn becomes large. Axial flow distribution is also investigated and shown in contour plots.

On the onset of secondary flow and unsteady solutions through a loosely coiled rectangular duct for large aspect ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shaha, Poly Rani; Poddar, Nayan Kumar; Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com

The study of flows through coiled ducts and channels has attracted considerable attention not only because of their ample applications in Chemical, Mechanical, Civil, Nuclear and Biomechanical engineering but also because of their ample applications in other areas, such as blood flow in the veins and arteries of human and other animals. In this paper, a numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a loosely coiled rectangular duct of large aspect ratio. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number, Dn,more » for two types of curvatures of the duct. The main concern of the present study is to find out effects of curvature as well as formation of secondary vortices on unsteady solutions whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn is increased. Time evolution calculations as well as their phase spaces are performed with a view to study the non-linear behavior of the unsteady solutions, and it is found that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn’s and oscillates periodically or non-periodically (chaotic) between two- and twelve-vortex solutions, if Dn is increased. It is also found that the chaotic solution is weak for small Dn’s but strong as Dn becomes large. Axial flow distribution is also investigated and shown in contour plots.« less

Non-stationary dynamics in the bouncing ball: A wavelet perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

Dynamical aspects of behavior generation under constraints

PubMed Central

Harter, Derek; Achunala, Srinivas

2007-01-01

Dynamic adaptation is a key feature of brains helping to maintain the quality of their performance in the face of increasingly difficult constraints. How to achieve high-quality performance under demanding real-time conditions is an important question in the study of cognitive behaviors. Animals and humans are embedded in and constrained by their environments. Our goal is to improve the understanding of the dynamics of the interacting brain–environment system by studying human behaviors when completing constrained tasks and by modeling the observed behavior. In this article we present results of experiments with humans performing tasks on the computer under variable time and resource constraints. We compare various models of behavior generation in order to describe the observed human performance. Finally we speculate on mechanisms how chaotic neurodynamics can contribute to the generation of flexible human behaviors under constraints. PMID:19003514

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Chaotic Stochasticity: A Ubiquitous Source of Unpredictability in Epidemics

NASA Astrophysics Data System (ADS)

Rand, D. A.; Wilson, H. B.

1991-11-01

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Akgul, A.; Kaçar, S.; Çavuşoğlu, U.

2018-02-01

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

Chaotic Signal Denoising Based on Hierarchical Threshold Synchrosqueezed Wavelet Transform

NASA Astrophysics Data System (ADS)

Wang, Wen-Bo; Jing, Yun-yu; Zhao, Yan-chao; Zhang, Lian-Hua; Wang, Xiang-Li

2017-12-01

In order to overcoming the shortcoming of single threshold synchrosqueezed wavelet transform(SWT) denoising method, an adaptive hierarchical threshold SWT chaotic signal denoising method is proposed. Firstly, a new SWT threshold function is constructed based on Stein unbiased risk estimation, which is two order continuous derivable. Then, by using of the new threshold function, a threshold process based on the minimum mean square error was implemented, and the optimal estimation value of each layer threshold in SWT chaotic denoising is obtained. The experimental results of the simulating chaotic signal and measured sunspot signals show that, the proposed method can filter the noise of chaotic signal well, and the intrinsic chaotic characteristic of the original signal can be recovered very well. Compared with the EEMD denoising method and the single threshold SWT denoising method, the proposed method can obtain better denoising result for the chaotic signal.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

PubMed Central

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

PubMed

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

Terminal Model Of Newtonian Dynamics

NASA Technical Reports Server (NTRS)

Zak, Michail

1994-01-01

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

The grief map

NASA Astrophysics Data System (ADS)

Monteiro, L. H. A.

2014-12-01

Grieving is a natural human reaction to a significant loss. According to a psychiatric model, this process is characterized by a typical sequence of psychological changes. Here, I propose a discrete-time dynamical system, called the grief map, in order to represent the grieving process. The corresponding bifurcation diagram, which exhibits stationary, periodic, and chaotic behavior, is related to the stages of this sorrowful journey occurring during about 12 months post-loss.

Chaotic Modes in Scale Free Opinion Networks

NASA Astrophysics Data System (ADS)

Kusmartsev, Feo V.; Kürten, Karl E.

In this paper, we investigate processes associated with formation of public opinion in varies directed random, scale free and small-world social networks. The important factor of the opinion formation is the existence of contrarians which were discovered by Granovetter in various social psychology experiments1,2,3 long ago and later introduced in sociophysics by Galam.4 When the density of contrarians increases the system behavior drastically changes at some critical value. At high density of contrarians the system can never arrive to a consensus state and periodically oscillates with different periods depending on specific structure of the network. At small density of the contrarians the behavior is manifold. It depends primary on the initial state of the system. If initially the majority of the population agrees with each other a state of stable majority may be easily reached. However when originally the population is divided in nearly equal parts consensus can never be reached. We model the emergence of collective decision making by considering N interacting agents, whose opinions are described by two state Ising spin variable associated with YES and NO. We show that the dynamical behaviors are very sensitive not only to the density of the contrarians but also to the network topology. We find that a phase of social chaos may arise in various dynamical processes of opinion formation in many realistic models. We compare the prediction of the theory with data describing the dynamics of the average opinion of the USA population collected on a day-by-day basis by varies media sources during the last six month before the final Obama-McCain election. The qualitative ouctome is in reasonable agreement with the prediction of our theory. In fact, the analyses of these data made within the paradigm of our theory indicates that even in this campaign there were chaotic elements where the public opinion migrated in an unpredictable chaotic way. The existence of such a phase of social chaos reflects a main feature of the human being associated with some doubts and uncertainty and especially associated with contrarians which undoubtly exist in any society.

Chaotic Modes in Scale Free Opinion Networks

NASA Astrophysics Data System (ADS)

Kusmartsev, Feo V.; Kürten, Karl E.

2010-12-01

In this paper, we investigate processes associated with formation of public opinion in varies directed random, scale free and small-world social networks. The important factor of the opinion formation is the existence of contrarians which were discovered by Granovetter in various social psychology experiments1,2,3 long ago and later introduced in sociophysics by Galam.4 When the density of contrarians increases the system behavior drastically changes at some critical value. At high density of contrarians the system can never arrive to a consensus state and periodically oscillates with different periods depending on specific structure of the network. At small density of the contrarians the behavior is manifold. It depends primary on the initial state of the system. If initially the majority of the population agrees with each other a state of stable majority may be easily reached. However when originally the population is divided in nearly equal parts consensus can never be reached. We model the emergence of collective decision making by considering N interacting agents, whose opinions are described by two state Ising spin variable associated with YES and NO. We show that the dynamical behaviors are very sensitive not only to the density of the contrarians but also to the network topology. We find that a phase of social chaos may arise in various dynamical processes of opinion formation in many realistic models. We compare the prediction of the theory with data describing the dynamics of the average opinion of the USA population collected on a day-by-day basis by varies media sources during the last six month before the final Obama-McCain election. The qualitative ouctome is in reasonable agreement with the prediction of our theory. In fact, the analyses of these data made within the paradigm of our theory indicates that even in this campaign there were chaotic elements where the public opinion migrated in an unpredictable chaotic way. The existence of such a phase of social chaos reflects a main feature of the human being associated with some doubts and uncertainty and especially associated with contrarians which undoubtly exist in any society.

How many universes are in the multiverse?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Linde, Andrei; Vanchurin, Vitaly

2010-04-15

We argue that the total number of distinguishable locally Friedmann 'universes' generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e{sup e3N}, where N is the number of e-folds of slow-roll posteternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant {Lambda} the number of distinguishable universes is bounded by e{sup |{Lambda}|-3/4}. Inmore » the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.« less

Saturnʼs Inner Satellites: Orbits, Masses, and the Chaotic Motion of Atlas from New Cassini Imaging Observations

NASA Astrophysics Data System (ADS)

Cooper, N. J.; Renner, S.; Murray, C. D.; Evans, M. W.

2015-01-01

We present numerically derived orbits and mass estimates for the inner Saturnian satellites, Atlas, Prometheus, Pandora, Janus, and Epimetheus from a fit to 2580 new Cassini Imaging Science Subsystem astrometric observations spanning 2004 February to 2013 August. The observations are provided as machine-readable and Virtual Observatory tables. We estimate G{{M}Atlas} = (0.384 ± 0.001) × 10-3 km3 s-2, a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. We also find G{{M}Prometheus} = (10.677 ± 0.006) × 10-3 km3 s-2, G{{M}Pandora} = (9.133 ± 0.009) × 10-3 km3 s-2, G{{M}Janus} = (126.51 ± 0.03) × 10-3 km3 s-2, and G{{M}Epimetheus} = (35.110 ± 0.009) × 10-3 km3 s-2, consistent with previously published values, but also with significant reductions in uncertainties. We show that Atlas is currently librating in both the 54:53 co-rotation-eccentricity resonance (CER) and the 54:53 inner Lindblad (ILR) resonance with Prometheus, making it the latest example of a coupled CER-ILR system, in common with the Saturnian satellites Anthe, Aegaeon, and Methone, and possibly Neptune's ring arcs. We further demonstrate that Atlas's orbit is chaotic, with a Lyapunov time of ˜10 years, and show that its chaotic behavior is a direct consequence of the coupled resonant interaction with Prometheus, rather than being an indirect effect of the known chaotic interaction between Prometheus and Pandora. We provide an updated analysis of the second-order resonant perturbations involving Prometheus, Pandora, and Epimetheus based on the new observations, showing that these resonant arguments are librating only when Epimetheus is the innermost of the co-orbital pair, Janus and Epimetheus. We also find evidence that the known chaotic changes in the orbits of Prometheus and Pandora are not confined to times of apse anti-alignment.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Chaos in a neural network circuit

NASA Astrophysics Data System (ADS)

Kepler, Thomas B.; Datt, Sumeet; Meyer, Robert B.; Abott, L. F.

1990-12-01

We have constructed a neural network circuit of four clipped, high-grain, integrating operational amplifiers coupled to each other through an array of digitally programmable resistor ladders (MDACs). In addition to fixed-point and cyclic behavior, the circuit exhibits chaotic behavior with complex strange attractors which are approached through period doubling, intermittent attractor expansion and/or quasiperiodic pathways. Couplings between the nonlinear circuit elements are controlled by a computer which can automatically search through the space of couplings for interesting phenomena. We report some initial statistical results relating the behavior of the network to properties of its coupling matrix. Through these results and further research the circuit should help resolve fundamental issues concerning chaos in neural networks.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson

1997-01-01

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, S.L.; Miller, W.M.; McWhorter, P.J.

1997-10-21

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.

Using Chaotic System in Encryption

NASA Astrophysics Data System (ADS)

Findik, Oğuz; Kahramanli, Şirzat

In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

Design and Hardware Implementation of a New Chaotic Secure Communication Technique

PubMed Central

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness. PMID:27548385

Design and Hardware Implementation of a New Chaotic Secure Communication Technique.

PubMed

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness.

Chaotic Strings in AdS /CFT

NASA Astrophysics Data System (ADS)

de Boer, Jan; Llabrés, Eva; Pedraza, Juan F.; Vegh, David

2018-05-01

Holographic theories with classical gravity duals are maximally chaotic; i.e., they saturate the universal bound on the rate of growth of chaos [J. Maldacena, S. H. Shenker, and D. Stanford, J. High Energy Phys. 08 (2016) 106, 10.1007/JHEP08(2016)106]. It is interesting to ask whether this property is true only for leading large N correlators or if it can show up elsewhere. In this Letter, we consider the simplest setup to tackle this question: a Brownian particle coupled to a thermal ensemble. We find that the four-point out-of-time-order correlator that diagnoses chaos initially grows at an exponential rate that saturates the chaos bound, i.e., with a Lyapunov exponent λL=2 π /β . However, the scrambling time is parametrically smaller than for plasma excitations, t*˜β log √{λ } instead of t*˜β log N2. Our result shows that, at least in certain cases, maximal chaos can be attained in the probe sector without the explicit need of gravitational degrees of freedom.

Anomalous transport in Charney-Hasegawa-Mima flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leoncini, Xavier; Agullo, Olivier; Benkadda, Sadruddin

2005-08-01

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around {mu}=1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law {gamma}={mu}+1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero ofmore » the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.« less

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

NASA Astrophysics Data System (ADS)

Pejić, N.; Vujković, M.; Maksimović, J.; Ivanović, A.; Anić, S.; Čupić, Ž.; Kolar-Anić, Lj.

2011-12-01

The non-periodic, periodic and chaotic regimes in the Bray-Liebhafsky (BL) oscillatory reaction observed in a continuously fed well stirred tank reactor (CSTR) under isothermal conditions at various inflow concentrations of the sulfuric acid were experimentally studied. In each series (at any fixed temperature), termination of oscillatory behavior via saddle loop infinite period bifurcation (SNIPER) as well as some kind of the Andronov-Hopf bifurcation is presented. In addition, it was found that an increase of temperature, in different series of experiments resulted in the shift of bifurcation point towards higher values of sulfuric acid concentration.

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

NASA Astrophysics Data System (ADS)

Tong, Xiaojun; Cui, Minggen; Wang, Zhu

2009-07-01

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

Is thermodynamic irreversibility a consequence of the expansion of the Universe?

NASA Astrophysics Data System (ADS)

Osváth, Szabolcs

2018-02-01

This paper explains thermodynamic irreversibility by applying the expansion of the Universe to thermodynamic systems. The effect of metric expansion is immeasurably small on shorter scales than intergalactic distances. Multi-particle systems, however, are chaotic, and amplify any small disturbance exponentially. Metric expansion gives rise to time-asymmetric behaviour in thermodynamic systems in a short time (few nanoseconds in air, few ten picoseconds in water). In contrast to existing publications, this paper explains without any additional assumptions the rise of thermodynamic irreversibility from the underlying reversible mechanics of particles. Calculations for the special case which assumes FLRW metric, slow motions (v ≪ c) and approximates space locally by Euclidean space show that metric expansion causes entropy increase in isolated systems. The rise of time-asymmetry, however, is not affected by these assumptions. Any influence of the expansion of the Universe on the local metric causes a coupling between local mechanics and evolution of the Universe.

A New Method for Suppressing Periodic Narrowband Interference Based on the Chaotic van der Pol Oscillator

NASA Astrophysics Data System (ADS)

Lu, Jia; Zhang, Xiaoxing; Xiong, Hao

The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

NASA Astrophysics Data System (ADS)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Chaotic Behavior of a Generalized Sprott E Differential System

NASA Astrophysics Data System (ADS)

Oliveira, Regilene; Valls, Claudia

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.

A variable structure fuzzy neural network model of squamous dysplasia and esophageal squamous cell carcinoma based on a global chaotic optimization algorithm.

PubMed

Moghtadaei, Motahareh; Hashemi Golpayegani, Mohammad Reza; Malekzadeh, Reza

2013-02-07

Identification of squamous dysplasia and esophageal squamous cell carcinoma (ESCC) is of great importance in prevention of cancer incidence. Computer aided algorithms can be very useful for identification of people with higher risks of squamous dysplasia, and ESCC. Such method can limit the clinical screenings to people with higher risks. Different regression methods have been used to predict ESCC and dysplasia. In this paper, a Fuzzy Neural Network (FNN) model is selected for ESCC and dysplasia prediction. The inputs to the classifier are the risk factors. Since the relation between risk factors in the tumor system has a complex nonlinear behavior, in comparison to most of ordinary data, the cost function of its model can have more local optimums. Thus the need for global optimization methods is more highlighted. The proposed method in this paper is a Chaotic Optimization Algorithm (COA) proceeding by the common Error Back Propagation (EBP) local method. Since the model has many parameters, we use a strategy to reduce the dependency among parameters caused by the chaotic series generator. This dependency was not considered in the previous COA methods. The algorithm is compared with logistic regression model as the latest successful methods of ESCC and dysplasia prediction. The results represent a more precise prediction with less mean and variance of error. Copyright © 2012 Elsevier Ltd. All rights reserved.

Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

NASA Astrophysics Data System (ADS)

Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N.

2018-06-01

This paper is focused on the resonant responses and chaotic dynamics of a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix. Based on the two-degree-of-freedom non-autonomous nonlinear equations of this system, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation. The resonant case considered here is the primary parametric resonance-1/2 subharmonic resonance and 1:1 internal resonance. Corresponding to several selected parameters, the frequency-response curves are obtained. From the numerical results, we find that the hardening-spring-type behaviors and jump phenomena are exhibited. The jump phenomena also occur in the amplitude curves of the temperature parameter excitation. Moreover, it is found that the temperature parameter excitation, the coupling degree of two order modes and the detuning parameters can effect the nonlinear oscillations of this system. The periodic and chaotic motions of the composite laminated circular cylindrical shell clamped along a generatrix are demonstrated by the bifurcation diagrams, the maximum Lyapunov exponents, the phase portraits, the waveforms, the power spectrums and the Poincaré map. The temperature parameter excitation shows that the Pomeau-Manneville type intermittent chaos occur under the certain initial conditions. It is also found that there exist the twin phenomena between the Pomeau-Manneville type intermittent chaos and the period-doubling bifurcation.

Bit-level plane image encryption based on coupled map lattice with time-varying delay

NASA Astrophysics Data System (ADS)

Lv, Xiupin; Liao, Xiaofeng; Yang, Bo

2018-04-01

Most of the existing image encryption algorithms had two basic properties: confusion and diffusion in a pixel-level plane based on various chaotic systems. Actually, permutation in a pixel-level plane could not change the statistical characteristics of an image, and many of the existing color image encryption schemes utilized the same method to encrypt R, G and B components, which means that the three color components of a color image are processed three times independently. Additionally, dynamical performance of a single chaotic system degrades greatly with finite precisions in computer simulations. In this paper, a novel coupled map lattice with time-varying delay therefore is applied in color images bit-level plane encryption to solve the above issues. Spatiotemporal chaotic system with both much longer period in digitalization and much excellent performances in cryptography is recommended. Time-varying delay embedded in coupled map lattice enhances dynamical behaviors of the system. Bit-level plane image encryption algorithm has greatly reduced the statistical characteristics of an image through the scrambling processing. The R, G and B components cross and mix with one another, which reduces the correlation among the three components. Finally, simulations are carried out and all the experimental results illustrate that the proposed image encryption algorithm is highly secure, and at the same time, also demonstrates superior performance.

Detecting dynamic causal inference in nonlinear two-phase fracture flow

NASA Astrophysics Data System (ADS)

Faybishenko, Boris

2017-08-01

Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time, but can then become spontaneously decoupled or non-correlated. In his 2002 paper (Faybishenko, 2002), the author performed a nonlinear dynamical and chaotic analysis of time-series data obtained from the fracture flow experiment conducted by Persoff and Pruess (1995), and, based on the visual examination of time series data, hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. In the current paper, the author explores an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author infers that his hypothesis is correct, and presents a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes, for example, infiltration and pumping tests in heterogeneous subsurface media, and climatic processes, for example, to find correlations between various meteorological parameters, such as temperature, solar radiation, barometric pressure, etc.

Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems

NASA Astrophysics Data System (ADS)

He, Jianbin; Yu, Simin; Cai, Jianping

2016-12-01

Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.

Mathematical Models to Determine Stable Behavior of Complex Systems

NASA Astrophysics Data System (ADS)

Sumin, V. I.; Dushkin, A. V.; Smolentseva, T. E.

2018-05-01

The paper analyzes a possibility to predict functioning of a complex dynamic system with a significant amount of circulating information and a large number of random factors impacting its functioning. Functioning of the complex dynamic system is described as a chaotic state, self-organized criticality and bifurcation. This problem may be resolved by modeling such systems as dynamic ones, without applying stochastic models and taking into account strange attractors.

Application of Chaos Theory to 1/f Noise

DTIC Science & Technology

1988-02-12

recently, we lacked the mathematical sophistication to analyze chaotic behavior. However, that situation is changing rapidly. We are now beginning to...along with nonlinear coupling between dependent variables. Linked with the notion of chaos is a mathematical construct known as a "strange attractor". 11...flow 12 S as the Reynolds number, Re, is increased above some critical value. We can observe this transition in the mathematics by watching the

Markov Chain Models for Stochastic Behavior in Resonance Overlap Regions

NASA Astrophysics Data System (ADS)

McCarthy, Morgan; Quillen, Alice

2018-01-01

We aim to predict lifetimes of particles in chaotic zoneswhere resonances overlap. A continuous-time Markov chain model isconstructed using mean motion resonance libration timescales toestimate transition times between resonances. The model is applied todiffusion in the co-rotation region of a planet. For particles begunat low eccentricity, the model is effective for early diffusion, butnot at later time when particles experience close encounters to the planet.

Dynamics of a network of phase oscillators with plastic couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nekorkin, V. I.; Kasatkin, D. V.; Moscow Institute of Physics and Technology

The processes of synchronization and phase cluster formation are investigated in a complex network of dynamically coupled phase oscillators. Coupling weights evolve dynamically depending on the phase relations between the oscillators. It is shown that the network exhibits several types of behavior: the globally synchronized state, two-cluster and multi-cluster states, different synchronous states with a fixed phase relationship between the oscillators and chaotic desynchronized state.

An Investigation of Chaotic Kolmogorov Flows

DTIC Science & Technology

1990-08-01

plane for the Poincare sections used later. The choice of the constant D controls apparent positioning of the hyperplane in the phase...discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and...examine in some detail the behavior of the flow and its transition states for a range of the bifurcation parameter Re. We use Poincare sections to

Adaptive sliding mode control for a class of chaotic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Farid, R.; Ibrahim, A.; Zalam, B., E-mail: ramy5475@yahoo.com

2015-03-30

Chaos control here means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, an Adaptive Sliding Mode Controller (ASMC) is presented based on Lyapunov stability theory. The well known Chua's circuit is chosen to be our case study in this paper. The study shows the effectiveness of the proposed adaptive sliding mode controller.

Generation of magnetic fields by chaotic fluid convection - The fast dynamo problem

NASA Technical Reports Server (NTRS)

Finn, John M.

1992-01-01

In the kinematic fast dynamo problem, the underlying nonlinear dynamics of the flow play a critical role in the behavior of a dynamo field. It is presently noted that the two important facets of the problem are the approximately lognormal distribution of vector lengths, and the presence of partial cancellation. It is suggested that these features may be reflected in the magnetic fields observed on the sun.

Cardiac arrhythmias and degradation into chaotic behavior prevention using feedback control

NASA Astrophysics Data System (ADS)

Uzelac, Ilija; Sidorov, Veniamin; Wikswo, John; Gray, Richard

2012-02-01

During normal heart rhythm, cardiac cells behave as a set of oscillators with a distribution of phases but with the same frequency. The heart as a dynamical system in a phase space representation can be modeled as a set of oscillators that have closed overlapping orbits with the same period. These orbits are not stable and in the case of disruption of the cardiac rhythm, such as due to premature beats, the system will have a tendency to leave its periodic unstable orbits. If these orbits become attracted to phase singularities, their disruption may lead to chaotic behavior, which appears as a life-threating ventricular fibrillation. By using closed-loop feedback in the form of an adjustable defibrillation shock, any drift from orbits corresponding to the normal rhythm can be corrected by forcing the system to maintain its orbits. The delay through the feedback network coincides with the period of normal heart beats. To implement this approach we developed a 1 kW arbitrary waveform voltage-to-current converter with a 1 kHz bandwidth driven by a photodiode system that records an optical electrocardiogram and provides a feedback signal in real time. Our goal is to determine whether our novel method to defibrillate the heart will require much lower energies than are currently utilized in single shock defibrillators.

The Induction of Chaos in Electronic Circuits Final Report-October 1, 2001

DOE Office of Scientific and Technical Information (OSTI.GOV)

R.M.Wheat, Jr.

2003-04-01

This project, now known by the name ''Chaos in Electronic Circuits,'' was originally tasked as a two-year project to examine various ''fault'' or ''non-normal'' operational states of common electronic circuits with some focus on determining the feasibility of exploiting these states. Efforts over the two-year duration of this project have been dominated by the study of the chaotic behavior of electronic circuits. These efforts have included setting up laboratory space and hardware for conducting laboratory tests and experiments, acquiring and developing computer simulation and analysis capabilities, conducting literature surveys, developing test circuitry and computer models to exercise and test ourmore » capabilities, and experimenting with and studying the use of RF injection as a means of inducing chaotic behavior in electronics. An extensive array of nonlinear time series analysis tools have been developed and integrated into a package named ''After Acquisition'' (AA), including capabilities such as Delayed Coordinate Embedding Mapping (DCEM), Time Resolved (3-D) Fourier Transform, and several other phase space re-creation methods. Many computer models have been developed for Spice and for the ATP (Alternative Transients Program), modeling the several working circuits that have been developed for use in the laboratory. And finally, methods of induction of chaos in electronic circuits have been explored.« less

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2006-04-07

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6410--06-8948 Computations of Chaotic Flows in Micromixers April 7, 2006 Approved for...PAGES 17. LIMITATION OF ABSTRACT Computations of Chaotic Flows in Micromixers Carolyn R. Kaplan, Junhui Liu, David R. Mott, and Elaine S. Oran NRL/MR...striations form in time 1 _______________ Manuscript approved December 8, 2005. COMPUTATIONS OF CHAOTIC FLOWS IN MICROMIXERS or distance. Sometimes it is

Performance of Multi-chaotic PSO on a shifted benchmark functions set

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan

2015-03-10

In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. The purpose of shifted benchmark functions is to simulate the time-variant real-world problems. The results of chaotic PSO are compared with canonical version of the algorithm. It is concluded that using the multi-chaotic approach can lead to better results in optimization of shifted functions.

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2016-01-01

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter

NASA Astrophysics Data System (ADS)

Kiani-B, Arman; Fallahi, Kia; Pariz, Naser; Leung, Henry

2009-03-01

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper, for the first time, a fractional chaotic communication method using an extended fractional Kalman filter is presented. The chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication achieves a satisfactory, typical secure communication scheme. In the proposed system, security is enhanced based on spreading the signal in frequency and encrypting it in time domain. In this paper, the main advantages of using fractional order systems, increasing nonlinearity and spreading the power spectrum are highlighted. To illustrate the effectiveness of the proposed scheme, a numerical example based on the fractional Lorenz dynamical system is presented and the results are compared to the integer Lorenz system.

Design and simulation of the micromixer with chaotic advection in twisted microchannels.

PubMed

Jen, Chun-Ping; Wu, Chung-Yi; Lin, Yu-Cheng; Wu, Ching-Yi

2003-05-01

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.

A superparticle on the super Riemann surface

NASA Astrophysics Data System (ADS)

Matsumoto, Shuji; Uehara, Shozo; Yasui, Yukinori

1990-02-01

The free motion of a nonrelativistic superparticle on the super Riemann surface (SRS) of genus h≥2 is investigated. Geodesics or classical paths are given explicitly on the super Poincaré upper half-plane SH, a universal covering space of the SRS, and the paths with some suitable initial conditions yield periodic orbits on the SRS. The periodic orbits are unstable and the system is chaotic. Quantum mechanics is solved on the universal covering space SH and the heat kernel is given on the SRS. This leads to a superanalog of the Selberg trace formula. The Selberg super zeta function is introduced whose zero points and poles determine the energy spectrum on the SRS.

Nonlinear surge motions of a ship in bi-chromatic following waves

NASA Astrophysics Data System (ADS)

Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis

2018-03-01

Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with a perturbed pendulum with bias.

The equal combination synchronization of a class of chaotic systems with discontinuous output

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Runzi; Zeng, Yanhui

This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

Modelling of long-wave chaotic radar system for anti-stealth applications

NASA Astrophysics Data System (ADS)

Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi

2018-04-01

Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.

A new chaotic oscillator with free control

NASA Astrophysics Data System (ADS)

Li, Chunbiao; Sprott, Julien Clinton; Akgul, Akif; Iu, Herbert H. C.; Zhao, Yibo

2017-08-01

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrio, Roberto, E-mail: rbarrio@unizar.es; Serrano, Sergio; Angeles Martínez, M.

2014-06-01

We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines—exact bifurcation curves. We demonstrate how the organizing centers—points corresponding to codimension-two homoclinic bifurcations—along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.

Chaotic behaviour of Zeeman machines at introductory course of mechanics

NASA Astrophysics Data System (ADS)

Nagy, Péter; Tasnádi, Péter

2016-05-01

Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine.

Short-term data forecasting based on wavelet transformation and chaos theory

NASA Astrophysics Data System (ADS)

Wang, Yi; Li, Cunbin; Zhang, Liang

2017-09-01

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Embracing chaos and complexity: a quantum change for public health.

PubMed

Resnicow, Kenneth; Page, Scott E

2008-08-01

Public health research and practice have been guided by a cognitive, rational paradigm where inputs produce linear, predictable changes in outputs. However, the conceptual and statistical assumptions underlying this paradigm may be flawed. In particular, this perspective does not adequately account for nonlinear and quantum influences on human behavior. We propose that health behavior change is better understood through the lens of chaos theory and complex adaptive systems. Key relevant principles include that behavior change (1) is often a quantum event; (2) can resemble a chaotic process that is sensitive to initial conditions, highly variable, and difficult to predict; and (3) occurs within a complex adaptive system with multiple components, where results are often greater than the sum of their parts.

A combination chaotic system and application in color image encryption

NASA Astrophysics Data System (ADS)

Parvaz, R.; Zarebnia, M.

2018-05-01

In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.

Timing variation in an analytically solvable chaotic system

NASA Astrophysics Data System (ADS)

Blakely, J. N.; Milosavljevic, M. S.; Corron, N. J.

2017-02-01

We present analytic solutions for a chaotic dynamical system that do not have the regular timing characteristic of recently reported solvable chaotic systems. The dynamical system can be viewed as a first order filter with binary feedback. The feedback state may be switched only at instants defined by an external clock signal. Generalizing from a period one clock, we show analytic solutions for period two and higher period clocks. We show that even when the clock 'ticks' randomly the chaotic system has an analytic solution. These solutions can be visualized in a stroboscopic map whose complexity increases with the complexity of the clock. We provide both analytic results as well as experimental data from an electronic circuit implementation of the system. Our findings bridge the gap between the irregular timing of well known chaotic systems such as Lorenz and Rossler and the well regulated oscillations of recently reported solvable chaotic systems.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Quantification of chaotic strength and mixing in a micro fluidic system

NASA Astrophysics Data System (ADS)

Kim, Ho Jun; Beskok, Ali

2007-11-01

Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in micro fluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. The 'chaotic electroosmotic stirrer' of Qian and Bau (2002 Anal. Chem. 74 3616-25) is utilized as the benchmark case due to its well-defined flow kinematics. Lagrangian particle tracking methods are utilized to study particle dispersion in the conceptual device using spectral element and fourth-order Runge-Kutta discretizations in space and time, respectively. Stirring efficiency is predicted using the stirring index based on the box counting method, and Poincaré sections are utilized to identify the chaotic and regular regions under various actuation conditions. Finite time Lyapunov exponents are calculated to quantify the chaotic strength, while the probability density function of the stretching field is utilized as an alternative method to demonstrate the statistical analysis of chaotic and partially chaotic cases. Mixing index inverse, based on the standard deviation of scalar species distribution, is utilized as a metric to quantify the mixing efficiency. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing time (tm) is characterized as a function of the Pe number, and tm ~ ln(Pe) scaling is demonstrated for fully chaotic cases, while tm ~ Peα scaling with α ≈ 0.33 and α = 0.5 are observed for partially chaotic and regular cases, respectively. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified.

Disorder effects in the quantum Hall effect of graphene p-n junctions

NASA Astrophysics Data System (ADS)

Li, Jian; Shen, Shun-Qing

2008-11-01

The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder and are accompanied by universal conductance fluctuations in the bipolar regime, which is in good agreement with theoretical predictions of the random matrix theory on quantum chaotic cavities. The calculated Fano factors can be used in an experimental identification of the underlying transport character.

Chaos: Understanding and Controlling Laser Instability

NASA Technical Reports Server (NTRS)

Blass, William E.

1997-01-01

In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.

Scaling in geology: landforms and earthquakes.

PubMed Central

Turcotte, D L

1995-01-01

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior. Images Fig. 6 PMID:11607562

Evidence of Deterministic Components in the Apparent Randomness of GRBs: Clues of a Chaotic Dynamic

PubMed Central

Greco, G.; Rosa, R.; Beskin, G.; Karpov, S.; Romano, L.; Guarnieri, A.; Bartolini, C.; Bedogni, R.

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short – as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration – seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole. PMID:22355609

Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

PubMed

Greco, G; Rosa, R; Beskin, G; Karpov, S; Romano, L; Guarnieri, A; Bartolini, C; Bedogni, R

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short - as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration - seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

PubMed

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium

NASA Astrophysics Data System (ADS)

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash

2017-06-01

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data.

PubMed

Marwan, Norbert; Wessel, Niels; Meyerfeldt, Udo; Schirdewan, Alexander; Kurths, Jürgen

2002-08-01

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

Breathers and thermal relaxation as a temporal process: A possible way to detect breathers in experimental situations

NASA Astrophysics Data System (ADS)

Castrejón Pita, A. A.; Castrejón Pita, J. R.; Sarmiento G., A.

2005-06-01

Breather stability and longevity in thermally relaxing nonlinear arrays is investigated under the scrutiny of the analysis and tools employed for time series and state reconstruction of a dynamical system. We briefly review the methods used in the analysis and characterize a breather in terms of the results obtained with such methods. Our present work focuses on spontaneously appearing breathers in thermal Fermi-Pasta-Ulam arrays but we believe that the conclusions are general enough to describe many other related situations; the particular case described in detail is presented as another example of systems where three incommensurable frequencies dominate their chaotic dynamics (reminiscent of the Ruelle-Takens scenario for the appearance of chaotic behavior in nonlinear systems). This characterization may also be of great help for the discovery of breathers in experimental situations where the temporal evolution of a local variable (like the site energy) is the only available/measured data.

Parameter space of experimental chaotic circuits with high-precision control parameters.

PubMed

de Sousa, Francisco F G; Rubinger, Rero M; Sartorelli, José C; Albuquerque, Holokx A; Baptista, Murilo S

2016-08-01

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

Synchronization and an application of a novel fractional order King Cobra chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com; Ratnavelu, K., E-mail: kuru052001@gmail.com

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness ofmore » the proposed theoretical results.« less

Analytically solvable chaotic oscillator based on a first-order filter.

PubMed

Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N

2016-02-01

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Analytically solvable chaotic oscillator based on a first-order filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform formore » any stable infinite-impulse response filter is chaotic.« less

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

NASA Astrophysics Data System (ADS)

Abdolmohammadi, Hamid Reza; Khalaf, Abdul Jalil M.; Panahi, Shirin; Rajagopal, Karthikeyan; Pham, Viet-Thanh; Jafari, Sajad

2018-06-01

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

Chaotic ultra-wideband radio generator based on an optoelectronic oscillator with a built-in microwave photonic filter.

PubMed

Wang, Li Xian; Zhu, Ning Hua; Zheng, Jian Yu; Liu, Jian Guo; Li, Wei

2012-05-20

We induce a microwave photonic bandpass filter into an optoelectronic oscillator to generate a chaotic ultra-wideband signal in both the optical and electrical domain. The theoretical analysis and numerical simulation indicate that this system is capable of generating band-limited high-dimensional chaos. Experimental results coincide well with the theoretical prediction and show that the power spectrum of the generated chaotic signal basically meets the Federal Communications Commission indoor mask. The generated chaotic carrier is further intensity modulated by a 10 MHz square wave, and the waveform of the output ultra-wideband signal is measured for demonstrating the chaotic on-off keying modulation.

The chaotic saddle of a three degrees of freedom scattering system reconstructed from cross-section data

NASA Astrophysics Data System (ADS)

Drótos, G.; Jung, C.

2016-06-01

The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.

A new transiently chaotic flow with ellipsoid equilibria

NASA Astrophysics Data System (ADS)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Cross-Correlations in Quasar Radio Emission

NASA Astrophysics Data System (ADS)

Nefedyev, Yuri; Panischev, Oleg; Demin, Sergey

The main factors forming the complex evolution of the accretive astrophysical systems are nonlinearity, intermittency, nonstationarity and also collective phenomena. To discover the dynamic processes in these objects and to detain understanding their properties we need to use all the applicable analyzing methods. Here we use the Flicker-Noise Spectroscopy (FNS) as a phenomenological approach to analyzing and parameterizing the auto- and cross-correlations in time series of astrophysical objects dynamics. As an example we consider the quasar flux radio spectral density at frequencies 2.7 GHz and 8.1 GHz. Data have been observed by Dr. N. Tanizuka (Laboratory for Complex Systems Analysis, Osaka Prefecture University) in a period of 1979 to 1988 (3 309 days). According to mental habits quasar is a very energetic and distant active galactic nucleus containing a supermassive black hole by size 10-10,000 times the Schwarzschild radius. The quasar is powered by an accretion disc around the black hole. The accretion disc material layers, moving around the black hole, are under the influence of gravitational and frictional forces. It results in raising the high temperature and arising the resonant and collective phenomena reflected in quasar emission dynamics. Radio emission dynamics of the quasar 0215p015 is characterized by three quasi-periodic processes, which are prevalent in considering dynamics. By contrast the 1641p399's emission dynamics have not any distinguish processes. It means the presence of high intermittency in accretive modes. The second difference moment allows comparing the degree of manifesting of resonant and chaotic components in initial time series of the quasar radio emission. The comparative analysis shows the dominating of chaotic part of 1641p399's dynamics whereas the radio emission of 0215p015 has the predominance of resonant component. Analyzing the collective features of the quasar radio emission intensity demonstrates the significant differences in behavior of considering objects. The 0215p015’s evolution has the distinct quasi-periodic structure in cross-correlation dependence. It connected by prevalent the resonant (long range) component of radio emission dynamics. By contrast 1641p399's shows the disrupted of phase synchronization because of dominating the chaotic part of activity. Thus we demonstrate the FNS approach capabilities in time series analysis of separate signals and collective dynamics of astrophysical object activity. It allows to derive a qualitative new results and advance in understanding the structure and evolution of accretive quasi-stellar objects. The reported study was partially supported by RFBR, research project No. 12-02-97000-a.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Spatiotemporal chaos involving wave instability.

PubMed

Berenstein, Igal; Carballido-Landeira, Jorge

2017-01-01

In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables.

Spatiotemporal chaos involving wave instability

NASA Astrophysics Data System (ADS)

Berenstein, Igal; Carballido-Landeira, Jorge

2017-01-01

In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables.