Martingales, nonlinearity, and chaos
William A. Barnett; Apostolos Serletis
2000-01-01
In this article we provide a review of the literature with respect to the efficient markets hypothesis and chaos. In doing so, we contrast the martingale behavior of asset prices to nonlinear chaotic dynamics, discuss some recent techniques used in distinguishing between probabilistic and deterministic behavior in asset prices, and report some evidence. Moreover, we look at the controversies that
Chaos without nonlinear dynamics.
Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N
2006-07-14
A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system. PMID:16907450
A. Ugulava; S. Chkhaidze; L. Chotorlishvili; Z. Rostomashvili
2009-02-17
The hodographs of magnetization of nonlinear nuclear magnetic resonance are investigated in the conditions of resonance on the unshifted frequency. It is shown that, depending on the value of amplitude of the variable field and value of frequency shift, topologically different hodographs separated from each other by separatrix are obtained.
Scaling of chaos in strongly nonlinear lattices
Mulansky, Mario, E-mail: mulansky@pks.mpg.de [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24, D-14476 Potsdam-Golm (Germany) [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24, D-14476 Potsdam-Golm (Germany); Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany); Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden (Germany)
2014-06-15
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.
Chaos in nonlinear field instability
NASA Astrophysics Data System (ADS)
Malik, S. K.; Khosla, H. K.; Singh, M.
1993-04-01
The normal field instability is investigated under the influence of external modulations near a point of bifurcation Hc. A time varying magnetic field is superimposed on the system. Numerical integration of the evolution equation yields a cascade of period-doubling sequences and saddle node bifurcation. The orbits of odd periods are also observed. The existence of a strange attractor and the intermittency route to chaos is exhibited in the numerical simulation.
Digital Communication using Chaos and Nonlinear Lucas Illing
Illing, Lucas
through an optical fiber or radiated from an antenna. Each block in the re- ceiver chain performs research on the chaotic dynamics of nonlinear sys- tem has focused on the problem of chaos control [1 circuits or optical systems as carriers for information transmission. The simplicity of many chaos
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Carlos Pedro Gonçalves
2012-02-29
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
Nonlinear system vibration---The appearance of chaos
Hunter, N.F. Jr.
1990-01-01
This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.
Chaos in Nonlinear Dynamical Systems Helicopter Flight-data Analysis
Taylor, James H.
Chaos in Nonlinear Dynamical Systems Helicopter Flight-data Analysis James H. Taylor1 and S dynamic behaviour of a modern, multi-purpose helicopter is considered in this article. The main objective of this study is to characterize the helicopter's vibration mechanism(s) i.e., to determine if the vibrations
Linear vs nonlinear and infinite vs finite: An interpretation of chaos
Protopopescu, V.
1990-10-01
An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.
Nonlinear dynamics, chaos and complex cardiac arrhythmias
NASA Technical Reports Server (NTRS)
Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.
1987-01-01
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Chaos in a 4D dissipative nonlinear fermionic model
NASA Astrophysics Data System (ADS)
Aydogmus, Fatma
2015-12-01
Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.; Fratalocchi, A.
2013-01-01
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
Wm C. McHarris
2011-01-01
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a
Fundamental threshold of chaos in some nonlinear oscillators
Ryabov, V.B. [Institute of Radio Astronomy, 4 Krasnoznamennaya St., 310002 Kharkov (Ukraine)
1996-06-01
A technique for predicting chaos arising in a broad class of nonlinear oscillatory systems is proposed. It is based on the notion of running Lyapunov exponents and uses the local stability properties of trajectories for determining the {open_quote}{open_quote}safe{close_quote}{close_quote} areas in the phase space where any trajectory is regular and stable in the sense of Lyapunov. The combination of this approach with harmonic balance method permits to obtain the corresponding {open_quote}{open_quote}safe{close_quote}{close_quote} regions in the control parameter space. The borders of these regions may be considered as threshold lines delimiting the areas of possible chaotic instability. An example of the two-well Duffing oscillator demonstrates good agreement between theoretically predicted values of control parameters where chaos arises with those obtained numerically. The technique is especially effective for rather high dissipation levels when other known methods such as Melnikov{close_quote}s criterion or combination of harmonic balance with analysis of variational equations fail to provide correct results. {copyright} {ital 1996 American Institute of Physics.}
Transition to chaos in a simple nonlinear circuit driven by a sinusoidal voltage source
ABDENNASSER AZZOUZ; RAYMOND DUHR; MARTIN HASLER
1983-01-01
A circuit composed of a sinusoidal voltage source, a linear resistor, a linear inductor, and a diode in series is investigated. Subharmonic solutions of various orders have been found by computer simulations and there is evidence for the presence of chaotic solutions. The diode model used involves a nonlinear capacitor. The transition to chaos follows the same pattern as for
Major open problems in chaos theory and nonlinear Y. Charles Li
Li, Charles
]), and ecology (R. May [20]). By now chaos theory has spread to almost every scientific area and beyond. Overall nonlinear dynamics in general) in ecology is not (or poorly) understood. In classical mechanics, dynamics is generally governed by a system of finitely many ordinary differential equations, and numerical simulations
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
ERIC Educational Resources Information Center
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
NASA Technical Reports Server (NTRS)
Hooker, John C.
1991-01-01
Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).
NASA Astrophysics Data System (ADS)
Felk, E. V.; Kuznetsov, A. P.; Savin, A. V.
2014-09-01
The effect of small nonlinear dissipation on the dynamics of a system with the stochastic web which is linear oscillator driven by pulses is studied. The scenario of coexisting attractors evolution with the increase of nonlinear dissipation is revealed. It is shown that the period-doubling transition to chaos is possible only for the third-order resonance and only hard transitions can be seen for all other resonances.
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
1988-01-01
Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been impossible without the aid and moral support provided by Tormod Riste. Gerd Jarrett helped and befriended me and my family in more ways than I should wish to count, and the entire physics staff at IFE, E Andersen, A F Andresen, G Jarrett, K Otnes, T Riste, A Skjeltorp and O. Steinsvoll helped to slake my heavy thirst for Norwegian history and culture, and agreed from the start to speak Norwegian to me daily in order to help me in my effort to learn to speak that language. Gerd Jarrett performed above and beyond the call of duty by tirelessly typing the original lecture notes, which appear as the internal report IFE/I-86/003 + KGF. I also owe thanks to Lynn Smith for typing the revisions that yielded this final version at the University of Houston. I willingly thank J Fröyland, J Palmore and F Ravndal for several helpful discussions and comments, and M Golubitsky, J Palmore, D Schiller and O Steinsvoll for proof-reading several of the chapters (blame for remaining errors is entirely my own, however). I also wish to thank P Alström, E Aurell, T Bohr, P Cvitanovic, E H Hauge, P C Hemmer, J Hertz, J Ketoja, T Kohonen, J Kurkijärvi, K Lindgren, J Myrheim, R Ritala and S Stenholm for interesting discussions during my journeys to other Scandinavian institutions. I am especially grateful to J Fröyland for guestfriendship at the University of Oslo, and to A K M F Hussain for encouraging in 1984 that I should put my lecture notes into print. Finally, my academic free-year was supported financially by the American Scandinavian Foundation, NORDITA and the University of Houston. All my travel costs within Scandinavia were paid by NORDITA
ERIC Educational Resources Information Center
Crutchfield, James P.; And Others
1986-01-01
Discusses how the discovery of chaos has created a new paradigm in scientific modeling and how findings are contributing to changes in thought about many different branches of science. Includes explanations and examples of how chaotic behavior can be understood. (ML)
NSDL National Science Digital Library
High school teacher Glenn Elert wrote the original edition of the Chaos Hypertextbook for his M.S. degree in secondary science education at Teachers College, Columbia University. After graduation, Elert put the hypertext on the Internet for the benefit of people interested in mathematics, chaos, non-linear dynamics, and fractals. While the hypertext does require some mathematical knowledge, it is geared towards a wide audience. The hypertext addresses a variety of interesting topics including one-dimensional iterated maps; fractal construction; applications and definitions of dimension; and a comparison of non-linear and linear dynamics. The site also offers information about print, software, and Internet resources as well as a fun Eye Candy section. Site visitors can also link to other hypertexts by Elert including The Physics Factbook (an encyclopedia of scientific essays written by high school students), and the Physics Hypertextbook, which is currently under construction.
Parameter identification using experimental nonlinear dynamics and chaos
Chancellor, Roy Scott
1993-01-01
LIST OF FIGURES NOMENCLATURE . . CHAPTER xl xvl INTRODUCTION 1. 1 1. 2 1. 3 Review of Recent Crack Detection Literature Approach to Crack Detection Using Nonlinear Vibration Analysis Objectives 4 5 APPLICATION OF NONLINEAR DYNAMICS... Results From Tests on Stinger-Supported Beam. . . 91 5. 6 Analysis of Cracked Beams and Simulations of Dynamic Response . 92 VI CONCLUSION . 100 6. 1 Conclusions 6. 2 Recommendations 100 102 REFERENCES 104 SUPPLEMENTAL SOURCES CONSULTED APPENDIX...
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. PMID:25440951
Pattern selection and instability in nonlinear wave equation: an aspect of soliton and chaos
Imada, M.
1985-01-01
Pattern selection problems are found in a variety of phenomena. Fluid dynamical systems and nonlinear diffusion phenomena give typical examples of pattern formation problems in dissipative systems. In some cases the dissipation reduces the effective dimension of the system, and this fact leads to several strikingly universal behaviors which were initially found in simple model systems with a few degrees of freedom. Nonlinear wave equations themselves, however, describes systems without dissipation in which the situation is more complicated. In spite of this complexity, many completely integrable systems are known in nonlinear wave equations, where neither ergodicity nor chaos is expected. With addition of small perturbation to completely integrable systems, one can see the growth of instability and the role of coherent structures in the pattern selection problem. Two aspects are briefly discussed in the following sections.
Study of nonlinear dynamics and chaos in MEMS/NEMS resonators
NASA Astrophysics Data System (ADS)
Miandoab, Ehsan Maani; Yousefi-Koma, Aghil; Pishkenari, Hossein Nejat; Tajaddodianfar, Farid
2015-05-01
With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and phase portrait of the unperturbed system, the resonator dynamics is categorized to four physical situations and it is shown that the system undergoes homoclinic and heteroclinic orbits which are responsible for the appearance of chaos in the resonator response. Bifurcation diagram of nano resonator is plotted by variation of applied AC actuation voltage and it is shown that the system possess rich dynamic behavior such as periodic doubling, quasi-periodic, bifurcation and chaotic motion which are classified and studied in more details by plotting time response and phase plane of the each category. The main result of this paper indicates that the necessary condition for the creation of chaos in the resonator is intersection of the system steady state response with the homoclinic orbit. This occurs when the system steady state velocity or amplitude reaches to the homoclinic orbit maximum speed or amplitude. The critical oscillating amplitudes corresponding to these situations are derived based on the system parameters which can be used to propose the new analytical criteria for chaos detection in resonators.
Mutation and Chaos in Nonlinear Models of Heredity
Nasir Ganikhodjaev; Mansoor Saburov; Ashraf Mohamed Nawi
2013-04-21
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models. A numerical simulation assists us to get some clear picture about chaotic behaviors of such models.
Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1996-01-01
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
Chaos and related nonlinear noise phenomena in Josephson tunnel junctions
Miracky, R.F.
1984-07-01
The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial self-inductance have been thoroughly investigated. The current-voltage characteristics of these devices exhibit stable regions of negative differential resistance. Very large increases in the low-frequency voltage noise with equivalent noise temperatures of 10/sup 6/ K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes. Moderate increases in the noise, with temperatures of about 10/sup 3/ K, arise from chaotic behavior. Analog and digital simulations indicate that under somewhat rarer circumstances the same junction system can sustain a purely deterministic hopping between two unstable subharmonic modes, accompanied by excess low-frequency noise. Unlike the noise-induced case, this chaotic process occurs over a much narrower range in bias current and is destroyed by the addition of thermal noise. The differential equation describing the junction system can be reduced to a one-dimensional mapping in the vicinity of one of the unstable modes. A general analytical calculation of switching processes for a class of mappings yields the frequency dependence of the noise spectrum in terms of the parameters of the mapping. Finally, the concepts of noise-induced hopping near bifurcation thresholds are applied to the problem of the three-photon Josephson parametric amplifier. Analog simulations indicate that the noise rise observed in experimental devices arises from occasional hopping between a mode at the pump frequency ..omega../sub p/ and a mode at the half harmonic ..omega../sub p//2. The hopping is induced by thermal noise associated with the shunt resistance. 71 references.
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu
2009-01-01
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects.
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu
2009-01-01
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340
Watts, C.A.
1993-09-01
In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
Improving nonlinear modeling capabilities of functional link adaptive filters.
Comminiello, Danilo; Scarpiniti, Michele; Scardapane, Simone; Parisi, Raffaele; Uncini, Aurelio
2015-09-01
The functional link adaptive filter (FLAF) represents an effective solution for online nonlinear modeling problems. In this paper, we take into account a FLAF-based architecture, which separates the adaptation of linear and nonlinear elements, and we focus on the nonlinear branch to improve the modeling performance. In particular, we propose a new model that involves an adaptive combination of filters downstream of the nonlinear expansion. Such combination leads to a cooperative behavior of the whole architecture, thus yielding a performance improvement, particularly in the presence of strong nonlinearities. An advanced architecture is also proposed involving the adaptive combination of multiple filters on the nonlinear branch. The proposed models are assessed in different nonlinear modeling problems, in which their effectiveness and capabilities are shown. PMID:26057613
NSDL National Science Digital Library
This Physics Central feature provides historical background for chaos theory. It also describes three recent investigations in this field--weather patterns, population dynamics, and the dripping faucet. On the right side of the page, visitors will also find a link to further online resources to help educators teach about chaos.
Chaos computing: a unified view
Toshinori Munakata; Jun Takahashi; Munehisa Sekikawa; Kazuyuki Aihara
2010-01-01
Chaos computing is a non-traditional new paradigm that exploits the extreme non-linearity of chaotic systems. This article presents a unified theoretical view of chaos computing. It introduces the fundamental concept and the unique features that are characteristics of chaos computing, and discusses various implementation approaches. Basic aspects of digital chaos computing to realise logical gates are introduced, followed by two
Sorin Vlad; Paul Pascu; Nicolae Morariu
2010-01-20
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain precise symmetry (Feigenbaum numbers) is even more surprising. As an illustration of the ubiquity of chaos, three models among many other existing models that have chaotic features are presented here: the nonlinear feedback profit model, one model for the simulation of the exchange rate and one application of the chaos theory in the capital markets.
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems S. N. Gomes,1
Pavliotis, Grigorios
proposed to control, up to some extent, different aspects of chaotic dynamics (see e.g. [2] for a review of infinite-dimensional dynam- ical systems exhibiting low-dimensional spatiotemporal chaos. We show.27.De The ability to control a desired particular dynamic state in systems exhibiting chaos, i
Wallace M. Bess; Aline S. de Paul; Marcelo A. Savi
2009-01-01
Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. The idea that chaotic behavior may be controlled by small perturbations of physical parameters allows this kind of behav- ior to be desirable in different applications. In this work, chaos control is performed employing a variable structure
NASA Astrophysics Data System (ADS)
Zhang, Yongfang; Hei, Di; Lü, Yanjun; Wang, Quandai; Müller, Norbert
2014-03-01
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson- ?-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincaré map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
Milonni, P.W.
1989-01-01
The theoretical and experimental status of chaos in nonlinear optics and laser physics will be reviewed. Attention will then be focused on the possibility of chaotic behavior in individual atoms and molecules driven by intense radiation fields. 46 refs., 7 figs.
A Self-Check System for Mental Health Care based on Nonlinear and Chaos Analysis
NASA Astrophysics Data System (ADS)
Oyama-Higa, Mayumi; Miao, Tiejun; Cheng, Huaichang; Tang, Yuan Guang
2007-11-01
We applied nonlinear and chaos analysis to fingertip pulse wave data. The largest Lyapunov exponent, a measure of the "divergence" of the trajectory of the attractor in phase space, was found to be a useful index of mental health in humans, particularly for the early detection of dementia and depressive psychosis, and for monitoring mental changes in healthy persons. Most of the methods used for assessing mental health are subjective. A few of existing objective methods, such as those using EEG and ECG, for example, are not simple to use and expansive. Therefore, we developed an easy-to-use economical device, a PC mouse with an integrated sensor for measuring the pulse waves, and its required software, to make the measurements. After about 1 min of measurement, the Lyapunov exponent is calculated and displayed as a graph on the PC. An advantage of this system is that the measurements can be made very easily, and hence mental health can be assessed during operating a PC using the pulse wave mouse. Moreover, the measured data can be saved according to the time and date, so diurnal changes and changes over longer time periods can be monitored as a time series and history. At the time the pulse waves are measured, we ask the subject about his or her physical health and mood, and use their responses, along with the Lyapunov exponents, as factors causing variation in the divergence. The changes in the Lyapunov exponent are displayed on the PC as constellation graphs, which we developed to facilitate simpler self-diagnosis and problem resolution.
Louis Ehwerhemuepha; Godfrey E. Akpojotor
2013-06-05
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The visualized results obtained which highlight the hypersensitivity of the pendulum to initial conditions can be used to effectively introduce the physics of chaotic system. The simulation and visualization programme is written in Python codes.
NSDL National Science Digital Library
US News and World Report has ranked the Maryland Chaos Group number one in the country (tied with University of Texas, Austin) for Non-linear Dynamics, or Chaos. Chaos is an interdisciplinary science founded on the idea that "nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner." The site includes brief descriptions of the group's research interests as well as a Chaos Pictures Gallery. The publications section will be of most value to researchers as it contains general references, abstracts, and papers. The online papers (which come in a variety of formats) consist of preprints and published articles on bifurcations, fractal basin boundaries, quantum chaos, general chaos, and more. Papers and abstracts are searchable.
Sprott, Julien Clinton
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 9, No. 1, January, 2005. © 2005 Society for Chaos Theory in Psychology & Life Sciences. Dynamical Models of Happiness J. C. Sprott,1 University INTRODUCTION For many people, the pursuit of happiness is a dominant goal of life, and countless books have
Taylor, Richard
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, No. 1, pp. 145-154. © 2009 Society for Chaos Theory in Psychology & Life Sciences The Museum of Unnatural Form: A Visual and Tactile Experience technology is revolutionizing the world of design, allowing intricate patterns to be created
An investigation of the routes to chaos for complex nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Benner, Jeffrey William
This dissertation presents a study of how the routes to chaos change as system complexity is increased. Increasing complexity is achieved by increasing the number of degrees of freedom, increasing system coupling strength, distributing system excitation, and varying the excitation phasing for many dynamical models described by a set of ordinary differential equations. An additional goal is to identify any potential universalities associated with the breakdown of the quasi-periodic torus that leads to chaos. The investigation is conducted by coupling a series of Duffing oscillators together and observing the change in the system's routes to chaos along with the change in the quantitative aspects of the system's chaotic regions. The same analysis is conducted on a more specific model describing captive flight missile vibration. The numerical algorithms utilized in the time, frequency, and phase space domains are the Lyapunov spectrum, the power spectrum, and the Poincare section, respectively. Although the classic Duffing system is known to widely exhibit period doubling, as Duffing oscillators are coupled together the period doubling route disappears. This is the case for the 3, 4, 5 and 6 oscillator models. In these higher dimensional systems, initial period doubling cascades are interrupted by crisis. The strict universal features of the period doubling route to chaos discovered in one dimensional maps are not adhered to in these higher dimensional systems described by continuous time differential equations. As system complexity is increased, period doubling disappears while crisis and quasi-periodicity emerge. A new phenomenon is discovered relating to the breakdown of the quasi-periodic torus. First, it has been shown that quasiperiodicity, which is not present in the Duffing or the 2 oscillator model, emerges as the dominant behavior in the higher dimensional oscillator models. Stable 3 frequency motion on a 2 torus is commonplace. It has been shown that for the symmetrical systems all torii that lead to chaos must pass through a period 3 times the period of the forcing period. It is a necessary and sufficient condition that the torus passes through an n = 3 periodic window before chaos emerges. For the nonsymmetric 3 and 5 oscillator systems, it has been shown that the torus is destroyed by an n = 2 periodic window before chaos emerges. For the linearly coupled two oscillator system, the methods of introducing complexity by distributing the input force preclude chaotic activity. As the strength of the coupling stiffness is increased to cubic order, the crisis route to chaos is dominant. The period doubling route that was present in the linearly coupled case disappears. The low dimensional rigid body missile model displays interrupted period doubling bifurcations while the higher dimensional rigid body missile model exclusively experiences the crisis bifurcation event. The introduction of system flexibility using modal superposition does not move the chaotic regions within the control parameter domain. As additional modes are introduced, the intensity of the chaos increases; thus the divergence rate of the trajectories is increased. The only route to chaos present in the higher dimensional flexible systems is crisis. Therefore, as system complexity is increased in the missile models, the crisis route to chaos dominates.
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
George Sugihara; Robert M. May
1990-01-01
An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.
Peil, Michael; Jacquot, Maxime; Chembo, Yanne Kouomou; Larger, Laurent; Erneux, Thomas
2009-02-01
The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time tau approximately 10 ps and by a low cutoff frequency with a response time theta approximately 1 micros. Moreover, the optoelectronic feedback also consists of a significant delay tauD of the order of 100 ns. Depending on two key physical parameters, the loop gain beta and the nonlinearity operating point Phi, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants tau, theta, and tauD. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of Phi. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations). PMID:19391821
NASA Astrophysics Data System (ADS)
Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue
2013-03-01
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.
International Journal of Bifurcation and Chaos (IJBC)
NSDL National Science Digital Library
The International Journal of Bifurcation and Chaos is "widely regarded as the leading journal in the exciting field of chaos and nonlinear science." Feature articles from previous issues are available online as free samples, along with papers and letters, as long as you provide your name and email address. They also offer to send free emails with updates on the current issues's table of contents. Access to the full journal is available only by paid subscription. Links to information on related books and journals are also provided.
Roman Lavrov; Michael Peil; Maxime Jacquot; Laurent Larger; Vladimir Udaltsov; John Dudley
2009-01-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it
Matcheri S. Keshavan; J. David Cashmere; Jean Miewald; Vikram Kumar Yeragani
2004-01-01
Schizophrenia is characterized by disturbed sleep architecture. It has been thought that sleep abnormalities may underlie information processing deficits associated with this disorder. Nonlinear analyses of sleep data can provide valuable information on sleep characteristics that may be relevant to the functions of sleep. This study examined the predictability and nonlinear complexity of sleep EEG time series in two EEG
Modelling Laser-Diode Non-linearity in a Radio-over-Fibre Link
Haddadi, Hamed
Modelling Laser-Diode Non-linearity in a Radio-over-Fibre Link G. Baghersalimi, V. Postoyalko, T- diode non-linearity. Based on theory, an analytical model of the laser-diode input/output function]. In the optical part of a RoF system the main sources of non-linearity include the laser-diode light source
Identification of nonlinear dynamic systems using functional link artificial neural networks
Jagdish Chandra Patra; Ranendal N. Pal; B. N. Chatterji; Ganapati Panda
1999-01-01
We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of
D. M. Basko
2013-12-04
We study the discrete nonlinear Schr\\"oinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved, but on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density $\\rho$ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, $D(\\rho)=D_0\\rho^2$. An explicit expression for $D_0$ is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
NASA Astrophysics Data System (ADS)
Yau, Her-Terng
2008-03-01
This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller.
Study on the chaos anti-control technology in nonlinear vibration isolation system
Shu-Yong Liu; Xiang Yu; Shi-Jian Zhu
2008-01-01
The nonlinear vibration isolation system (NVIS) works in a chaotic state when its parameters are in chaotic range. Under single-frequency harmonic excitation, the system exhibits chaotic behavior with broad band frequency. This idea can be used to control the line spectra water-born noise of the underwater vehicle, and to improve its capability of concealment. In order to ensure that the
Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation
Philippe Faure; Henri Korn
2001-01-01
In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.
Chaos theory in technology forecasting
C. Wang; Xuanrui Liu; Daoling Xu
1999-01-01
This paper establishes that there is a strong relationship between chaos theory and technology evolution. The challenge in R&D investment in the long term is particularly acute, since the nonlinear system of technology has changed its qualitative characteristics into new phases. At the same time, what chaos theory reveals, especially bifurcation patterns, is that future performance of a system is
Chaos theory in technology forecasting
Clement Wang; Xuanrui Liu; Daoling Xu
1999-01-01
The authors describe how chaos theory can be used in technological forecasting. The paper proposes that technology evolutions be regarded as a nonlinear process exhibiting bifurcation, transient chaos and order state. It also examines the utility of this approach by introducing artificial neural networks and drawing implications for managerial decision making needs
Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control
NASA Astrophysics Data System (ADS)
Yau, Her-Terng
2008-02-01
This paper presents a robust fuzzy sliding mode control (FSMC) scheme for the synchronization of two chaotic nonlinear gyros subject to uncertainties and external disturbances. In the FSMC scheme, the reaching law required to drive the error state trajectory of the master-slave system to the sliding surface is inferred by a set of fuzzy logic rules based upon the output of a sliding mode controller (SMC). The feasibility and effectiveness of the FSMC scheme are demonstrated via a numerical simulation. The numerical results demonstrate the ability of the FSMC scheme to synchronize the chaotic gyro systems using a single control input and reveal that the control signal is chatter free. As a result, compared with conventional switching controllers, the proposed scheme has a lower implementation cost and complexity.
A Structure behind Primitive Chaos
NASA Astrophysics Data System (ADS)
Ogasawara, Yoshihito
2015-06-01
Recently, a new concept, primitive chaos, has been proposed as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [
Deterministic polarization chaos from a laser diode
Martin Virte; Krassimir Panajotov; Hugo Thienpont; Marc Sciamanna
2014-07-22
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
Practical chaos time series analysis with financial applications
Ikuo Matsuba; Hiroki Suyari; Sekjun Weon; D. Sato
2000-01-01
We describe the practical implementation of the nonlinear (chaos) time series analysis based on the paradigm of deterministic chaos. Some important techniques of statistical test for nonlinearity, phase space reconstruction, and nonlinear prediction are discussed with some applications to finance. The use of the nonlinear time series analysis is illustrated with particular emphasis on issues of choices of time delay
Chaos in driven Alfven systems
NASA Technical Reports Server (NTRS)
Hada, T.; Kennel, C. F.; Buti, B.; Mjolhus, E.
1990-01-01
The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.
Deterministic polarization chaos from a laser diode
NASA Astrophysics Data System (ADS)
Virte, Martin; Panajotov, Krassimir; Thienpont, Hugo; Sciamanna, Marc
2013-01-01
Fifty years after the invention of the laser diode, and forty years after the butterfly effect signified the unpredictability of deterministic chaos, it is commonly believed that a laser diode behaves like a damped nonlinear oscillator and cannot be driven into chaotic operation without additional forcing or parameter modulation. Here, we counter that belief and report the first example of a free-running laser diode generating chaos. The underlying physics comprises a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time series and show, theoretically, the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles noise-driven mode hopping, but shows opposite statistical properties. Our findings open up new research areas for the creation of controllable and integrated sources of optical chaos.
Nonlinearity Compensation in a Fiber-Optic Link by Optical Phase Conjugation
Paolo Minzioni
2009-01-01
This article is intended as a guide to the techniques for nonlinearity compensation in a fiber-optic communication link based on optical phase conjugation. In the first part, the basics of the phase conjugation process are illustrated from both a mathematical and physical point of view. Then, the more commonly used devices for optical phase conjugation are described, with particular attention
NSDL National Science Digital Library
2010-01-01
This lesson is designed to introduce students to the concept of chaos and how it relates to probability. The lesson briefly delves into the ideas of mean and variance as well. This lesson provides links to discussions and activities related to chaos as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. Note, reading level is not indicated because the lesson does not include student reading material.
Dynamic non-linear response of cross-linked actin networks: an energy dissipation approach
NASA Astrophysics Data System (ADS)
Majumdar, Sayantan; Gardel, Margaret L.
2014-03-01
Cross-linked bio-polymer networks that primarily maintain the shape and rigidity in eukaryotic cells show striking non-linear mechanical properties. Here, we study the steady-state energy dissipation (Ediss) over a complete sinusoidal shear strain cycle for a macroscopic assembly of reconstituted network of actin filaments cross-linked with Filamin A, over wide range of strain amplitude and frequency values. For small values of the applied strain amplitudes (linear regime) Ediss increases monotonously with the increasing frequency over the entire frequency range studied but in the non-linear regime (larger applied strain amplitudes), a clear saturation in Ediss is observed at higher frequencies. Also, the normalized dissipated energy distribution binned over the fixed strain intervals along the shear cycle show frequency dependence in the nonlinear regime but remains frequency independent in the linear regime. Remarkably, the monotonously increasing behavior of Ediss with frequency is also observed in the non-linear regime when a more rigid cross-linker A-Actinin is used, suggesting the importance of flexibility of cross-linkers in controlling the non-linear mechanical response in this class of materials. MRSEC Kadanoff-Rice Post Doctoral Fellowship.
Sprott, Julien Clinton
for Chaos Theory in Psychology & Life Sciences Chaos in Easter Island Ecology J. C. Sprott1 , Department dynamical model for the ecology of Easter Island admits periodic and chaotic attractors, not previously in such systems. Key Words: chaos, Easter Island, ecology, population dynamics INTRODUCTION The Easter Island
Sprott, Julien Clinton
for Chaos Theory in Psychology & Life Sciences.2 3 Spatiotemporal Chaos in Easter Island Ecology4 5 J. C proposed spatiotemporal8 model for the ecology of Easter Island admits periodic and chaotic attractors,9 that is ubiquitous in such12 systems.13 Key Words: chaos, Easter Island, ecology, population dynamics, Turing14
NASA Astrophysics Data System (ADS)
Yuan, Jie; Xue, Tian-Ming; Zhu, Guang-Hao
2012-11-01
We study the post nonlinearity compensation of differential-phase-shift-keying links employing pure soliton transmissions over a large number of spans. In addition to the distributed amplified spontaneous noises added by the inline amplifiers, lumped intensity noises initially resulting from transmitter imperfections are also considered. Based on the soliton perturbation theory, we derive simple and accurate formulae for the optimum operating phase, the variance of the residue phase noise, and the phase Q-factor improvement of the post nonlinearity compensation. We validate these derived formulae by comparing their results with numerical simulations built upon the split-step Fourier method.
Torrengo, E; Cigliutti, R; Bosco, G; Carena, A; Curri, V; Poggiolini, P; Nespola, A; Zeolla, D; Forghieri, F
2011-12-12
Link design for optical communication systems requires accurate modeling of nonlinear propagation in fibers. This topic has been widely analyzed in last decades with partial successes in special conditions, but without a comprehensive solution. Since the introduction of coherent detection with electronic signal processing the scenario completely changed because this category of systems shows better performances in links without in-line dispersion management. This change to uncompensated transmission allowed to modify the approach in the study of nonlinear fiber propagation and in recent years a series of promising analytical models have been proposed. In this paper, we present an experimental validation over different fiber types of an analytical model for nonlinear propagation over uncompensated optical transmission links. Considering an ultra-dense WDM system, we transmitted ten 120-Gb/s PM-QPSK signals over a multi-span system probing different fiber types: SSMF, PSCF and NZDSF. A good matching was found in all cases showing the potential of the analytical model for accurate performance estimation that could lead to powerful tools for link design. PMID:22274104
Nonlinear optimization-based device-free localization with outlier link rejection.
Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan
2015-01-01
Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406
Roy Choudhury; Kevin Brown
2000-01-01
A nonlinear stability analysis using a multiple scales perturbation procedure is performed for the instability of two layers of strongly anisotropic, magnetized, inviscid, arbitrarily compressible fluids in relative motion. Such configurations are of relevance in a variety of space and astrophysical configurations. For modes near the critical point of the linear neutral curve, the nonlinear evolution is shown to be
Photodetector nonlinearity limitations on a high-dynamic range 3 GHz fiber optic link
Keith J. Williams; Lee T. Nichols; Ronald D. Esman
1998-01-01
The performance of a dc to 3 GHz externally modulated link utilizing balanced high-power photodetection is presented. Nonlinearity measurements of high power photodiodes show 1 dB compression currents in excess of 55 mA and an output third-order intercept point of +32 to +34 dBm. These high current photodetectors permit the use of high power lasers as external modulator sources for
OFDM link performance with companding for PAPR reduction in the presence of non-linear amplification
Thomas G. Pratt; Nathan Jones; Leslie Smee; Michael Torrey
2006-01-01
Use of companding for peak-to-average-power ratio (PAPR) control is explored for a link involving a nonlinear transmit power amplifier with orthogonal frequency division multiplexing (OFDM). Specifically, the objective of the study was to determine if companding using u-law compression\\/expansion at the transmitter\\/receiver, respectively, provides end-to-end performance gains relative to a system without companding. We consider the use of companding to
Brian R. Hunt; Edward Ott
2015-04-28
In this paper we propose, discuss and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy", and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy, to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
Lennon O. Naraigh
2015-01-06
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal nonlinear system that not only highlights the phenomena of linear transient growth, subcritical transition and global modes, but is also of potential interest in its own right in the field of nonlinear optics. The second is the fairly familiar inhomogeneous nonlinear complex Ginzburg--Landau (CGL) equation. The two-level model is exactly solvable for the nonlinear global mode and its stability, while for the spatially-extended CGL equation, perturbative solutions for the global mode and its stability are presented, valid for inhomogeneities with arbitrary scales of spatial variation and global modes of small amplitude, corresponding to a scenario near criticality. For other scenarios, a numerical iterative nonlinear eigenvalue technique is preferred. Two global modes of different amplitudes are revealed in the numerical approach. For both the two-level system and the nonlinear CGL equation, the analytical calculations are supplemented with direct numerical simulation, thus showing the fate of unstable global modes. For the two-level model this results in unbounded growth of the full nonlinear equations. For the spatially-extended CGL model in the subcritical regime, the global mode of larger amplitude exhibits a `one-sided' instability leading to a chaotic dynamics, while the global mode of smaller amplitude is always unstable (theory confirms this). However, advection can stabilize the mode of larger amplitude.
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim
2003-01-01
Four theoretical streams--contexualism/ecology, systems theory, realism/constructivism, and chaos theory--contributed to a theory of individuals as complex, unique, nonlinear, adaptive chaotic and open systems. Individuals use purposive action to construct careers but can make maladaptive and inappropriate choices. (Contains 42 references.) (SK)
Reflective confocal laser scanning microscopy and nonlinear microscopy of cross-linked rabbit cornea
NASA Astrophysics Data System (ADS)
Krueger, Alexander; Hovakimyan, Marina; Ramirez, Diego F.; Stachs, Oliver; Guthoff, Rudolf F.; Heisterkamp, Alexander
2009-07-01
Cross-linking of the cornea with application of Ribovlavin and UV-A light is an evolving clinical treatment of the eye disease keratoconus. Despite the positive clinical track record of corneal cross-linking, the complex wound healing process after the treatment is still under investigation. In this study an animal model was used to clarify the state of wound healing 5 weeks after treatment. Cross-linked rabbit corneae were imaged with reflective confocal laser scanning and nonlinear microscopy, namely second harmonic imaging microscopy (SHIM) and two-photon excited autofluorescence. First results show that the NAD(P) H-autofluorescence of the corneal keratocytes and their scattering signal still show a signature of the treatment five weeks after the cross-linking procedure. The SHIM signals show the structural morphology of the fibrous collagen sheets in the stroma of the cornea. SHIM detected in the forward direction differs substantially from backward SHIM, but no signature of treatment was found in both detection channels of the SHIM signal.
Chaos in World Politics: A Reflection
NASA Astrophysics Data System (ADS)
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
NSDL National Science Digital Library
2003-01-01
Paul Bourke of the Astrophysics and Supercomputing department at Swinburne University of Technology is the author of this massive resource on fractals and chaos. He gives examples of many different kinds and classes of fractals, including the Mandelbrot set and various attractors; and brief explanations accompany each one. A substantial introduction to fractals covers the underlying principles and connection to chaos theory. Many stunning, high resolution fractal image galleries show elaborate patterns and colors. Examples of C and PovRay code used to create the remarkable images are provided. Bourke's homepage has many other sections of tutorials, papers, and notes on a diverse range of subjects.
Physicalism, Chaos and Reductionism
NASA Astrophysics Data System (ADS)
Scott, Alwyn
In addition to ignoring the severe practical problems posed by decoherence phenomena, quantum mind hypotheses are motivated by a misunderstanding of the nature of classical (i. e. nonquantum) dynamics. As presently understood, nonlinear dynamical systems — of which the brain is clearly one — exhibit the twin phenomena of chaos and emergence. The first of these impedes reductionist formulations as does quantum theory, and the second leads to hierarchical structures in biological organisms and cognitive systems, which are difficult to analyze reductively. Thus a quantum mind theory must rest on empirical evidence rather than philosophical speculation.
Synthesizing folded band chaos.
Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N
2007-04-01
A randomly driven linear filter that synthesizes Lorenz-like, reverse-time chaos is shown also to produce Rössler-like folded band wave forms when driven using a different encoding of the random source. The relationship between the topological entropy of the random source, dissipation in the linear filter, and the positive Lyapunov exponent for the reverse-time wave form is exposed. The two drive encodings are viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing both the Lorenz butterfly and Rössler folded band paradigms of nonlinear dynamics. PMID:17500950
Chaos in an imperfectly premixed model combustor
NASA Astrophysics Data System (ADS)
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P.; Paschereit, Christian O.
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Chaos in an imperfectly premixed model combustor.
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration. PMID:25725637
Chaos in Environmental Education.
ERIC Educational Resources Information Center
Hardy, Joy
1999-01-01
Explores chaos theory, the evolutionary capacity of chaotic systems, and the philosophical implications of chaos theory in general and for education. Compares the relationships between curriculum vision based on chaos theory and critical education for the environment. (Author/CCM)
Nonlinear behavior of ionically and covalently cross-linked alginate hydrogels
NASA Astrophysics Data System (ADS)
Hashemnejad, Seyedmeysam; Zabet, Mahla; Kundu, Santanu
2015-03-01
Gels deform differently under applied load and the deformation behavior is related to their network structures and environmental conditions, specifically, strength and density of crosslinking, polymer concentration, applied load, and temperature. Here, we investigate the mechanical behavior of both ionically and covalent cross-linked alginate hydrogel using large amplitude oscillatory shear (LAOS) and cavitation experiments. Ionically-bonded alginate gels were obtained by using divalent calcium. Alginate volume fraction and alginate to calcium ratio were varied to obtain gels with different mechanical properties. Chemical gels were synthesized using adipic acid dihdrazide (AAD) as a cross-linker. The non-linear rheological parameters are estimated from the stress responses to elucidate the strain softening behavior of these gels. Fracture initiation and propagation mechanism during shear rheology and cavitation experiments will be presented. Our results provide a better understanding on the deformation mechanism of alginate gel under large-deformation.
Apthorp, Deborah; Nagle, Fintan; Palmisano, Stephen
2014-01-01
Visually-induced illusions of self-motion (vection) can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP) over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP) in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods) was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway) significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA) of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open); this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures. PMID:25462216
Physics and applications of laser diode chaos
NASA Astrophysics Data System (ADS)
Sciamanna, M.; Shore, K. A.
2015-03-01
This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
Proceedings of the 2nd Experimental Chaos Conference
NASA Astrophysics Data System (ADS)
Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep
1995-02-01
The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud
Xia, Kelin
2013-01-01
Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderli...
Chaos theory as a model for interpreting information systems in organizations
Neil Mcbride
2005-01-01
Chaos theory concerns the qualitative study of unstable aperiodic behaviour in deterministic non-linear dynamical systems. Concepts from chaos theory have recently been applied as a model for interpreting organizational change and understanding organizational behaviour. This paper applies these concepts to the study of information systems in organizations. Key concepts from chaos theory are identified and used to develop an interpretive
Curri, Vittorio; Carena, Andrea; Poggiolini, Pierluigi; Bosco, Gabriella; Forghieri, Fabrizio
2013-02-11
We show the extension of the Gaussian Noise model, which describes non-linear propagation in uncompensated links of multilevel modulation formats, to systems using Raman amplification. We successfully validate the analytical results by comparison with numerical simulations of Nyquist-WDM PM-16QAM channels transmission over multi-span uncompensated links made of a single fiber type and using hybrid EDFA/Raman amplification with counter-propagating pumps. We analyze two typical high- and low-dispersion fiber types. We show that Raman amplification always induces a limited non-linear interference enhancement compared to the dominant ASE noise reduction. PMID:23481790
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
2006-11-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
1995-04-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03046 Iani Chaos
This image shows a small portion of Iani Chaos. The brighter floor material is being covered by sand, probably eroded from the mesas of the Chaos.
Image information: VIS instrument. Latitude 1.7S, Longitude 341.6E. 17 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.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos
This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed.
Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 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.
Applying Chaos Theory to Lesson Planning and Delivery
ERIC Educational Resources Information Center
Cvetek, Slavko
2008-01-01
In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…
De Luca, Alessandro
for a one-link flexible arm described by a non-linear model. Two meaningful system outputs are chosen (Bayo 1987). Other works utilize non-linear models and different approximate control techniques, the non-linear dynamic terms are here explicitly taken into account in the model. ln particular, two
Dynamical symmetry breaking and chaos in Duffing's equation
Olson, C.L.; Olsson, M.G. (Department of Physics, University of Wisconsin, Madison, Wisconsin (USA))
1991-10-01
In certain frequency ranges a nonlinear damped and driven oscillator will respond asymmetri-cally even though the potential energy is a single symmetric well. This dynamical symmetry breaking heralds the onset of a period doubling transition to chaos.
Improvement and empirical research on chaos control by theory of "chaos?+?chaos?=?order".
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. PMID:23278080
On the synchronization of a class of electronic circuits that exhibit chaos
Sprott, Julien Clinton
On the synchronization of a class of electronic circuits that exhibit chaos Er-Wei Bai a,*, Karl E Accepted 19 June 2001 Abstract The synchronization of two nonlinear electronic circuits that exhibit chaos that electronic circuits that consist of possibly one or two nonlinear elements can be used to verify several
Masahiro Tsuchiya; Takeshi Hoshida
1999-01-01
We report on our study on the nonlinear photodetection (NL-PD) scheme, which we have proposed and demonstrated as an extremely simple configuration for the optoelectronic millimeter-wave (MM-wave) mixing. The topics described in this paper are as follows: (1) advantageous optical MM-wave link architectures employing the NL-PD techniques; (2) operation principle of NL-PD; (3) detailed characterization of optoelectronic MM-wave mixer properties
Experimental Techniques for Investigating Chaos in Electronics
Tse, Chi K. "Michael"
. The quest for an explanation for the observed unusual behavior mo- tivates in-depth analysis18 Experimental Techniques for Investigating Chaos in Electronics Chi K. Tse 1 Department of experimental measurements and computer simulations in the study of nonlinear systems. A tutorial overview
Magnetic field induced dynamical chaos
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra, E-mail: bidhanchandra.bag@visva-bharati.ac.in [Department of Chemistry, Visva-Bharati, Santiniketan 731 235 (India)
2013-12-15
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x–y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.
Chaos, brain and divided consciousness.
Bob, Petr
2007-01-01
Modern trends in psychology and cognitive neuroscience suggest that applications of nonlinear dynamics, chaos and self-organization seem to be particularly important for research of some fundamental problems regarding mind-brain relationship. Relevant problems among others are formations of memories during alterations of mental states and nature of a barrier that divides mental states, and leads to the process called dissociation. This process is related to a formation of groups of neurons which often synchronize their firing patterns in a unique spatial maner. Central theme of this study is the relationship between level of moving and oscilating mental processes and their neurophysiological substrate. This opens a question about principles of organization of conscious experiences and how these experiences arise in the brain. Chaotic self-organization provides a unique theoretical and experimental tool for deeper understanding of dissociative phenomena and enables to study how dissociative phenomena can be linked to epileptiform discharges which are related to various forms of psychological and somatic manifestations. Organizing principles that constitute human consciousness and other mental phenomena from this point of view may be described by analysis and reconstruction of underlying dynamics of psychological or psychophysiological measures. These nonlinear methods in this study were used for analysis of characteristic changes in EEG and bilateral electrodermal activity (EDA) during reliving of dissociated traumatic and stressful memories and during psychopathological states. Analysis confirms a possible role of chaotic transitions in the processing of dissociated memory. Supportive finding for a possible chaotic process related to dissociation found in this study represent also significant relationship of dissociation, epileptiform discharges measured by typical psychopathological manifestations and characteristic laterality changes in bilateral EDA in patients with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519
ERIC Educational Resources Information Center
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Tracking Quasiclassical Chaos in Ultracold Boson Gases
Lepers, Maxence; Zehnle, Veronique; Garreau, Jean Claude [Laboratoire de Physique des Lasers, Atomes et Molecules, Universite des Sciences et Technologies de Lille, CNRS, F-59655 Villeneuve d'Ascq Cedex (France)
2008-10-03
We study the dynamics of an ultracold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from Kolmogorov-Arnold-Moser arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.
ERIC Educational Resources Information Center
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with some degree…
ERIC Educational Resources Information Center
Bedford, Crayton W.
1998-01-01
Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)
NASA Astrophysics Data System (ADS)
Yi, Xiaogang; Zhang, Fangzheng; Wu, Jian; Li, Yan; Li, Wei; Hong, Xiaobin; Guo, Hongxiang; Zuo, Yong; Lin, Jintong
2012-07-01
Nonlinear phase noise (NLPN) induced by the interaction between the amplified spontaneous emission noise (ASE) and the information signal in polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems at 42.8(112) Gbit/s over dispersion-managed (DM) link is investigated by numerical simulations. Both symbol-aligned non-return-to-zero (NRZ) PM-QPSK and symbol-interleaved return-to-zero (RZ) PM-QPSK formats are considered and compared. We find that for aligned NRZ-PM-QPSK systems, the impact of NLPN on system performance seems rather weak due to the strong interchannel cross-polarization modulation (XPolM). However, when the interleaved RZ-PM-QPSK format is used, in which the XPolM is suppressed significantly, the system performance is seriously degraded by NLPN, especially at low bit rates. Results of 1000-km transmission employing standard single-mode fiber (SSMF) over DM link show that for 42.8 Gbit/s coherent RZ-PM-QPSK systems, the nonlinear threshold (NLT) will decrease from 6 to 2 dBm due to nonlinear phase noise when symbol-interleaved format is used.
Nonlinear dynamics experiments in plasmas
Nurujjaman, Md
2009-01-01
The study of nonlinear dynamics or chaos theory has emerged in the last three decades or so as an important interdisciplinary area of research encompassing a wide range of fields like: fluids, plasmas, biomedical sciences, finance, turbulence, astronomy, material sciences, etc. In plasma chaos was first experimentally observed by Boswell. Different other nonlinear dynamics related phenomena like, the intermittency route to a chaos, Homoclinic chaos, Period adding route to chaos and period subtracting, mode locking, period pulling, etc., had been observed by several researchers. In this thesis, we have presented (a) anode glow related observation of chaos to order transition and homoclinic bifurcation; (b) coherence resonance and stochastic resonance; and self organized criticality behavior in glow discharge plasma.
Chaos in plasma simulation and experiment
Watts, C. [Texas Univ., Austin, TX (United States). Fusion Research Center; Newman, D.E. [Oak Ridge National Lab., TN (United States); Sprott, J.C. [Wisconsin Univ., Madison, WI (United States). Plasma Physics Research
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
NASA Astrophysics Data System (ADS)
Arwas, Geva; Vardi, Amichay; Cohen, Doron
2015-03-01
The hallmark of superfluidity is the appearance of a quantized metastable circulating current. The Landau criterion links the metastability of a vortex state to its spectral stability, i.e. to the inaccessibility of elementary excitations connecting it to other states with the same energy. In low dimensional systems, superfluid vortex states can exist due to their dynamical stability even if they are spectrally unstable. This traditional paradigm associate superfluid vortex states with stationary stable fixed points in phase space. Hence, Bogoliubov de Gennes (BdG) stability analysis is normally used to determine the feasibility of such states. In this work we challenge this traditional criterion and highlight the role of chaos in the analysis, thus explaining the existence of current carrying eigenstates which are neither spectrally-stable nor dynamically- stable.
Inducing Chaos by Resonant Perturbations: Theory and Experiment
NASA Astrophysics Data System (ADS)
Lai, Ying-Cheng; Kandangath, Anil; Krishnamoorthy, Satish; Gaudet, John A.; de Moura, Alessandro P.
2005-06-01
We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.
Hung, Shih-Hao
to its robustness and effectiveness [3, 4]. Hardware architectures of particle filters with the FPGAEFFICIENT PARALLELIZED PARTICLE FILTER DESIGN ON CUDA Min-An Chao, Chun-Yuan Chu, Chih-Hao Chao City 10617, Taiwan ABSTRACT Particle filtering is widely used in numerous nonlinear appli- cations
Properties of nonlinear noise in long, dispersion-uncompensated fiber links
Dar, Ronen; Mecozzi, Antonio; Shtaif, Mark
2013-01-01
We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the Gaussian noise model which follows from the frequency domain approach, and the time-domain approach according to which NLIN is not additive and its nature strongly depends on the modulation format. Upon reviewing the two approaches we attribute the discrepancy to several subtle, but critical assumptions that were made in the frequency domain analysis and that we believe to be unjustified. The predictions of the time domain approach are validated numerically in simulations.
Reflective confocal laser scanning microscopy and nonlinear microscopy of cross-linked rabbit cornea
Alexander Krueger; Marina Hovakimyan; Diego F. Ramirez; Oliver Stachs; Rudolf F. Guthoff; Alexander Heisterkamp
2009-01-01
Cross-linking of the cornea with application of Ribovlavin and UV-A light is an evolving clinical treatment of the eye disease keratoconus. Despite the positive clinical track record of corneal cross-linking, the complex wound healing process after the treatment is still under investigation. In this study an animal model was used to clarify the state of wound healing 5 weeks after
Parabolic Resonance: A Route to Hamiltonian Spatiotemporal Chaos
Shlizerman, Eli; Rom-Kedar, Vered [Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Post Office Box 26, Rehovot 76100 (Israel)
2009-01-23
We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schroedinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and initial profiles that lead to such intermittency are predicted by utilizing a novel geometrical description of the integrable unforced equation.
The chaos paradigm: developments and applications in engineering and science
Katz, R.A. (ed.) (Naval Undersea Warfare Center, New London, Connecticut (United States))
1994-01-01
These proceedings are a compilation of technical topics presented at the Office of Naval Research (ONR)/Naval Undersea Warfare Center (NUWS) Technical Conference on Nonlinear Dynamics and Full-spectrum processing. The topics discussed consisted of synchronization and control of chaos, mechanical sources of chaos, turbulences, and advanced signal processing methods. There were eighteen papers presented at the conference and none is abstracted for the Energy Science and Technology database. (AIP)
Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles
NASA Astrophysics Data System (ADS)
Turner, M. R.; Gilbert, Andrew D.
This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external strain field is smoothly switched off, the cat's eyes may persist, or they may disappear as the vortex relaxes back to axisymmetry. A numerical study obtains criteria for the persistence of cat's eyes as a function of the strength and time scale of the imposed strain field, for a Gaussian vortex profile.In the limit of a weak external strain field and high Reynolds number, the disturbance decays exponentially, with a rate that is linked to a Landau pole of the linear inviscid problem. For stronger strain fields, but not strong enough to give persistent cat's eyes, the exponential decay of the disturbance varies: as time increases the decay slows down, because of the nonlinear feedback on the mean profile of the vortex. This is confirmed by determining the decay rate given by the Landau pole for these modified profiles. For strain fields strong enough to generate persistent cat's eyes, their location and rotation rate are determined for a range of angular velocities of the external strain field, and are again linked to Landau poles of the mean profiles, modified through nonlinear effects.
NASA Technical Reports Server (NTRS)
2004-01-01
[figure removed for brevity, see original site]
Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos.
The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 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.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image was collected during Southern Fall and shows part of the Aureum Chaos.
Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 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.
Oestreicher, Christian
2007-01-01
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865
Stability analysis and control of stochastic dynamic systems using polynomial chaos
Fisher, James Robert
2009-05-15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 B. Wiener-Askey Polynomial Chaos . . . . . . . . . . . . . . . . . 30 C. Stochastic Linear Dynamics and Polynomial Chaos . . . . . . 32 D. Stochastic Nonlinear Dynamics and Polynomial Chaos . . . . 37 1. Preliminaries... that have an associated probability distribution (either continuous or discrete). When this is the case and P(d?) = f(?)d? we can write the expectation operator as E[X(?)] =integral.disp ? X(?)f(?)d? (II.1) when f(?) is piecewise continuous and E...
Sprott, Julien Clinton
Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, No. 3, pp. 271-278. Â© 2009 Society, University of Wisconsin, Madison, Wisconsin 53706. E-mail: sprott@physics.wisc.edu 271 bzxyz yrxxzy xyx
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
Lithwick, Yoram [Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 (United States); Wu Yanqin [Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4 (Canada)
2011-09-20
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within {approx}25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
Linking Nonlinear Tactile Elements by Cell-Bridge System Takayuki Hoshi and Hiroyuki Shinoda
Shinoda, Hiroyuki
various touch feelings, and is soft and stretchable. We are developing a tactile sensor array by linking by calculating the spatial centroid from the measured contact forces. Keywords : Tactile sensor, Robot skin in order to obtain rich tactile information. In that situation, a large number of sensor elements
Properties of nonlinear noise in long, dispersion-uncompensated fiber links
Feder, Meir
) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling codes: (060.2330) Fiber optics communications, (060.2360) Fiber optics links and sub- systems References in Optical Fiber Telecommunications IIIA, P. Kaminow and T. L. Koch eds. (Academic Press, 1997). 3. E. Ip, J
Joji Maeda; Yutaka Fukuchi
2005-01-01
In fiber links with a bit rate greater than 100 Gb\\/s per wavelength channel, the third-order dispersion (TOD), known as the dispersion slope, becomes a major factor that limits transmission capabilities. This paper presents a numerical study on the propagation of picosecond pulses in anomalous dispersion fibers, the dispersion slope of which is periodically compensated for by lumped compensators. In
Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses
NASA Astrophysics Data System (ADS)
Simon, A.
2010-12-01
The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event triggered a debris flow which cutoff tributary channels to Glacier Creek and redirected Step and Loowit Creeks thereby forcing enhanced flow volumes through the main channel. Very coarse, armored bed materials were mobilized allowing for deep incision into the substrate. Incision continues today at slower rates but it is again the lateral shifting and widening of the channels that is dominant. Low and moderate flows undercut the toe of 30 m-high pyroclastic flow deposits causing significant erosion. As the channel continues to widen incision will attenuate non-linearly. Channels such as the multiple Step Creek channels will coalesce as narrow ridges erode by undercutting and mass failure much as reaches of lower Loowit Creek did in the late 1980’s. The resulting enlarged and over-widened sections will then again (as in downstream reaches) have lowered transporting power.
Decoherence, determinism and chaos
Noyes, H.P.
1994-01-01
The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is `deterministic`. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of `test-particle` is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as `particles` or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a `scale invariance bounded from below` by measurement accuracy, then Tanimura`s generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of `particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated.
Quantum Chaos and Quantum Computing Structures
Carlos Pedro Gonçalves
2012-08-13
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \\mathbb{C} through the iterative action of path-dependent quantum gates. The effects of emerging nonlinear dynamics and chaos upon the quantum averages of relevant observables and quantum probabilities are exemplified for a version of Chirikov's standard map on \\mathbb{C} . Both the individual orbits and ensemble properties are addressed so that the Poincar\\'e map for Chirikov's standard map, in the current quantum setting, is reinterpreted in terms of a quantum ensemble which is then formally introduced within the formalized system of quantum computing structures, in terms of quantum register machines, revealing three phases of quantum ensemble dynamics: the regular, the chaotic and an intermediate phase called complex quantum stochastic phase which shares similarities to the edge of chaos notion from classical cellular automata and classical random boolean networks' evolutionary computation.
Current Self-Oscillations and Chaos in Semiconductor Superlattices
H. T. Grahn
Weakly coupled semiconductor superlattices represent a non-linear system, which exhibits tunable current self-oscillations\\u000a and chaos. The non-linearity originates from resonant tunneling between two-dimensional subbands in adjacent wells. The current\\u000a oscillations are due to a recycling motion of a charged monopole over several superlattice periods. The charged monopole appears,\\u000a because the nonlinearity of the system in connection with a large carrier
Current Self-Oscillations and Chaos in Semiconductor Superlattices
H. T. Grahn
2000-01-01
Weakly coupled semiconductor superlattices represent a non-linear system, which exhibits tunable current self-oscillations and chaos. The non-linearity originates from resonant tunneling between two-dimensional subbands in adjacent wells. The current oscillations are due to a recycling motion of a charged monopole over several superlattice periods. The charged monopole appears, because the nonlinearity of the system in connection with a large carrier
Cyberterrorism: Postmodern State of Chaos
Jonathan Matusitz
2010-01-01
This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,
Cyberterrorism: Postmodern State of Chaos
Jonathan Matusitz
2008-01-01
This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,
ERIC Educational Resources Information Center
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
ERIC Educational Resources Information Center
Moseley, Bryan; Dustin, Daniel
2008-01-01
In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…
Marat Akhmet; Mehmet Onur Fen
2012-09-09
A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily cyclic, if the perturbations are strong and/or diameter of the limit cycle is small. Sensitivity as a main and a unique ingredient is considered and, in addition, period-doubling route to chaos is chosen for extension. The results may be of strong importance for engineering sciences, brainwaves and biomusicology phenomena as well as can be developed for hydrodynamics. Theoretical results are supported by simulations and discussions over Chua's oscillators, entrainment of chaos by toroidal attractors and controlling problems. Moreover, through an example, by means of the Lyapunov functions method, a chaotic attractor is provided.
Chai, Dongyul; Juhasz, Tibor; Brown, Donald J.; Jester, James V.
2013-01-01
Abstract. In this study we test the hypothesis that nonlinear optical (NLO) multiphoton photoactivation of riboflavin using a focused femtosecond (FS) laser light can be used to induce cross-linking (CXL) and mechanically stiffen collagen as a potential clinical therapy for the treatment of keratoconus and corneal ectasia. Riboflavin-soaked, compressed collagen hydrogels are cross-linked using a FS laser tuned to 760 nm and set to either 100 mW (NLO CXL I) or 150 mW (NLO CXL II) of laser power. FS pulses are focused into the hydrogel using a 0.75 NA objective lens, and the hydrogel is three-dimensionally scanned. Measurement of hydrogel stiffness by indentation testing show that the calculated elastic modulus (E) values are significantly increased over twofold following NLO CXL I and II compared with baseline values (P<0.05). Additionally, no significant differences are detected between NLO CXL and single photon, UVA CXL (P>0.05). This data suggests that NLO CXL has a comparable effect to conventional UVA CXL in mechanically stiffening collagen and may provide a safe and effective approach to localize CXL at different regions and depths within the cornea. PMID:23515869
ASYMPTOTIC AND INCREASING PROPAGATION OF CHAOS EXPANSIONS FOR GENEALOGICAL PARTICLE MODELS
Del Moral , Pierre
ASYMPTOTIC AND INCREASING PROPAGATION OF CHAOS EXPANSIONS FOR GENEALOGICAL PARTICLE MODELS PIERRE with genealogical tree models. Applications to nonlinear filtering problems and interacting Markov chain Monte Carlo algorithms are discussed. Key words. Interacting particle systems, historical and genealogical tree models
NASA Astrophysics Data System (ADS)
Kandrup, H. E.
2002-09-01
This talk summarises a combined theoretical and numerical investigation of the role of chaos and transient chaos in time-dependent Hamiltonian systems which aim to model elliptical galaxies. The existence of large amounts of chaos in near-equilibrium configurations is of potential importance because configurations incorporating large numbers of chaotic orbits appear to be substantially more susceptible than nearly integrable systems to various irregularities associated with, e.g., internal substructures, satellite galaxies, and/or the effects of a high density environment. Alternatively, transient chaos, reflecting exponential sensitivity over comparatively short time intervals, can prove important by significantly increasing the overall efficiency of violent relaxation so as to facilitate a more rapid evolution towards a `well-mixed' equilibrium. Completely conclusive `smoking gun' evidence for chaos and chaotic mixing has not yet been obtained, although evidence for the presence of chaos can in principle be extracted from such data sets as provided by the Sloan Digital Sky Survey. Interestingly, however, arguments completely analogous to those applied to self-gravitating systems also suggest the presence of chaos in charged particle beams, a setting which is amenable to controlled experiments.
Chaos in Bohmian quantum mechanics
NASA Astrophysics Data System (ADS)
Efthymiopoulos, C.; Contopoulos, G.
2006-02-01
This paper presents a number of numerical investigations of orbits in the de Broglie-Bohm version of quantum mechanics. We first clarify how the notion of chaos should be implemented in the case of Bohmian orbits. Then, we investigate the Bohmian orbits in three different characteristic quantum systems: (a) superposition of three stationary states in the Hamiltonian of two uncoupled harmonic oscillators with incommensurable frequencies, (b) wave packets in a Hénon-Heiles-type Hamiltonian and (c) a modified two-slit experiment. In these examples, we identify regular or chaotic orbits and also orbits exhibiting a temporarily regular and then chaotic behaviour. Then, we focus on a numerical investigation of the Bohm-Vigier (Bohm and Vigier 1954 Phys. Rev. 26 208) theory, that an arbitrary initial particle distribution P should asymptotically tend to |?|2, by considering the role of chaotic mixing in causing irregularity of Madelung's flow, a necessary condition for P to tend to |?|2. We find that the degree of chaos of a particular system correlates with the speed of convergence of P to |?|2. In the case of wave-packet dynamics, our numerical data show that the time of convergence scales exponentially with the inverse of the effective perturbation from the harmonic oscillator Hamiltonian. The latter result can be viewed as a quantum analogue of Nekhoroshev's (Nekhoroshev 1977 Russ. Math. Surveys 32 1) theorem of exponential stability in classical nonlinear Hamiltonian dynamics.
NASA Astrophysics Data System (ADS)
Tauxe, L.
2002-12-01
When I finished graduate school I suppose I imagined myself as my dad. He worked hard, loved his job and family, made a good living. But I also saw myself as my mom - making a home, raising kids, cooking dinner, saving the world. I thought: I can handle being my mom and my dad. I can handle being a scientist and a mother. I can DO this.ÿ What I never imagined was the chaotic dynamic of the two career couple. The motions of bodies moving in response to the force of gravity cannot be predicted exactly if there are too many bodies. They dance in a jerky jumble, now faster, then slowly, bouncing, jostling, bumping and flying apart. Just so are the career trajectories of the two career couple. One rises up, the other, slower, pulls it down; overtaking, blocking preventing, now supporting, pulling along, now holding back - not moving, leap frogging, racing in opposite directions and snapping back together with a crack.ÿ The problem is non-linear. The outcome depends on feedback, whether positive or negative. The outcome cannot be predicted. Cannot be determined.ÿ Perhaps it cannot be done. Perhaps both husband and wife cannot be both mother and father. Too many mothers, too many fathers. Chaos.ÿ But I believe it can be done. Not like our mothers and fathers but a different way. And maybe our jerky paths will keep us sharp, make us work harder, and lead us through lives that at least cannot be described as dull.ÿ
Regularity and chaos in 0+ states of the interacting boson model using quantum measures
NASA Astrophysics Data System (ADS)
Karampagia, S.; Bonatsos, Dennis; Casten, R. F.
2015-05-01
Background: Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large numbers of bosons renders possible additional studies of chaos that can provide a direct comparison with similar classical studies of chaos. Purpose: We intend to provide complete quantum chaotic dynamics at zero angular momentum in the vicinity of the arc of regularity and link the results of the study of chaos using statistical measures with those of the study of chaos using classical measures. Method: Statistical measures of chaos are applied on the spectrum and the transition intensities of 0+ states in the framework of the interacting boson model. Results: The energy dependence of chaos is provided for the first time using statistical measures of chaos. The position of the arc of regularity was also found to be stable in the limit of large boson numbers. Conclusions: The results of the study of chaos using statistical measures are consistent with previous studies using classical measures of chaos, as well as with studies using statistical measures of chaos, but for small number of bosons and states with angular momentum greater than 2.
Nonlinear Time-Frequency Control Theory with Applications
Liu, Mengkun 1978-
2012-10-04
Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband ...
Zharnitsky, Vadim
Search on the brink of chaos This article has been downloaded from IOPscience. Please scroll down for more Home Search Collections Journals About Contact us My IOPscience #12;IOP PUBLISHING NONLINEARITY Nonlinearity 25 (2012) 30233047 doi:10.1088/0951-7715/25/11/3023 Search on the brink of chaos Yu Baryshnikov
Chaos, Fractals, and Polynomials.
ERIC Educational Resources Information Center
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
Di Xiao; Xiaofeng Liao; Shaojiang Deng
\\u000a This chapter focuses on the construction of chaos-based hash function. Hash function is a special kind of one-way function\\u000a which takes a variable-length input and returns a fixed-length value. As one of the cores of Cryptography, hashing is a basic\\u000a technique widely used in information security. Utilizing chaos to construct hash function is a promising direction which attracts\\u000a more and
Propagation and conditional propagation of chaos for pressureless gas equations
Azzouz Dermoune
2003-01-01
We study the existence and uniqueness of a weak solution of a viscous d-dimensional system of pressureless gas equations. We construct a nonlinear diffusion by using the propagation and conditional propagation of chaos. The latter diffusion is associated with the above pressureless gas equations.
Organisational Leadership and Chaos Theory: Let's Be Careful
ERIC Educational Resources Information Center
Galbraith, Peter
2004-01-01
This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…
Control of chaos: Methods and applications in engineering
Alexander L. Fradkov; Robin J. Evans
2005-01-01
A survey of the emerging field termed “control of chaos” is given. Several major branches of research are discussed in detail: feedforward or “nonfeedback control” (based on periodic excitation of the system); “OGY method” (based on linearization of the Poincaré map), “Pyragas method” (based on a time-delay feedback), traditional control engineering methods including linear, nonlinear and adaptive control, neural networks
Chaos in a three-species food chain
A. Hastings; T. Powell
1991-01-01
A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its
Quantum chaos in QCD and hadrons
Harald Markum; Willibald Plessas; Rainer Pullirsch; Bianka Sengl; Robert F. Wagenbrunn
2005-05-13
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
Fractal Patterns and Chaos Games
ERIC Educational Resources Information Center
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Chaos and The Changing Nature of Science and Medicine. Proceedings
Herbert, D.E. [Department of Radiology, College of Medicine, University of South Alabama, Mobile, AL 36688 (United States); Croft, P. [Department of Geology and Geography, University of South Alabama, Mobile, AL 36688 (United States); Silver, D.S.; Williams, S.G. [Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688 (United States); Woodall, M. [Department of Radiology, College of Medicine, University of South Alabama, Mobile, AL 36688 (United States)
1996-09-01
These proceedings represent the lectures given at the workshop on chaos and the changing nature of science and medicine. The workshop was sponsored by the University of South Alabama and the American Association of Physicists in Medicine. The topics discussed covered nonlinear dynamical systems, complexity theory, fractals, chaos in biology and medicine and in fluid dynamics. Applications of chaotic dynamics in climatology were also discussed. There were 8 lectures at the workshop and all 8 have been abstracted for the Energy Science and Technology database.(AIP)
Distributional chaos via semiconjugacy
NASA Astrophysics Data System (ADS)
Oprocha, Piotr; Wilczynski, Pawel
2007-11-01
We develop a new method for proving the existence of distributional chaos. It is based on the special properties of semiconjugacy. As an application we prove that the equation \\dot{z}=v(t,z)=(1+\\rme^{\\rmi\\kappa t}|z|^2)\\bar{z} + zg(t,z) + f(t) is uniformly distributionally chaotic, provided ? ? (0, 0.796] and g and f are small enough. We also give an example which shows that distributional chaos (DC1) does not transfer via semiconjugacy.
NASA Astrophysics Data System (ADS)
Chien, Wei-Zang
Problems in nonlinear mechanics are examined in reviews and reports of theoretical and experimental investigations. Of the 247 papers included, 134 are by Chinese authors. Topics addressed include the constitutive equations in nonlinear continuum mechanics, finite deformation and nonlinear elasticity, and the mathematical theory of plasticity. Consideration is given to fluid mechanics and nonlinear waves; nonlinear oscillations; and bifurcations, catastrophy, chaos, and nonlinear stability.
Chaos in a Fractional Order Chua System
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory
1996-01-01
This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.
Deterministic chaos in geomagnetic reversals
NASA Astrophysics Data System (ADS)
Sidorovskaia, N.; Richter, C.; Rypina, I.
2013-12-01
In a recent publication Gissinger (Eur. Phys. J. B 85,137, 2012) proposed a new deterministic chaos model for the generation of the Earth's magnetic field and an explanation of the observed statistics of geomagnetic pole reversal occurrences. The new model is described by a system of three coupled non-linear differential equations limited to quadratic terms. If such a low degree of freedom system is adequate for the description of Earth's geomagnetic dynamo, it has to reflect in statistics and non-linear dynamic characteristics of the temporal interval between geomagnetic reversals. We present the results of the extended statistical analysis of the 2012 compilation of magnetic reversal data spanning the last 170 m.yr. We calculate the Grassberger-Procaccia correlation dimension in the context of a single-variable dataset of waiting times between measured geomagnetic reversals in paleomagnetic records to predict the complexity of the underlying geomagnetic dynamo system. First, we inspect if the time series of geomagnetic reversals has the same or a different correlation dimension than a random time series with the same number of points. This allows us to determine whether geomagnetic reversals are indistinguishable from a stochastic process, or are described by a chaotic rather than stochastic process. Next, higher-dimensional vectors are constructed from the time series of geomagnetic reversals, and correlation dimension is calculated for these higher-dimensional vectors to find out if the correlation dimension has a convergence limit as we increase the vector space dimension. If the convergence limit is revealed from the experimental dataset, then the geomagnetic reversals are chaotic rather than stochastic and are described by a system with limited number of degrees of freedom determined by the correlation dimension. If one expects to describe the geomagnetic dynamo by a low-order system of non-linear differential equations, the system should have a low dimension (self-organized) strange attractor in its phase space indicated by a low correlation dimension of observable data.
Chaos in neurons and its application: perspective of chaos engineering.
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain. PMID:23278097
Chaos in neurons and its application: Perspective of chaos engineering
NASA Astrophysics Data System (ADS)
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.
Chaos and Synchronized Chaos in an Earthquake Model
Maria de Sousa Vieira
1998-11-20
We show that chaos is present in the symmetric two-block Burridge-Knopoff model for earthquakes. This is in contrast with previous numerical studies, but in agreement with experimental results. In this system, we have found a rich dynamical behavior with an unusual route to chaos. In the three-block system, we see the appearance of synchronized chaos, showing that this concept can have potential applications in the field of seismology.
Periodicity and chaos in coupled nonlinear oscillators.
Gollub, J P; Brunner, T O; Danly, B G
1978-04-01
A system of coupled tunnel diode relaxation oscillators shows a variety of complex periodic states as the external voltage is varied. The existence of chaotic or nonperiodic states is more dependent on the nature of the coupling than on the number of degrees of freedom. A simple but accurate numerical model shows many of the phenomena observed experimentally. PMID:17847328
Stable chaos in fluctuation driven neural circuits
David Angulo-Garcia; Alessandro Torcini
2014-03-03
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, on the other hand the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of Stable Chaos.
Nonlinear aspects of shock response in isolated accelerometers
Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States); Hunter, N. [Los Alamos National Lab., NM (United States)
1992-04-01
Numerous investigations have studied the potential for chaotic vibrations of nonlinear systems. It has been shown for many simple nonlinear systems, that when they are excited severely enough, or with the appropriate parametric combinations, that they will execute chaotic vibrations. The present investigation considers the potential for the occurrence of chaos in a practical nonlinear system -- the isolated accelerometer. A simple, first order model is proposed for the isolated accelerometer, and it is shown that chaos can occur in the isolated accelerometer. A preliminary investigation into the bearing that this chaos potential has on the measurement of shock response is summarized. 7 refs.
A chaos model of meandering rivers
Stoelum, H.H.
1991-03-01
A meandering river is a nonlinear dynamic system, and fractal geometry describes well the meander bends of such rivers. Based on a qualitative, sedimentological model of the process of meandering, a chaos model is proposed, describing meandering as the outcome of two processes: the feedback interaction between river curvature and a high-velocity thalweg channel within the river; and the interaction between meander bends causing abandonment and straightening of the river course. The system, when initiated from a nearly straight river course, moves toward a dynamic equilibrium in which the meander bends are fractal. This development is a case of self-organized criticality. The equilibrium represents a state of optimal energy dissipation in a situation where two counteracting processes are balancing each other. Sedimentology may be seen as the science that describes how nonlinear dynamic processes interact to create a depositional system. As indicated by the example of meandering rivers, the use of chaos and fractal models may give sedimentology a new turn toward understanding sedimentary processes and the 3-D architecture of sediment bodies.
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.
Warshawsky, Nora E; Joseph, M Lindell; Fowler, Debra L; Edmonson, Cole; Nelson-Brantley, Heather V; Kowalski, Karren
2015-03-01
The 2014 International Nursing Administration Research Conference, "Pioneering Through Chaos: Leadership for a Changing World," was held at the Texas Woman's University in Dallas, Texas, in the fall of 2014. The program drew more than 100 attendees from 4 countries. The conference informed attendees from both academe and practice about the role of nursing administration in navigating the dynamic healthcare climate. This article will report on the insights from the conference presenters. PMID:25689497
Xiaojian Bai; Junde Chen; Bum-Hoon Lee; Taeyoon Moon
2014-06-23
We investigate the chaotic behavior of a circular test string in the Lifshitz spacetimes considering the critical exponent $z$ as an external control parameter. It is demonstrated that two primary tools to observe chaos in this system are Poincar\\'{e} section and Lyapunov exponent. Finally, the numerical result shows that if $z=1$, the string dynamics is regular, while in a case slightly larger than $z=1$, the dynamics can be irregular and chaotic.
Nonlinear models Nonlinear Regression
Penny, Will
Nonlinear models Will Penny Nonlinear Regression Nonlinear Regression Priors Energies Posterior Metropolis-Hasting Proposal density References Nonlinear models Will Penny Bayesian Inference Course, WTCN, UCL, March 2013 #12;Nonlinear models Will Penny Nonlinear Regression Nonlinear Regression Priors
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.
Classical chaos and its correspondence in superconducting qubits
NASA Astrophysics Data System (ADS)
Neill, C.; Campbell, B.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fang, M.; Hoi, I.; Kelly, J.; Megrant, A.; O'Malley, P.; Quintana, C.; Vainsencher, A.; Wenner, J.; White, T.; Barends, R.; Chen, Yu; Fowler, A.; Jeffrey, E.; Mutus, J.; Roushan, P.; Sank, D.; Martinis, J. M.
2015-03-01
Advances in superconducting qubits have made it possible to experimentally investigate quantum-classical correspondence by constructing quantum systems with chaotic classical limits. We study the quantum equivalent of a classical spinning top using three fully coupled qubits that behave as a single spin-3/2 and subject the spin to a sequence of non-linear rotations. The resulting entanglement bears a striking resemblance to the classical phase space, including bifurcation, and suggests that classical chaos manifests itself as quantum entanglement. Studying the orientation of the spin-3/2 reveals that the rotations which generate chaos and entanglement are at the same time the source of disagreement between the quantum and classical trajectories. Our experiment highlights the correspondence between classical non-linear dynamics and interacting quantum systems.
Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja
2014-11-01
We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal. PMID:25401887
Counseling Chaos: Techniques for Practitioners
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim E. H.
2006-01-01
The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…
Chaos Theory and Post Modernism
ERIC Educational Resources Information Center
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
NASA Astrophysics Data System (ADS)
Geddada, Nagesh; Karanki, Srinivas B.; Mishra, Mahesh K.
2014-06-01
This paper proposes a modified four-leg distribution static compensator (DSTATCOM) topology for compensation of unbalanced and nonlinear loads in three-phase four-wire distribution system. DSTATCOM, connected in parallel to the load, supplies reactive and harmonic powers demanded by unbalanced nonlinear loads. In this proposed topology, the voltage source inverter (VSI) of DSTATCOM is connected to point of common coupling (point of interconnection of source, load, DSTATCOM) through interface inductor and series capacitance, unlike the conventional topology which consists of interface inductor alone. Load compensation with a lower value of input DC link voltage of VSI is possible in this modified topology compared to conventional topology. A comparative study on modified and conventional topologies in terms of voltage rating of inverter power switches, switching losses in VSI and power rating of input DC capacitor of VSI is presented. The detailed design aspects of DC link capacitor and interface series capacitor are also presented. The reference filter currents are generated using instantaneous symmetrical component theory and are tracked using hysteresis current control technique. A detailed simulation study is carried out, to compare the compensation performances of conventional, modified topologies using PSCAD simulator and experimental studies are done to validate the simulation results.
Route to chaos for combustion instability in ducted laminar premixed flames.
Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R I
2012-06-01
Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario. PMID:22757536
Complex chaos in the conditional dynamics of qubits
Kiss, T. [Research Institute for Solid State Physics and Optics, P. O. Box 49, H-1525 Budapest (Hungary); Jex, I.; Vymetal, S. [Department of Physics, FJFI CVUT, Brehova 7, 115 19 Prague 1-Stare Mesto (Czech Republic); Alber, G. [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2006-10-15
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex parameter. In contrast to the usual notion of quantum chaos, exponential sensitivity to the initial state occurs here. We calculate analytically the Lyapunov exponent based on the overlap of quantum states, and find that it is positive. We present a few illustrative examples of the emerging dynamics.
Virgil Baran; Aldo Bonasera
1998-04-13
The asymptotic distance between trajectories $d_{\\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\\infty}$ in simple unidimensional maps. Near a critical point $d_{\\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.
Shujun Li
2005-12-12
This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift map and their analogues, even in a high-precision floating-point arithmetic. Although the results cannot directly generalized to most chaotic systems, the risk of using digital computers to numerically study continuous dynamical systems is shown clearly. As a result, we reach the old saying that "it is impossible to do everything with computers only".
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.
Complex Gaussian Multiplicative Chaos
NASA Astrophysics Data System (ADS)
Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent
2015-07-01
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2 D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c = 1 central charge, and derive the original KPZ formula for these fields.
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1976-01-01
Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.
Self-pulsing in Tm-doped YAlO3 lasers: Excited-state absorption and chaos
NASA Astrophysics Data System (ADS)
Wu, Ka S.; Henderson-Sapir, Ori; Veitch, Peter J.; Hamilton, Murray; Munch, Jesper; Ottaway, David J.
2015-04-01
Tm:YAlO 3 lasers suffer from self-pulsing. A four-level rate equation analysis suggested that the self-pulsing could be due to excited-state absorption. We report a measurement of the cross section for this absorption and show that it is too small to be the sole cause of the self-pulsing. We propose nonlinear dynamical chaos as an alternative explanation and present a chaos analysis of the output of a cw-pumped Tm:YAlO 3 laser, including experimental evidence of chaos.
Adaptive functional systems: Learning with chaos
NASA Astrophysics Data System (ADS)
Komarov, M. A.; Osipov, G. V.; Burtsev, M. S.
2010-12-01
We propose a new model of adaptive behavior that combines a winnerless competition principle and chaos to learn new functional systems. The model consists of a complex network of nonlinear dynamical elements producing sequences of goal-directed actions. Each element describes dynamics and activity of the functional system which is supposed to be a distributed set of interacting physiological elements such as nerve or muscle that cooperates to obtain certain goal at the level of the whole organism. During "normal" behavior, the dynamics of the system follows heteroclinic channels, but in the novel situation chaotic search is activated and a new channel leading to the target state is gradually created simulating the process of learning. The model was tested in single and multigoal environments and had demonstrated a good potential for generation of new adaptations.
NASA Astrophysics Data System (ADS)
Faria, Luiz; Kasimov, Aslan; Rosales, Rodolfo
2012-11-01
We propose the following simple model equation that describes chaotic shock waves: ut +1/2 (u2 -uus)x = f (x ,us) . It is given on the half-line x < 0 and the shock is located at x = 0 for any t >= 0 . Here us(t) is the shock state and f is a given source term [1]. The equation is a modification of the Burgers equation that includes non-locality via the presence of the shock-state value of the solution in the equation itself. The model predicts steady-state solutions, their instability through a Hopf bifurcation, and a sequence of period-doubling bifurcations leading to chaos. This dynamics is similar to that observed in the one-dimensional reactive Euler equations that describe detonations. We present nonlinear numerical simulations as well as a complete linear stability theory for the equation. Supported by DMS-0907955 and KAUST Office of Competitive Research Grants.
Explore the chaos behaviour of water quality variability: a case study at Huaihe River, China
NASA Astrophysics Data System (ADS)
Shi, Bi; Jiang, Jiping; Sivakumar, Bellie; Wang, Peng; Zhou, Weiwen
2015-04-01
Few studies investigated the nonlinear behaviour of water quality time series in natural surface waters. The work examines water quality time series in a Chinese River based on phase space reconstruction and optimal embedding dimension of chaos theories. It covers 3 regular water quality index (DO, CODMn, NH3-N) and 27 online monitoring stations. Through calculating and determining embedding dimension, m value, we analysis the chaotic characteristic of water quality variability in the river. Results shown the correlation dimension of typical water quality time series and the spatial variability. Reliability of dimension estimate and relationship between those chaos behaviours and impact factors were also discussed. It will improves the understanding of the nonlinear characteristics of water quality variation and chaos predication model.
NASA Astrophysics Data System (ADS)
Sander, Evelyn; Yorke, James A.
There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.
NASA Astrophysics Data System (ADS)
Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo
2014-10-01
The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (?y/?x) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.
Role of chaos for the validity of statistical mechanics laws: diffusion and conduction
Massimo Cencini; Fabio Cecconi; Massimo Falcioni; Angelo Vulpiani
2008-04-04
Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?
NASA Astrophysics Data System (ADS)
Ghosh, Dibakar; Roy, Barnana
2015-02-01
This paper examines the chaotic dynamics of certain damped and forced versions of classical counterpart of generalized quantum nonlinear oscillator endowed with position dependent mass (PDM). Various bifurcations such as symmetry breaking, period doubling, inverse period doubling, interior and boundary crises are reported. Sensitivity of the mass parameter ? to the chaotic dynamics of the system is demonstrated by the appearance of completely different route to chaos for ? > 0 and ? < 0. In the former case the chaotic motion is found to set in through period doubling route while in the latter case there is quasiperiodic route to chaos via strange non-chaotic attractor. Fractal boundaries are observed in chaos plots for ? > 0.
NSDL National Science Digital Library
Johanna Voolich
2003-01-01
This chaos game applet features a game board with the Sierpinski triangle computed down to level 2 with nine smaller triangles. One smaller triangle appears green and is the target. The game requires the student to move a point found on the lower right corner of the Sierpinski triangle to the target's interior. Each move consists of clicking one vertex of the large triangle to move the point half the distance to that vertex. The goal is to get the point to the interior of the target in four moves. The student is challenged to find the algorithm for successfully moving the point to the target's interior in four moves. The applet keeps a record of moves and is playable in progressively harder modes and in several variations. Copyright 2005 Eisenhower National Clearinghouse
Ercsey-Ravasz, Mária; Toroczkai, Zoltán
2012-01-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = ?log10 ? can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4. PMID:23061008
Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?
ERIC Educational Resources Information Center
Wong, Marina
2013-01-01
This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…
On the synchronization of a class of electronic circuits that exhibit chaos
Er-Wei Bai; Karl E. Lonngren; J. C. Sprott
2002-01-01
The synchronization of two nonlinear electronic circuits that exhibit chaos is numerically demonstrated using techniques from modern control theory. These circuits have been used to model a “jerk” equation and can either be identical or not identical. The technique is initially described using linear circuits.
Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy
Cvitanovc', Predrag
Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy MARC W. SLUTZKY,1. UPOs of multiple periods were highly prevalent in experiments from all three epilepsy models: 73, Epilepsy, Nonlinear, Un- stable periodic orbit, Lyapunov exponent, Determinism, Potas- sium, GABA
Reshaping-induced order-chaos routes in a damped driven Helmholtz oscillator
F. Balibrea; R. Chacón; M. A. López
2005-01-01
We study the structural stability of the Helmholtz oscillator under changes of the shape of periodic nonlinear perturbations. In particular, we determine the order-chaos threshold by means of Melnikov's method for the case of periodic perturbations given in terms of Jacobian elliptic functions. Computer simulations confirm our theoretical predictions.
Bifurcations and chaos in register transitions of excised larynx experiments Isao T. Tokudaa
Tokuda, Isao
Bifurcations and chaos in register transitions of excised larynx experiments Isao T. Tokudaa School November 2007; published online 14 January 2008 Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables
El Nino on the Devil's Staircase: Annual Subharmonic Steps to Chaos
Fei-Fei Jin; J. David Neelin; Michael Ghil
1994-01-01
The source of irregularity in El Nino, the large interannual climate variation of the Pacific ocean-atmosphere system, has remained elusive. Results from an El Nino model exhibit transition to chaos through a series of frequency-locked steps created by nonlinear resonance with the Earth's annual cycle. The overlapping of these resonances leads to the chaotic behavior. This transition scenario explains a
Sub-Poissonian statistics in order-to-chaos transition
Kryuchkyan, Gagik Yu. [Yerevan State University, Manookyan 1, Yerevan 375049, (Armenia); Institute for Physical Research, National Academy of Sciences, Ashtarak-2 378410, (Armenia); Manvelyan, Suren B. [Institute for Physical Research, National Academy of Sciences, Ashtarak-2 378410, (Armenia)
2003-07-01
We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q parameter and Wigner function that the statistics of oscillatory excitation numbers is drastically changed in the order-to-chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime, the system exhibits the range of sub-Poissonian and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed. The scaling invariance of the quantum statistics is demonstrated and its relation to dissipation and decoherence is studied.
Quantum chaos experiments using interacting atoms in a BEC
NASA Astrophysics Data System (ADS)
Shrestha, Rajendra; Summy, Gil
2011-05-01
The delta-kicked rotor has been one of the workhorses of both theoretical and experimental studies of quantum chaos. Most experimental work has been accomplished using cold atoms exposed to pulses from standing wave optical potentials. Atoms in these systems are assumed to be independent particles even in experiments done with dilute gasses of Bose-Einstein condensates where atomic collisional interactions can be ignored. Nevertheless, theoretical work has suggested that interactions can play a significant role in modifying the behavior of this system. The presence of atomic collisions adds non-linearity to the Schrodinger equation, making it more reminiscent of classical chaos. We will present results from experiments carried out using Rb87 BECs which have had the atomic interactions manipulated using a Feshbach resonance.
Intermittency and chaos in intracavity doubled lasers. II
NASA Astrophysics Data System (ADS)
James, Glenn E.; Harrell, Evans M., II; Roy, Rajarshi
1990-03-01
We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer [J. Opt. Soc. Am. B 3, 1175 (1986)] observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota [Opt. Lett. 13, 805 (1988)] demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.
Random bit generation using polarization chaos from free-running laser diode
NASA Astrophysics Data System (ADS)
Virte, Martin; Mercier, Emeric; Thienpont, Hugo; Panajotov, Krassimir; Sciamanna, Marc
2014-05-01
During the last five years, optical chaos-based random bit generators (RBGs) attracted a lot of attention and demonstrated impressive performances with bit rates up to hundreds of Gbps. However all the suggested schemes use external injection schemes (optical injection or feedback) to turn the lasers into chaos, hence strongly increasing setup complexity. On the other hand, we reported that a laser diode can generate a chaotic output without the need for external perturbation or forcing, hence unveiling a highly simplified way to generate an optical chaos at high frequency. However the low dimension and limited number of positive Lyapunov exponent casted doubts about its direct use for chaos-based applications. Here we make a proof-of-concept demonstration for a Random Bit Generator based on polarization chaos. We therefore suggest a highly simplified RBG scheme using only a free-running laser and small-bandwidth acquisition electronics and demonstrate convincing performances with bit rates up to 100 Gbps without unusual or complex post-processing methods. We link these performances to the double-scroll structure of the chaotic attractor rather than the bandwidth of the dynamics, hence bringing new light on the importance of chaos topology for chaos-based applications. In addition our scheme exhibit a strong potential as it enables a low-cost and/or integrated in parallel on-chip scheme.
Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential
Ishkhanyan, H. A.; Krainov, V. P., E-mail: vpkrainov@mail.ru [Moscow Institute of Physics and Technology (State University) (Russian Federation)
2011-09-15
We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.
Deterministic chaos in government debt dynamics with mechanistic primary balance rules
Jussi Ilmari Lindgren
2011-09-05
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich nonlinear behaviour and it can exhibit deterministic chaos with certain parameter regimes. Deterministic chaos means the existence of the butterfly effect which in turn is qualitatively very important, as it shows that even deterministic budget rules produce unpredictable behaviour of the debt-to-GDP ratio, as chaotic systems are extremely sensitive to initial conditions.
NSDL National Science Digital Library
Osmond, Andrew.
For the third time in the last 14 months, Russian President Boris Yeltsin deposed his Prime Minister and Cabinet, intensifying the political chaos in a country beleaguered by economic insolvency, administrative corruption, and governmental mismanagement. The dismissals handed down on Wednesday, which included the popular PM Yevgeny M. Primakov, occurred the day before impeachment proceedings were to begin against Yeltsin in the lower house of the Russian parliament, the communist-led State Duma. Russia's first democratically elected President faces five impeachment charges, including initiating the collapse of the USSR, ordering an attack on parliament in 1993, destroying the armed forces, punishing the Russian people through harsh economic policies, and waging an illegal war against the secessionist Chechnya in 1994 through 1996. Political analysts forecast that only the last charge has a chance of passing the necessary two-thirds vote, slated for Saturday, in the 450-seat State Duma. Even if charged, it is unlikely that Yeltsin will be removed from office because the charge must also be approved by the Constitutional Court, the Supreme Court, and the Council of Federation, the parliament's upper house. However, the political imbroglio will paralyze the Russian government for months to come, and has already disrupted Russian diplomatic efforts to mediate a resolution to the crisis in Yugoslavia. The sites listed provide insight into this current Russian political crisis.
NASA Astrophysics Data System (ADS)
Murali, K.; Sinah, Sudeshna; Ditto, William
2004-03-01
Recently there has been a new theoretical direction in harnessing the richness of spatially extended chaotic systems, namely the exploitation of coupled chaotic elements to do flexible computations [1]. The aim of this presentation is to demonstrate the use a single chaotic element to emulate different logic gates and perform different arithmetic tasks. Additionally we demonstrate that the elements can be controlled to switch easily between the different operational roles. Such a computing unit may then allow a more dynamic computer architecture and serve as ingredients of a general-purpose device more flexible than statically wired hardware. The theoretical scheme for flexible implementation of all these fundamental logical operations utilizing low dimensional chaos [1] will be reviewed along with a specific realization of the theory in a chaotic circuit [2]. Results will also be presented from experiments done on leech neurons. [1] Sinha, S., Munakata, T. and Ditto, W.L., Phys. Rev. E 65 036216 [2] "Experimental realization of the fundamental NOR Gate using a chaotic circuit," K. Murali, Sudeshna Sinha and William L. Ditto Phys. Rev. E 68, 016205 (2003).
Flach, Sergej
the nonlinear Kerr effect in disordered photonic lattices [6], or atomic Bose-Einstein condensate interactions transport PACS 63.20.Pw Phonons in crystal lattices: Localized modes Abstract We observe a crossover], acoustics [3], microwaves [4], and matter waves [5]. In many experimental situations, AL can be strongly
Hamiltonian chaos in a coupled BEC-optomechanical-cavity system
Zhang, K. [State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062 (China); Chen, W.; Bhattacharya, M.; Meystre, P. [B2 Institute, Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)
2010-01-15
We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.
Chaos in a Relativistic 3-body Self-Gravitating System
F. J. Burnell; R. B. Mann; T. Ohta
2003-03-03
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to their non-relativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of non-linearity in the system. We find numerical evidence for a countably infinite class of non-chaotic orbits, yielding a fractal structure in the outer regions of the Poincare plot.
Exploration of Order in Chaos with Replica Exchange Monte Carlo
Tatsuo Yanagita; Yukito Iba
2008-11-20
A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of rare initial conditions and for the combined search of rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and search for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.
Chaos in a three-species food chain
Hastings, A.; Powell, T. (University of California, Davis (United States))
1991-06-01
A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food webs must contend with the question of how to couple the large number of interacting species.
Chaos control in passive walking dynamics of a compass-gait model
NASA Astrophysics Data System (ADS)
Gritli, Hassène; Khraief, Nahla; Belghith, Safya
2013-08-01
The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.
The Promise of Chaos... Chaos Article. . . continued from front cover
Chen, Guanrong "Ron"
regulate dynamical re- sponses of mechanical and electronic devices (e.g., diodes, laser machines in the multi-planetary space system.A suitable modification of cha- otic dynamics such as stability conversion/decoding efficiency in signal and image communications. Other application examples of chaos control and anti
Observing chaos for quantum-dot microlasers with external feedback.
Albert, Ferdinand; Hopfmann, Caspar; Reitzenstein, Stephan; Schneider, Christian; Höfling, Sven; Worschech, Lukas; Kamp, Martin; Kinzel, Wolfgang; Forchel, Alfred; Kanter, Ido
2011-01-01
Chaos presents a striking and fascinating phenomenon of nonlinear systems. A common aspect of such systems is the presence of feedback that couples the output signal partially back to the input. Feedback coupling can be well controlled in optoelectronic devices such as conventional semiconductor lasers that provide bench-top platforms for the study of chaotic behaviour and high bit rate random number generation. Here we experimentally demonstrate that chaos can be observed for quantum-dot microlasers operating close to the quantum limit at nW output powers. Applying self-feedback to a quantum-dot microlaser results in a dramatic change in the photon statistics wherein strong, super-thermal photon bunching is indicative of random-intensity fluctuations associated with the spiked emission of light. Our experiments reveal that gain competition of few quantum dots in the active layer enhances the influence of self-feedback and will open up new avenues for the study of chaos in quantum systems. PMID:21694714
Urban chaos and replacement dynamics in nature and society
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2014-11-01
Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.
Experimental study on chaos of a liquid-filled tank under vertical excitation
Okazaki, K.; Watanabe, K. [Yamagata Univ., Yonezawa (Japan). Dept. of Mechanical System Engineering; Tani, J. [Tohoku Univ., Sendai (Japan). Inst. of Fluid Science
1995-11-01
This paper is concerned with an experimental study on the chaos of a partially liquid-filled cylindrical tank under vertical excitation. The test cylinder made of polyester film was harmonically excited with constant displacement amplitude. It has been well known that the partially liquid-filled cylindrical tank under periodic vertical excitation gives rise to the parametoric resonance. As the excitation amplitude increases, the nonlinear response characteristics of soft and hard spring types as well as chaos were found to appear in this system. The occurrence of chaos was recognized by the time history, Poincare map, phase trajectory, and power spectrum. Furthermore, the sloshing and chaotic motion of the liquid surface were found to appear in the lower frequency range than the parametric resonance and chaotic motion of the cylindrical shell wall.
Chaos concepts as diagnostic tools for assessing rotating machinery vibration signatures
Adams, M.L. [Department of Mechanical and Aerospace Engineering, The Case School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106 (United States); Loparo, K.A. [Department of Systems Engineering, The Case School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106 (United States)
1996-06-01
Chaos content in measured vibration signals is of some practical importance in rotordynamical systems. Of particular interest is the relationship between the occurrence of determinsite chaos and the diagnosis of mechanical failures in rotating machinery. Two nonlinear rotordynamical systems were studied using simulation and various forms of subharmonic, quasiperiodic and chaotic vibrations were observed. Different routes into and out of chaos show important signs for wear assessment and failure prediction. Experimental test facilities are currently under development and the next steps involve experimental verification of the simulation results and the development of signal processing techniques for extracting the dynamical features of the vibration signatures from measured time series data. {copyright} {ital 1996 American Institute of Physics.}
Meaning Finds a Way: Chaos (Theory) and Composition
ERIC Educational Resources Information Center
Kyburz, Bonnie Lenore
2004-01-01
The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.
A Simple Circuit for Demonstrating Regular and Synchronized Chaos.
ERIC Educational Resources Information Center
Carroll, Thomas L.
1995-01-01
Discusses the physics behind the synchronization of chaos. Describes an easy to build an electronic circuit which can be used to demonstrate chaos and the synchronization of chaos. Contains 19 references. (JRH)
Quantum Fluctuations and Dynamical Chaos
Matinyan, S.G.; Mueller, B. [Department of Physics, Duke University, Durham, North Carolina 27708-0305 (United States)] [Department of Physics, Duke University, Durham, North Carolina 27708-0305 (United States); Matinyan, S.G. [Yerevan Physics Institute, Yerevan (Armenia)] [Yerevan Physics Institute, Yerevan (Armenia)
1997-03-01
We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using massless scalar electrodynamics as an example, we show how the radiatively induced spontaneous symmetry breaking stabilizes the vacuum state against chaos. {copyright} {ital 1997} {ital The American Physical Society}
NASA Technical Reports Server (NTRS)
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
ERIC Educational Resources Information Center
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
ChaosBook.org |||||||||||||||||||||-version
Lopes, Artur Oscar
wrote in the introduction to the announcement of Kepler's third law, Harmonice Mundi (Linz, 1619; Appendix A A brief history of chaos Laws of attribution 1. Arnol'd's Law: everything that is discov- ered is named after someone else (including Arnol'd's law) 2. Berry's Law: sometimes, the sequence of an
M. Lecar; F. Franklin; M. Holman; N. Murray
2001-11-30
The physical basis of chaos in the solar system is now better understood: in all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its Kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new ``short-period'' comet is discovered each year. They are believed to come from the ``Kuiper Belt'' (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury, in 10^{12} years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 10^9 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
Chaos Rules! Robert L. Devaney
Devaney, Robert L.
Chaos Rules! Robert L. Devaney #3; September 16, 2003 #3; Please address all correspondence to Robert L. Devaney, Department of Mathematics, Boston University, Boston MA 02215, or email bob@bu.edu. 1 of this #12;gure are all bounded by the well known Koch snow ake fractal! Figure 2: The Sierpinski hexagon
Nonlinear dynamics, fractals, cardiac physiology and sudden death
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.
1987-01-01
The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.
NASA Astrophysics Data System (ADS)
Lundqvist, S.
Reviews and reports of theoretical, numerical, and experimental investigations of chaotic and other nonlinear phenomena in physics are presented. The topics examined are chaos in low-dimensionality systems, pattern formation, turbulence, computational aspects, and quantum systems. Consideration is given to the transition from periodic motion to unbounded chaos in a simple pendulum, the chaotic dynamics of instabilities in solids, neutron scattering from a convecting nematic, patterns and noise in hydrodynamic systems, pattern formation and chaos in synergetic systems, ergodic aspects of turbulence theory, drift and diffusion in reversible computation, and Farey organization of the fractional Hall effect.
Hong Kong Polytechnic University: Nonlinear Circuits and Systems
NSDL National Science Digital Library
Hong Kong Polytechnic University's project on Nonlinear Circuits and Systems began in 1991 with a focus on switching power electronics systems. The project has expanded its focus to include signal processing and chaos communications, with an emphasis on practical systems and applications. Seminar slides and Flash movies on chaos and circuit theories and Life Phenomena (such as fireflies, the pendulum and the butterfly effect) are informative. Other graphs represent the SARS virus propagation, the Hong Kong Coast, and the Koch Curve.
NASA Astrophysics Data System (ADS)
Ma, Shao-Juan; Xu, Wei; Li, Wei; Fang, Tong
2006-06-01
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
BOOK REVIEW: Chaos: A Very Short Introduction
NASA Astrophysics Data System (ADS)
Klages, R.
2007-07-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book is also getting a bit too intricate for the complete layman, and experts may not agree on all details of the more conceptual discussions. Altogether I thoroughly enjoyed reading this book. It was a happy companion while travelling and a nice bedtime literature. It is furthermore an excellent reminder of the `big picture' underlying nonlinear science as it applies to the real world. I will gladly recommend this book as background literature for students in my introductory course on dynamical systems. However, the book will be of interest to anyone who is looking for a very short account on fundamental problems and principles in modern nonlinear science.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image is located in a different part of Aureum Chaos. Compare the surface textures with yesterday's image. This image was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -4.1, Longitude 333.9 East (26.1 West). 35 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.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image continues the northward trend through the Iani Chaos region. Compare this image to Monday's and Tuesday's. This image was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -0.1 Longitude 342.6 East (17.4 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.
ERIC Educational Resources Information Center
McKay, Hannah; Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
Chaos career counseling, based on the Chaos Theory of Careers (R. G. L. Pryor & J. E. H. Bright, 2003a, 2003b), was compared with trait matching career counseling and a wait list control. Sixty university students who attended the Careers Research and Assessment Service seeking career advice were randomly assigned to the chaos intervention, the…
Does chaos assist localization or delocalization?
Tan, Jintao; Luo, Yunrong; Hai, Wenhua, E-mail: whhai2005@aliyun.com [Department of Physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 (China); Lu, Gengbiao [Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004 (China)
2014-12-01
We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M. [Radio Astronomy Institute of Ukrainian Academy of Sciences, 4 Krasnoznamennaya Street, 310002 Kharkov (Ukraine)
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
Haotic, Fractal, and Nonlinear Signal Processing. Proceedings
Katz, R.A. [Naval Undersea Warfare Center, Newport, RI (United States)
1996-10-01
These proceedings include papers presented at the Third Technical Conference on Nonlinear Dynamics and Full{minus}Spectrum Processing held in Mystic, Connecticut. The Conference focus was on the latest advances in chaotic, fractal and nonlinear signal processing methods. Topics of discussion covered in the Conference include: mathematical frontiers; predictability and control of chaos, detection and classification with applications in acoustics; advanced applied signal processing methods(linear and nonlinear); stochastic resonance; machinery diagnostics; turbulence; geophysics; medicine; and recent novel approaches to modeling nonlinear systems. There were 58 papers in the conference and all have been abstracted for the Energy Science and Technology database. (AIP)
Habib, S; Doherty, A; Greenbaum, B; Hopkins, A; Jacobs, K; Mabuchi, H; Schwab, K; Shizume, K; Steck, D; Sundaram, B; Habib, Salman; Bhattacharya, Tanmoy; Doherty, Andrew; Greenbaum, Benjamin; Hopkins, Asa; Jacobs, Kurt; Mabuchi, Hideo; Schwab, Keith; Shizume, Kosuke; Steck, Daniel; Sundaram, Bala
2005-01-01
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.
Salman Habib; Tanmoy Bhattacharya; Andrew Doherty; Benjamin Greenbaum; Asa Hopkins; Kurt Jacobs; Hideo Mabuchi; Keith Schwab; Kosuke Shizume; Daniel Steck; Bala Sundaram
2005-05-07
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured quantum systems, necessary to explain actual experimental results. The dynamics of such systems is intrinsically nonlinear even at the level of distribution functions, both classically as well as quantum mechanically. Aside from being physically more complete, this treatment reveals the existence of dynamical regimes, such as chaos, that have no counterpart in the linear case. Here, we present a short introductory review of some of these aspects, with a few illustrative results and examples.
Origin of chaos in the circulation: open loop analysis with an artificial heart.
Yambe, T; Nanka, S; Kobayashi, S; Tanaka, A; Yoshizawa, M; Abe, K; Tabayashi, K; Takeda, H; Nitta, S
1998-01-01
To develop the optimal automatic control algorithm for an in vivo artificial heart system, investigation of the basic characteristics of the cardiovascular system may be important. The clinical significance of chaotic dynamics in the cardiovascular system has attracted attention. The circulation is a so-called complex system with many feedback circuits, making it very difficult to investigate the origin of chaos within the system. In this study, we investigated the origin of chaos by open loop analysis with an artificial heart (which has no fluctuation in pumping rate or contraction power) in chronic animal experiments with healthy adult goats. As a result, in the artificial heart circulatory time series data, low dimensional deterministic chaos was discovered by nonlinear mathematical analysis, suggesting the importance of blood vessels in the chaotic dynamics of the cardiovascular system. To investigate the origin of chaos further, sympathetic activity was directly measured in animals with artificial hearts. Chaotic dynamics was also recognized in sympathetic action potentials, even during artificial heart circulation. Coupling of the nonlinear information between blood vessels and sympathetic activity was suggested by analysis of mutual information. In chaotic dynamics, the central nervous system (CNS) played an important role through sympathetic activity. These findings may be useful for the development of an automatic control algorithm for an artificial heart. PMID:9804525
Controlling Fast Chaos in Delay Dynamical Systems
J. N. Blakely; L. Illing; D. J. Gauthier
2004-04-27
We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of ~12 ns. Our approach is a prescription for how to implement existing chaos control algorithms in a way that exploits the system's inherent time-delay and allows control even in the presence of substantial control-loop latency (the finite time it takes signals to propagate through the components in the controller). This research paves the way for applications exploiting fast control of chaos, such as chaos-based communication schemes and stabilizing the behavior of ultrafast lasers.
Chaos and schizophrenia: does the method fit the madness?
Paulus, Martin P; Braff, David L
2003-01-01
Over the past 30 years, investigators have used nonlinear and so-called chaos theory-based techniques to examine a wide range of phenomena ranging from electroencephalogram and cardiac rate and rhythm analyses to stock market and weather predictions. Psychiatric neuroscientists are now beginning to apply nonlinear methods to mental disorders such as schizophrenia. These applications are relevant from the level of complex genetic architecture and calcium channel dynamics to the symptomatic, behavioral, and functional outcome of schizophrenia. The key point of this surge of interest is distinguishing complex, nonlinear but lawfully mediated systems from truly random systems. The application of these methods to studies in schizophrenia has yielded findings that are consistent with the general hypothesis that an altered sequential or temporal architecture is a key feature of this disorder. Specifically, we propose that the temporal architecture of schizophrenia is characterized by bursts of complex, nonlinear phenomena alternating with truly random events. Analyzing these patterns of molecular (e.g., calcium channel activity) to molar (e.g., symptom level) phenomena via nonlinear systems methods can provide new approaches to understanding complex temporal and sequential shifts in neural substrate activity, pathophysiology, and the course and treatment and outcome of schizophrenia. PMID:12513940
Sheridan, T.E. [Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810 (United States)
2005-08-15
Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48{+-}0.05 is observed. The largest Lyapunov exponent is positive.
BBC News: Mathematicians Crochet Chaos
NSDL National Science Digital Library
This article from BBC News discusses how two mathematicians made a crochet model of chaos. The mathematicians, whose research focuses on developing a computer model to describe complex surfaces, were able to represent the Lorenz equations using 25,511 crochet stitches. The pattern was published in the journal Mathematics Intelligencer and the mathematicians are challenging others to repeat the effort. The model stretches almost a meter across and was used as a Christmas decoration.
Invariant chaos in mixmaster cosmology
NASA Astrophysics Data System (ADS)
Szydlowski, Marek; Szczesny, Jerzy
1994-07-01
We discuss mathematical aspects of determining local instability parameters by using invariant characteristics of the internal pseudo-Riemannian geometry with the Jacobi metric (in principle, for Hamiltonian dynamical systems). Analytical formulas allowing one to compute the separation rate of nearby trajectories are given and the fundamental difference between the behavior of geodesics in the Riemannian and pseudo-Riemannian spaces carrying Jacobi metrics is stressed. The formalism developed here is used as an invariant tool to detect chaos in general relativity.
Troy Shinbrot; Celso Grebogi; Jack Wisdom; James A. Yorke
1992-01-01
A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent lambda=7.5+\\/-1.5 s-1. Numerical simulations performed on an idealized model give good agreement, with the
Dynamic Equilibrium, Self-Organizing Systems, and Chaos Theory
NSDL National Science Digital Library
Enright, Rachel
It is commonly thought that the behavior of physical systems is controlled by deterministic laws, yet physical processes appear to be unpredictable. This Topic in Depth discusses how the concepts of self-regulating systems, dynamic equilibrium, and chaos theory help to rectify this conundrum. The first website ({1--http://dbhs.wvusd.k12.ca.us/Equilibrium/Dynamic-Equilibrium.html}), developed by John L. Park at Chem Team, addresses dynamic equilibrium as it applies to chemical systems. High school students will find two equilibrium examples illustrating how, by means of forward and reverse reactions, the system becomes constant. In the next website (2), the MadSci Network discusses the issue of dynamic equilibrium in terms of the components of earth systems. Visitors can learn how the carbon dioxide cycle in the atmosphere has been disrupted by humans and how the system copes with this change. The Chaos Group at the University of Maryland developed the third website 3) to promote its research in chaotic dynamics. Visitors can learn about the group's work in Pattern Formation and Granular Dynamics, magnetic and fluid dynamics, and more. The next website (4) is an online articleby Donald Turcotte and John Rundle discussing the difficulty in addressing self-organizing complexity. This website, made available by PubMed Central, provides examples of complexities in systems such as drainage networks and global climate. Visitors can also learn about deterministic and stochastic components in systems. A. Mary Selvam at the Indian Institute of Tropical Meteorology teaches users about the relationship atmospheric flows have with quantumlike mechanics and determinist chaos in the fifth website (5). In this online scientific article, visitors can learn how the author's conclusions may be applicable to the design of artificial intelligence systems. The last website (6) discusses the research efforts of Mercer University Physics Department concerning nonlinear phenomena that are the fundamentals of chaos and complexity. This extensive website provides visitors with explanations of the group's research efforts in neurodynamics, granular physics, and mind body dynamics. Students can also find out about the history of the synchronization of chaos.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
NASA Astrophysics Data System (ADS)
Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia
2014-12-01
In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.
Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^
NASA Astrophysics Data System (ADS)
Mackey, Peter Francis
1995-01-01
These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately, despite ungovernable fate and chance, Bloom asserts his will with Stephen and Molly, proving that he will live on, attempting to create his own destiny, wresting hope from the "chaos" of his experience.
Advising Undecided Students: Lessons from Chaos Theory.
ERIC Educational Resources Information Center
Beck, Amy
1999-01-01
Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's…
Is this chaos, at least in theory?
T Kippenberger
1999-01-01
Looks at chase theory - the unpredictable yet creative behavioural nature of complex systems. States the Y2K bug may provide one of the most valuable insights into the implications of chaos theory in business and management to date. Looks at chaos theory in brief with discovery, choice and action and both negative and positive feedback. Uses 2 Tables to show
A method for designing dynamical S-boxes based on discrete chaos map system
Gang Xu; Geng Zhao; Lequan Min
2009-01-01
This paper presents a method for obtaining dynamically cryptographically strong substitution boxes (Sboxes) based on discrete chaos map system (DCMS). The cryptographical properties such as bijection, nonlinearity, strict avalanche, output bits independence and equiprobable input\\/output XOR distribution of these S-boxes are analyzed in detail. The results of numerical analysis show that all the criteria for designing good S-box can be
Game as a Career Metaphor: A Chaos Theory Career Counselling Application
ERIC Educational Resources Information Center
Pryor, Robert George Leslie; Bright, Jim E. H.
2009-01-01
The potential of game as a career metaphor for use in counselling is explored and it is argued that it has been largely overlooked in the literature to date. This metaphor is then explicitly linked with the Chaos Theory of Careers (CTC), by showing how the notion of attractors within the CTC can be illustrated effectively using games metaphors.…
The route to chaos for the Kuramoto-Sivashinsky equation
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1991-01-01
The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609 .... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
Common prescriptions for psychology derived from dialectical materialism and chaos theory.
Gilgen, A R
2000-04-01
During the entire Soviet period (1917-1991), Russian psychologists labored to create a psychology which would be consonant with Marxist-Leninist assumptions derived from dialectical materialism. Some of their early prescriptions, in particular those put forward by Konstantin N. Kornilov in the 1920s and early 1930s, are identical to strategies being advanced by contemporary American psychologists who propose that chaos theory and nonlinear meta-modeling techniques in general, given advances in computer and television technologies, can be designed for research capable of dealing with the complexities, nonlinearities, self-organizational processes, and abrupt transformations characteristic of human psychological functioning. PMID:10840901
Nonlinear lattice waves in heterogeneous media
NASA Astrophysics Data System (ADS)
Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S.
2014-12-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
Decoherence, determinism and chaos revisited
Noyes, H.P.
1994-11-15
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
Quantum Chaos and Effective Thermalization
NASA Astrophysics Data System (ADS)
Altland, Alexander; Haake, Fritz
2012-02-01
We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a “quantum smoothened” approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.
Laurent Larger; Roman Lavrov; Maxime Jacquot
2010-01-01
We report on very recent achievements in optical chaos communications. Electro-optic phase modulation principles have been used to design a new chaos generator based on nonlinear delay dynamics. A multiple delay (both short and long) architecture allowed for an enhanced chaotic complexity, as well as a more accurate synchronization capability, over the full bandwidth of a typical 10 Gb\\/s binary
Markov transitions and the propagation of chaos
Gottlieb, A.
1998-12-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.
Titration of chaos with added noise.
Poon, C S; Barahona, M
2001-06-19
Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple "litmus test" for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems. PMID:11416195
Edge of chaos and genesis of turbulence
NASA Astrophysics Data System (ADS)
Chian, Abraham C.-L.; Muñoz, Pablo R.; Rempel, Erico L.
2013-11-01
The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable traveling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.
Competitive coexistence in stoichiometric chaos
NASA Astrophysics Data System (ADS)
Deng, Bo; Loladze, Irakli
2007-09-01
Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.
Wave chaos in the nonequilibrium dynamics of the Gross-Pitaevskii equation
Brezinova, Iva; Ludwig, Katharina; Burgdoerfer, Joachim [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Collins, Lee A. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Schneider, Barry I. [Physics Division, National Science Foundation, Arlington, Virginia 22230 (United States); Electron and Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)
2011-04-15
The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of nonlinear Schroedinger equations which are known to feature dynamical instability and collapse for attractive nonlinear interactions. We show that the GPE with repulsive nonlinear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials, as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wave functions is to be distinguished from the notion of nonintegrability of nonlinear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.
Wave chaos in the nonequilibrium dynamics of the Gross-Pitaevskii equation
NASA Astrophysics Data System (ADS)
B?ezinová, Iva; Collins, Lee A.; Ludwig, Katharina; Schneider, Barry I.; Burgdörfer, Joachim
2011-04-01
The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of nonlinear Schrödinger equations which are known to feature dynamical instability and collapse for attractive nonlinear interactions. We show that the GPE with repulsive nonlinear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials, as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wave functions is to be distinguished from the notion of nonintegrability of nonlinear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.
Continuous control of chaos based on the stability criterion.
Yu, Hong Jie; Liu, Yan Zhu; Peng, Jian Hua
2004-06-01
A method of chaos control based on stability criterion is proposed in the present paper. This method can stabilize chaotic systems onto a desired periodic orbit by a small time-continuous perturbation nonlinear feedback. This method does not require linearization of the system around the stabilized orbit and only an approximate location of the desired periodic orbit is required which can be automatically detected in the control process. The control can be started at any moment by choosing appropriate perturbation restriction condition. It seems that more flexibility and convenience are the main advantages of this method. The discussions on control of attitude motion of a spacecraft, Rössler system, and two coupled Duffing oscillators are given as numerical examples. PMID:15244704
Embracing chaos and complexity: a quantum change for public health.
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. PMID:18556599
Embracing Chaos and Complexity: A Quantum Change for Public Health
Resnicow, Kenneth; Page, Scott E.
2008-01-01
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. PMID:18556599
DIFFUSION PARAMETER CONTROL OF SPATIOTEMPORAL CHAOS
Colet, Pere
Mallorca, Spain. PERE COLET, y Instituto Mediterr â?? aneo de Estudios Avanzados, IMEDEA (CSICÂUIB) EÂ07071 Palma de Mallorca, Spain. Submitted to Int. J. Bifurcation and Chaos, 31 Agost 1997 The stabilization
Quantum Chaos and Symmetries in Nuclear Spectroscopy
NASA Astrophysics Data System (ADS)
Tambergs, J.; Krasta, T.; Dumbr?js, O.
2003-06-01
There is no generally acceptable quantum chaos definition in physics yet, hence we believe that the application of existing approaches to various specific physical systems would help to solve this problem. In our approach to quantum chaos problem we employ the dynamical quantum chaos criterion ?k = ?spr (k)/D0, introduced by V.Bunakov, where ?spr (k) - fragmentation width of the unperturbed quantum state, D0 - averaged distance between the levels of unperturbed system. This criterion is associated with physical system symmetries via the conservation laws for corresponding quantum numbers. We consider the application of Bunakov's criterion ?k both to the traditional (Nilson single-particle) nuclear model as well as to the algebraic microscopic strictly restricted dynamics nuclear model (SRDM). In the case of SRDM dynamical criterion ?k seems to be more sensitive indicator of quantum chaos, in comparision with the statistical one, associated with level spacing distributions.
Homoclinic chaos and energy condition violation
J. Mark Heinzle; N. Rohr; C. Uggla
2006-07-31
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be non-tilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density $\\rho>0$ that evolve through the singularity and beyond as solutions with negative matter energy density $\\rho<0$. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass.In addition, we discuss more general models: for solutions that are not locally rotionally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.
Geodesic Deviation Equation Approach to Chaos
NASA Astrophysics Data System (ADS)
Szczesny, J.; Dobrowolski, T.
1999-11-01
A geodesic deviation equation is introduced. In an "adiabatic" approximation its exact solution is found. Perturbation theory in general case is formulated. A geometrical criterion of local instability which may lead to chaos is formulated.
Order and chaos : articulating support, housing transformation
Boehm, William Hollister
1990-01-01
This thesis presents an exploration on the theme of order and chaos, as a formal and social phenomenon, particularly as it relates to housing. The work stems from an attraction to the messy vitality we find in certain ...
Chomp, Recurrences and Chaos(?) DORON ZEILBERGER*,
Zeilberger, Doron
by "weird" recurrences. Keywords: Chomp; Recurrence equations; Chaos; Difference equations SABER ELAYDI When sense. In this article, we will encounter weird recurrences that in addition to using all the previous
New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process
Ying Song; Zengqiang Chen; Zhuzhi Yuan
2007-01-01
In this letter, a novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented. The TCPSO incorporating tent-map chaos, which can avoid trapping to local minima and improve the searching performance of standard particle swarm optimization (PSO), is applied to perform the nonlinear optimization to enhance the convergence and accuracy.
Lei Lv; Lei Han
2008-01-01
Ultrasonic wire bonding is one of the main methods in the package of the chip and substrate of the chip. The vibrations of transducer were tested. Surrogate-data method of phase-randomized based on correlation dimension is proposed to identify the nonlinear chaos of data obtained by ultrasonic wire bonding system. The result indicate there is nonlinear factor in the axial direction
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
the nonlinearity and the possible chaos of normal HRV [2]. Nonlinear HRV methods were rarely applied on ECG data days after returning (R+5) and one month after returning to earth (R+30). 2.2 Analysis First, some (SampEn) and Noise Limit (NL) are calculated. An overview of these methods is recently given by Aubert
IP Fast Rerouting for Double-Link Failure Recovery
Chao, Jonathan
IP Fast Rerouting for Double-Link Failure Recovery Kang Xi and H. Jonathan Chao August 2006 New of Science Technology and Academic Research #12;1 IP Fast Rerouting for Double-Link Failure Recovery Kang Xi recovery in the IP layer using fast rerouting has gained much attention recently. When a failure occurs
Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos
Snieder, Roel
Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos Roel Snieder for imaging are invariant for time reversal. The physical reason for this is that in imaging one propagates the recorded waves backward in time to the place and time when the waves interacted with the medium
arXiv:chao-dyn/9909024v215Aug2000 Chaos, Dissipation and Quantal Brownian Motion
Cohen, Doron
arXiv:chao-dyn/9909024v215Aug2000 Chaos, Dissipation and Quantal Brownian Motion (Lecture notes. -- Quantum dissipation, the theory of energy spreading and quantal Brownian motion are considered: · Classical Brownian motion; · The ZCL model and the DLD model; · The white noise approximation; · The reduced
Corron, Ned J; Blakely, Jonathan N; Stahl, Mark T
2010-06-01
A novel chaotic oscillator is shown to admit an exact analytic solution and a simple matched filter. The oscillator is a hybrid dynamical system including both a differential equation and a discrete switching condition. The analytic solution is written as a linear convolution of a symbol sequence and a fixed basis function, similar to that of conventional communication waveforms. Waveform returns at switching times are shown to be conjugate to a chaotic shift map, effectively proving the existence of chaos in the system. A matched filter in the form of a delay differential equation is derived for the basis function. Applying the matched filter to a received waveform, the bit error rate for detecting symbols is derived, and explicit closed-form expressions are presented for special cases. The oscillator and matched filter are realized in a low-frequency electronic circuit. Remarkable agreement between the analytic solution and the measured chaotic waveform is observed. PMID:20590319
Hamiltonian structure of Hamiltonian chaos
NASA Astrophysics Data System (ADS)
Tang, X. Z.; Boozer, A. M.
1997-02-01
From a kinematical point of view, the geometrical information of Hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are found to be determined by a new Hamiltonian of the same number of degrees of freedom as the original one. This new Hamiltonian defines a flow field with characteristically chaotic trajectories. The direction and the magnitude of the phase flow field give the (un) stab le direction and the finite time Lyapunov exponent of the original Hamiltonian. Our analysis was based on a 1 1/2 degree of freedom Hamiltonian system.
ATTRACTOR AND PATTERN CONTROL IN NONLINEAR MEDIA BY LOCALIZED DEFECTS
S. Vakulenko; B. Kazmierczak
2004-01-01
Summary We consider pattern and attractor control in nonlinear dissipative systems. We develop an analytic approach to attractor control for neural, genetic networks systems of coupled oscillators and spatially extended systems. In particular, we apply this method for some systems of Ginzburg-Landau's type and others. 1. Introduction. In the last decade, a great attention has been given to chaos existence
Analyzing Thought-related Electroencephalographic Data Using Nonlinear Techniques
NASA Technical Reports Server (NTRS)
Skidmore, Trent
1990-01-01
A unique method is presented for collecting, studying and interpreting thought-related electroencephalogram (EEG) data. The use of a chaos based nonlinear analysis technique is shown to be promising in providing insight into relating conscious thought to specific EEG data. A discussion of the practical limitations of this technique is also included.
Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium
NASA Astrophysics Data System (ADS)
Chen, Jyh-Phen; Engelmann, Wolfgang; Baier, Gerold
1995-12-01
The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.
Nonlinear dynamics manuscript No. (will be inserted by the editor)
Paris-Sud XI, Université de
: gradient-based methods [11], genetic algorithms [12, 13], particle swarm optimization [14 18 the proposed technique. Keywords Chaos optimization algorithms · Nonlinear test functions · 2-D Discrete map and more recently in global optimization algorithms where introduction of chaotic numbers instead of random
NASA Astrophysics Data System (ADS)
Kravtsov, Nikolai V.; Sidorov, S. S.; Pashinin, Pavel P.; Firsov, V. V.; Chekina, S. N.
2004-04-01
The peculiarities of nonlinear dynamics of solid-state bidirectional ring Nd:YAG chip lasers are studied theoretically and experimentally during periodic modulation of mechanical stresses in the active element. It is shown that modulation of mechanical stresses is an effective method for exciting dynamic chaos in a monolithic chip laser.
Chaos, Boltzmann, Shannon and Electroencephalography
NASA Astrophysics Data System (ADS)
Albano, A. M.; Duckrow, R. B.
2008-06-01
Nonlinear dynamics has made possible the development of new tools for the quantitative analysis of electroencephalographic (EEG) signals. Some of the tools used in the initial applications required large quantities of noise-free, stationary data which are usually not available from biological systems. Information theoretic measures calculated using coarsegrained data are more appropriate for the analysis of these data. We review Nonlinear Dynamics and some nonlinear dynamical tools, introduce some Information Theoretic notions and use Mutual Information and Transfer Entropy to probe relationships among data streams in 19-channel scalp EEG recorded during three sleep stages-wakefulness, slow-wave sleep, and REM sleep.
Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence
NASA Technical Reports Server (NTRS)
Lipsitz, L. A.; Goldberger, A. L.
1992-01-01
The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.
Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure
NASA Technical Reports Server (NTRS)
Maestrello, L.
2000-01-01
Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.
ORNL/TM-13283 PROSPECTS FOR CHAOS CONTROL OF
Hively, Lee M.
ORNL/TM-13283 PROSPECTS FOR CHAOS CONTROL OF MACHINE TOOL CHATTER L. M. Hively V. A. Protopopescu N. #12;ORNL/TM-13283 PROSPECTS FOR CHAOS CONTROL OF MACHINE TOOL CHATTER L. M. Hively V. A. Protopopescu
Emergence of nonlinear behavior in the dynamics of ultracold bosons
Benoit Vermersch; Jean Claude Garreau
2015-01-28
We study the evolution of a system of interacting ultracold bosons, which presents nonlinear, chaotic, behaviors in the limit of very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches : Exact diagonalization, truncated Husimi method and mean-field (Gross-Pitaevskii) approximation, we put into evidence the destructive impact of quantum noise on the emergence of the nonlinear dynamics.
Emergence of nonlinear behavior in the dynamics of ultracold bosons
NASA Astrophysics Data System (ADS)
Vermersch, Benoît; Garreau, Jean Claude
2015-04-01
We study the evolution of a system of interacting ultracold bosons which presents nonlinear, chaotic behaviors in the limit of a very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches—exact diagonalization, the truncated Husimi method, and the mean-field (Gross-Pitaevskii) approximation—we put into evidence the destructive impact of quantum noise on the emergence of nonlinear dynamics.
Nonlinear analysis and prediction of pulsatile hormone secretion
Prank, K. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany)]|[Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States); Kloppstech, M. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany); Nowlan, S.J. [Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States); Harms, H.M.; Brabant, G.; Hesch, R. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany); Sejnowski, T.J. [Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States)
1996-06-01
Pulsatile hormone secretion is observed in almost every hormonal system. The frequency of episodic hormone release ranges from approximately 10 to 100 pulses in 24 hours. This temporal mode of secretion is an important feature of intercellular information transfer in addition to a dose-response dependent regulation. It has been demonstrated in a number of experiments that changes in the temporal pattern of pulsatile hormone secretion specifically regulate cellular and organ function and structure. Recent evidence links osteoporosis, a disease characterized by loss of bone mass and structure, to changes in the dynamics of pulsatile parathyroid hormone (PTH) secretion. In our study we applied nonlinear and linear time series prediction to characterize the secretory dynamics of PTH in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack periods of high predictability found in normal humans. In contrast to patients with osteoporosis patients with hyperparathyroidism, a condition which despite sometimes reduced bone mass has a preserved bone architecture, show periods of high predictability of PTH secretion. Using stochastic surrogate data sets which match certain statistical properties of the original time series significant nonlinear determinism could be found for the PTH time series of a group of healthy subjects. Using classical nonlinear analytical techniques we could demonstrate that the irregular pattern of pulsatile PTH secretion in healthy men exhibits characteristics of deterministic chaos. Pulsatile secretion of PTH in healthy subjects seems to be a first example of nonlinear determinism in an apparently irregular hormonal rhythm in human physiology. {copyright} {ital 1996 American Institute of Physics.}
Parameter identification using experimental nonlinear dynamics and chaos
Chancellor, Roy Scott
1993-01-01
III EXPERIMENTAL SETUP . 18 3. 1 3. 2 3. 3 3. 4 Overview . Overview of Complete Test Setup Vibration Hardware Electronic Integration Circuit 18 18 20 22 TABLE OF CONTENTS (continued) CHAPTER Page 3. 4. 1 Theory 3. 4. 2 Circuit Design... Transfer Function for Inverting Amplifier. . . . . . Transfer Function for Passive High-Pass Filter. . . Equations of Motion for Double Integrating Circuit 112 113 115 115 117 EXPERIMENTAL FREQUENCY RESPONSE PLOTS FOR PRELIMINARY INTEGRATOR DESIGN...
Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos Irving R. Epstein*
Showalter, Kenneth
, West Virginia UniVersity, Morgantown, West Virginia 26506-6045 ReceiVed: NoVember 30, 1995; In Final. I. Introduction If one were to show a freshman chemistry class two beakers of solution and suggest
Transition probability from matter-wave soliton to chaos.
Zhu, Qianquan; Hai, Wenhua; Rong, Shiguang
2009-07-01
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice. PMID:19658788
Controlling transition probability from matter-wave soliton to chaos
Zhu, Qianquan; Rong, Shiguang
2008-01-01
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice it is demonstrated that under a stochastic initial set and in a given parameter region the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically, and different chaotic regions associated with different chaos probabilities are found. The results suggest a feasible method for eliminating or strengthening chaos by modulating the moving superlattice experimentally.
Controlling transition probability from matter-wave soliton to chaos
Qianquan Zhu; Wenhua Hai; Shiguang Rong
2008-04-06
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice it is demonstrated that under a stochastic initial set and in a given parameter region the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically, and different chaotic regions associated with different chaos probabilities are found. The results suggest a feasible method for eliminating or strengthening chaos by modulating the moving superlattice experimentally.
Transition probability from matter-wave soliton to chaos
Zhu Qianquan; Hai Wenhua; Rong Shiguang [Department of Physics and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 (China)
2009-07-15
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.
Issues of Chaos and Recurrence in Infinite Dimensions
Y. Charles Li
2009-11-16
Various issues with regard to chaos and recurrence in infinite dimensions are discussed. The doctrine we are trying to derive is that Sobolev spaces over bounded spatial domains do host chaos and recurrence, while Sobolev spaces over unbounded spatial domains are lack of chaos and recurrence. Local Sobolev spaces over unbounded spatial domains can host chaos and are natural phase spaces e.g. for fluid problems, but are very challenging to study.
Genome chaos: survival strategy during crisis.
Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H
2014-01-01
Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment. PMID:24299711
Transition probability from matter-wave soliton to chaos
Zhu Qianquan; Hai Wenhua; Rong Shiguang
2009-01-01
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities
Controlling transition probability from matter-wave soliton to chaos
Qianquan Zhu; Wenhua Hai; Shiguang Rong
2008-01-01
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice it is demonstrated that under a stochastic initial set and in a given parameter region the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically, and different chaotic regions associated with different chaos probabilities
Dynamical Systems, Optimization, and Chaos John B. Moore
Moore, John Barratt
Dynamical Systems, Optimization, and Chaos John B. Moore Department of Systems Engineering. Usually, chaos is avoided in performing a system design or optimization. The challenge before en- gineers is to somehow exploit the fascinating properties of chaos to enhance their system designs, and to further
Nonhyperbolic homoclinic chaos G. Cicogna (\\Lambda) and M. Santoprete
: 03.20, 05.45 Keywords: homoclinic chaos, nonhyperbolic critical point, Melnikov theory, SitnikovNonhyperbolic homoclinic chaos G. Cicogna (\\Lambda) and M. Santoprete Dipartimento di Fisica, Universit`a di Pisa, Via Buonarroti 2, Ed. B IÂ56127, Pisa, Italy Abstract. Homoclinic chaos is usually
Gaussian multiplicative Chaos for symmetric isotropic Laurent Chevillard
define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction.-P. Kahane introduced the theory of Gaussian multiplicative chaos. Given a metric space and a reference logarithmic correlations. Since this seminal work, the theory of Gaussian multiplicative chaos has found many
REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit
Logan, David
REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit Bo Denga) and Gwendolen Hinesb of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption not be properly understood without understanding the role chaos plays in food chains. Yet chaos generating
The Capabilities of Chaos and Complexity
Abel, David L.
2009-01-01
To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? PMID:19333445
NASA Astrophysics Data System (ADS)
Gekelman, Walter; Dehaas, Tim; van Compernolle, Bart
2013-10-01
Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data. The permutation entropy can be calculated from the time series of the magnetic field data or flows is used to calculate the positions of the data on a Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. Other types of chaotic dynamical models (Gissinger , Lorentz and Henon) also fall on the map and can give a clue to the nature of the turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time, which reflects the change and possibly type of chaos associated with the ropes. Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data. The permutation entropy can be calculated from the time series of the magnetic field data or flows is used to calculate the positions of the data on a Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. Other types of chaotic dynamical models (Gissinger , Lorentz and Henon) also fall on the map and can give a clue to the nature of the turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time, which reflects the change and possibly type of chaos associated with the ropes. Work sponsoerd by a LANL-UC grant and done at the Basic Plasma Science Facility (supported by DOE and NSF).
Reexamination of measurement-induced chaos in entanglement-purification protocols
NASA Astrophysics Data System (ADS)
Guan, Yilun; Nguyen, Duy Quang; Xu, Jingwei; Gong, Jiangbin
2013-05-01
Entanglement-purification protocols, developed for the sake of high-fidelity communication through noisy quantum channels, are highly nonlinear quantum operations and can offer a very useful context to studies of nonlinear complex maps. Recently it was demonstrated that the feedback mechanism used in a typical purification protocol can cause the evolution dynamics of qubits to exhibit chaos [Kiss , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.100501 107, 100501 (2011)]. In this work we extend the investigation by considering the natural time evolution of qubits during a purification process, leading to a number of interesting findings that reflect the competition between the natural unitary evolution of qubits and nonlinear purification operations. As a result, the overall evolution dynamics of entanglement can be much richer. Possible applications are also proposed.
GENERAL: Bifurcation control and chaos in a linear impulsive system
NASA Astrophysics Data System (ADS)
Jiang, Gui-Rong; Xu, Bu-Gong; Yang, Qi-Gui
2009-12-01
Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.
Bifurcations and chaos in register transitions of excised larynx experiments
NASA Astrophysics Data System (ADS)
Tokuda, Isao T.; Horá?ek, Jaromir; Švec, Jan G.; Herzel, Hanspeter
2008-03-01
Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.
Topological approximation of the nonlinear Anderson model.
Milovanov, Alexander V; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t?+?. The second moment of the associated probability distribution grows with time as a power law ? t^{?}, with the exponent ?=1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport. PMID:25019865
Applications of chaos in biology and medicine
Ditto, W.L. [Applied Chaos Laboratory, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430 (United States)
1996-06-01
Before its discovery chaos was inevitably confused with randomness and indeterminacy. Because may systems {ital appeared} random, they were actually thought to {ital be} random. This was true despite the fact that many of these systems seemed to display intermittent almost periodic behavior before returning to more {open_quote}{open_quote}random{close_quote}{close_quote} or irregular motion. Indeed this observation leads to one of the defining features of chaos: the superposition of a very large number of unstable periodic motions. Thus the identification in biological systems of unstable periodic or fixed point behavior consistent with chaos makes new therapeutic strategies possible. Recently we were able to exploit such unstable periodic fixed points to achieve control in two experimental systems: in cardiac tissue and brain tissue. {copyright} {ital 1996 American Institute of Physics.}
Chaos, dynamical structure, and climate variability
Stewart, H.B. [Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States)
1996-06-01
Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here we propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. {copyright} {ital 1996 American Institute of Physics.}
Chaos Lab: An Orderly Pursuit of Disorder
NSDL National Science Digital Library
1969-12-31
Chaos Lab is a great piece of software that teaches users about fractals and chaos theory. The menu-driven interface is extremely easy to use; however, a significant drawback of the software is its poor documentation. This can make experimenting with the settings more fun, but it would be helpful to have better explanations of the more obscure functions. What Chaos Lab lacks in documentation, it makes up for in the remarkable visual representations of famous fractals. The Mandelbrot and Julia sets can be explored with simple zooming tools, equation definitions, and brilliant color selections. Many more options are available, making the program a powerful educational tool in a small package. It is a free download.
Chaos and fractals in digital holography
NASA Astrophysics Data System (ADS)
Wang, Tianji; Yang, Shining; Li, Yaotang; Zhang, Shichao; Fan, Shaowu; Wen, Huanrong
1997-05-01
Digital pixel holography on the basis of scalar diffraction theory has an effective security function in anti- counterfeiting technology. The digital pixel hologram is in reality a diffraction element. The digital pixel hologram is a laser lithographic image to produce high efficiency volume phase only computer generated holographic diffraction grating. The use of the Postscript language program and the chaos fractal patterns generating program as an interface between the mathematical coding and the laser lithographic device is effective, since this model has flexible and powerful security function for anti-counterfeiting technology. The Postscript files and chaos fractal patterns generating program can control the lithographic system which has a Postscript and chaos fractal patterns generating interpreter.
R. G. Andrzejak; G. Widman; K. Lehnertz; C. Rieke; P. David; C. E. Elger
2001-01-01
The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present
The uncertainty principle and quantum chaos
NASA Technical Reports Server (NTRS)
Chirikov, Boris V.
1993-01-01
The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.
On chaos synchronization and secure communication.
Kinzel, W; Englert, A; Kanter, I
2010-01-28
Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. PMID:20008407
Noise-induced chaos-order transitions
NASA Astrophysics Data System (ADS)
Gassmann, Fritz
1997-03-01
Numerical simulations of the Lorenzian water wheel have been used to investigate the influence of stochastic noise on the lifetimes of chaotic transients. Whereas, in one region of parameter space no noise dependency could be detected, a shortening of the lifetimes of more than four decades was found in another region. This large effect was produced by a significant modification of the attraction basin of a quasistable stationary state rather than by affecting the chaotic orbits before the chaos-order transitions occurred. This novel phenomenon of noise-induced chaos-order transitions is not related to stochastic resonance or other noise-induced effects.
Cultural chaos in the trenches: staff perspectives.
Untied, P
1999-03-01
When a hospital is acquired by a large health care organization, there are many challenges, for both the hospital and the organization. When the differences in culture are not addressed effectively by management at the time of acquisition, this can result in cultural chaos for the staff and a lengthened transition time. In this article, a staff member shares the observations, opinions, and feelings she experienced during such a time of cultural chaos between two well-respected organizations. Her opinions and observations are juxtaposed with the lives of two amalgamated fictionalized characters. PMID:10373980
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…
Borgogno, D. [Dipartimento di Energetica, Politecnico di Torino, Torino (Italy); Grasso, D. [CNR Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Dipartimento di Energetica, Politecnico di Torino, Torino (Italy); Pegoraro, F. [Department of Physics, Pisa University, Pisa CNISM (Italy); Schep, T. J. [Department of Physics, Eindhoven University of Technology, Eindhoven (Netherlands)
2011-10-15
The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
NASA Astrophysics Data System (ADS)
Makarov, D. V.; Kon’kov, L. E.
2015-03-01
The motion of a randomly driven quantum nonlinear pendulum is considered. Utilizing a one-step Poincaré map, we demonstrate that the classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study the influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. The transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
Denis Makarov; Leonid Kon'kov
2015-02-06
Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. Transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
Chaos in an Eulerian Based Model of Sickle Cell Blood Flow
NASA Astrophysics Data System (ADS)
Apori, Akwasi; Harris, Wesley
2001-11-01
A novel Eulerian model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This Eulerian model was based on extending previous models of sickle cell blood flow which were limited due to their Lagrangian formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.
Cantrell, John H; Adler, Laszlo; Yost, William T
2015-02-01
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5?MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2?nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported. PMID:25725651
NASA Astrophysics Data System (ADS)
Cantrell, John H.; Adler, Laszlo; Yost, William T.
2015-02-01
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.
NASA Astrophysics Data System (ADS)
Luo, Shaohua; Wu, Songli; Gao, Ruizhen
2015-07-01
This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.
Order, chaos and nuclear dynamics: An introduction
Swiatecki, W.J.
1990-08-01
This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs.
Propagation of Chaos in a Coagulation Model
Escobedo, Miguel
2011-01-01
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the corresponding coagulation equation is recovered and global in time propagation of chaos holds.
Les ordinateurs quantiques affrontent le chaos
Bertrand Georgeot; Dima L. Shepelyansky
2003-01-01
Quantum computers facing chaos. Quantum parallelism allows to perform computation in a radically new manner. A quantum computer based on these new principles may resolve certain problems exponentially faster than a classical computer. We discuss how quantum computers can simulate complex dynamics, in particularly the dynamics of chaotic systems, where the errors of classical computation grow exponentially fast. ----- Le
Chaos in Practice: Techniques for Career Counsellors
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim
2005-01-01
The chaos theory of careers emphasises continual change, the centrality and importance of chance events, the potential of minor events to have disproportionately large impacts on subsequent events, and the capacity for dramatic phase shifts in career behaviour. This approach challenges traditional approaches to career counselling, assumptions…
Automotive 2020 Clarity beyond the chaos
Automotive 2020 Clarity beyond the chaos Automotive IBM Institute for Business Value IBM Global@us.ibm.com for more information. #12;1 The automotive ecosystem is in the midst of significant change, with increasing for information, environmental responsibility and safety. Automotive companies are racing to develop new business
Fractional chaos based communication systems —an introduction
Juebang Yu
2008-01-01
As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research
The Chemical Imaging Initiative Dr. Chao Yang
Berkeley National Laboratory "Computational Approaches to Largescale Xray Image Electron Analysis The Chemical Imaging Initiative Presents Dr. Chao Yang Computational Research Division Lawrence" May 20, 2011 EMSL 1077 11:00 am The latest advances in Xray and electron light source
Neural control: Chaos control sets the pace
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2010-03-01
Even simple creatures, such as cockroaches, are capable of complex responses to changes in their environment. But robots usually require complicated dedicated control circuits to perform just a single action. Chaos control theory could allow simpler control strategies to realize more complex behaviour.
Chaos: Connecting Science and the Humanities
NSDL National Science Digital Library
David Paddy
2005-01-01
In this article, we learn about a team-taught course entitled Chaos in Science and Literature. The goals of the course were to place science in a nontechnological context, emphasizing its intellectual and cultural aspects, and to provide a forum for the exchange of ideas between "scientists" and "humanists," with the authors serving as role models.
Propagation of Chaos in a Coagulation Model
Miguel Escobedo; Federica Pezzotti
2011-10-13
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the corresponding coagulation equation is recovered and global in time propagation of chaos holds.
Introduction to Chaos in Deterministic Systems
Carlos Gershenson
2004-10-07
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using the logistic map and its bifurcation diagram. We also show the universality found in "the route to chaos". The user is only required to have notions of algebra, so it is quite accessible. The formal basis of chaos theory are not covered in this introduction, but are pointed out for the reader interested in them. Therefore, this package is also useful for people who are interested in going deep into the mathematical theories, because it is a simple introduction of the terminology, and because it points out which are the original sources of information (so there is no danger in falling in the trap of "Learn Chaos in 48 hours" or "Bifurcation Diagrams for Dummies"). The included exercises are suggested for consolidating the covered topics. The on-line resources are highly recommended for extending this brief induction.
CHAOS THEORY AND DYNAMICAL SYSTEMS MICHAEL KRIHELI
Megrelishvili, Michael
CHAOS THEORY AND DYNAMICAL SYSTEMS MICHAEL KRIHELI Contents 1. Iterates and Orbits 1 2. Fixed Points and Periodic Points 1 3. Attracting and Repelling Fixed Points 2 4. Bifurcation 2 5. The Magic a S is said to be a fixed point of f if f(a) = a. 2. Fixed Points and Periodic Points Definition 2.1. Let f
Chaos-based cryptography: a brief overview
Ljupco Kocarev
2001-01-01
Over the past decade, there has been tremendous interest in studying the behavior of chaotic systems. They are characterized by sensitive dependence on initial conditions, similarity to random behavior, and continuous broad-band power spectrum. Chaos has potential applications in several functional blocks of a digital communication system: compression, encryption and modulation. The possibility for self-synchronization of chaotic oscillations has sparked
Chaos-Assisted Tunneling in Atom Optics
Daniel A. Steck
2003-01-01
The study of atomic motion in time-dependent optical lattices has become an important paradigm in the field of quantum chaos. We have extended this line of research to the study of precisely prepared, uncertainty-limited wave packets in phase space. These wave packets can resolve features in a mixed classical phase space, where stable and chaotic behaviors coexist, opening up intriguing
Dimensie en Dispersie het `meten' van chaos
Broer, H.W.
. . . Een manier om dit te begrijpen gaat als volgt. Neem eenheidsinterval [0, 1] Hoeveel intervalletjes ter III De Sierpinski driehoek Sp. Neem zijde van lengte 1. Overdekking met driehoekjes met zijde Direct (1857-1918) (1941-) Chaos Â p.11 #12;Dispersie exponent I Neem de Bakkers transformatie B : x [0, 1] 2
Chaos in three species food chains
Aaron Klebanoff; Alan Hastings
1994-01-01
We study the dynamics of a three species food chain using bifurcation theory to demonstrate the existence of chaotic dynamics in the neighborhood of the equilibrium where the top species in the food chain is absent. The goal of our study is to demonstrate the presence of chaos in a class of ecological models, rather than just in a specific
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image of a portion of the Iani Chaos region was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -2.6 Longitude 342.4 East (17.6 West). 36 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.
Xin-She Yang; LEEDS LS
2001-01-01
A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks with time delay and nonlinear interaction show chaotic features in the system response when nonlinear interaction is strong enough or the length scale is large enough. In
Nonlinear Lattice Waves in Random Potentials
Sergej Flach
2014-09-10
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.
Bifurcation and chaos in the spontaneously firing spike train of cultured neuronal network
NASA Astrophysics Data System (ADS)
Chen, Wenjuan; Li, Xiangning; Zhu, Geng; Zhou, Wei; Zeng, Shaoqun; Luo, Qingming
2008-02-01
Both neuroscience and nonlinear science have focused attention on the dynamics of the neural network. However, litter is known concerning the electrical activity of the cultured neuronal network because of the high complexity and moment change. Instead of traditional methods, we use chaotic time series analysis and temporal coding to analyze the spontaneous firing spike train recorded from hippocampal neuronal network cultured on multi-electrode array. When analyzing interspike interval series of different firing patterns, we found when single spike and burst alternate, the largest Lyapunov exponent of interspike interval (ISI) series is positive. It suggests that chaos should exist. Furthermore, a nonlinear phenomenon of bifurcation is found in the ISI vs. number histogram. It determined that this complex firing pattern of neuron and the irregular ISI series were resulted from deterministic factors and chaos should exist in cultured term.These results suggest that chaotic time series analysis and temporal coding provide us effective methods to investigate the role played by deterministic and stochastic component in neuron information coding, but further research should be carried out because of the high complexity and remarkable noise of the electric activity.
Neutral line chaos and phase space structure
NASA Technical Reports Server (NTRS)
Burkhart, Grant R.; Speiser, Theodore W.; Martin, Richard F., Jr.; Dusenbery, Paul B.
1991-01-01
Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.
Quasiperiodicity and chaos in cardiac fibrillation.
Garfinkel, A; Chen, P S; Walter, D O; Karagueuzian, H S; Kogan, B; Evans, S J; Karpoukhin, M; Hwang, C; Uchida, T; Gotoh, M; Nwasokwa, O; Sager, P; Weiss, J N
1997-01-01
In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillation-like activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches. PMID:9005999
A Chaos-Based Robust Software Watermarking
Fenlin Liu; Bin Lu; Xiangyang Luo
2006-01-01
\\u000a In this paper we propose a robust software watermarking based on chaos against several limitations of existing software watermarking.\\u000a The algorithm combines the anti-reverse engineering technique, chaotic system and the idea of Easter Egg software watermarks.\\u000a The global protection for the program is provided by dispersing watermark over the whole code of the program with chaotic\\u000a dispersion coding; the resistance
Chaos in the lowest Landau level
Emery, V.J.
1991-01-01
The problem of a few electrons in the lowest Landau level is discussed. Low-lying states of the three-and four-electron problems are constructed. In the classical limit, the three-body problem is integrable but there is numerical evidence of chaotic motion in the four-body problem. Consequences of classical chaos for the statistics of energy levels are described and the possibility of carrying out relevant experiments in semiconductor heterostructures is discussed. 9 refs.
Chaos-Based Public-Key Cryptography
Igor Mishkovski; Ljupco Kocarev
\\u000a In this chapter we give an overview and the state of the art in the field of Chaos-based cryptography. The public key cryptosystems\\u000a based on Chebyshev polynomials enjoy some nice chaotic properties, which makes them suitable for use in both encryption and\\u000a digital signature. The cryptosystem can work either on real or integer numbers. The cryptosystem that works on real
Reducing or enhancing chaos using periodic orbits
Romain Bachelard; Cristel Chandre; Xavier Leoncini
2006-01-19
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.
Nuclear Level Density, Quantum Chaos and Thermalization
NASA Astrophysics Data System (ADS)
Zelevinsky, Vladimir; Sen'kov, Roman
An algorithm for calculating the level density for a given shell-model Hamiltonian without diagonalzation of a huge matrix is presented and explained. The level density is expressed in terms of the moments (traces) of the Hamiltonian over the restricted orbital space. The underlying physics is that of quantum chaos and intrinsic thermalization in closed systems of interacting particles. We show the examples of the approach and briefly discuss the dependence of the level density on the interaction parameters.
Chaos, dynamical structure and climate variability
Stewart, H.B. [Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science
1995-09-01
Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.
Detecting chaos in irregularly sampled time series.
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. PMID:24089946
Probing temperature chaos through thermal boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut
2015-03-01
Using population annealing Monte Carlo, we numerically study temperature chaos in the three-dimensional Edwards-Anderson Ising spin glass using thermal boundary conditions. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. By studying salient features in the specific heat we show evidence of temperature chaos. Our results suggest that these bumps are mainly caused by system-size excitations where the free energy of two boundary conditions cross. Furthermore, we study the scaling of both entropy and energy at boundary condition crossings and find that the scaling of the energy is very different from the scaling obtained by a simple change of boundary conditions. We attribute this difference to the stronger finite-size effects induced via a simple change of boundary conditions. Finally, we show that temperature chaos occurs more frequently at higher temperatures within the spin-glass phase and for larger system sizes, while the normalized distribution function with respect to temperature is about the same for different system sizes. The work is supported from NSF (Grant No. DMR-1208046).
Nonlinear Dynamics, Magnitude-Period Formula and Forecasts on Earthquake
Chang, Yi-Fang
2008-01-01
Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold value of rock due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum. From the nonlinear equations of fluid mechanics, a simplified nonlinear solution of momentum corresponding the accumulation of the energy could be derived. Otherwise, a chaos equation could be obtained, in which chaos corresponds to the earthquake, which shows complexity on seismology, and impossibility of exact prediction of earthquakes. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, the magnitude-period formula of the earthquake may be derived approximately, and some results can be calculated quantitatively. For example, we forecast a series of earthquakes of 2004, 2009 and 2014, especially in 2019 in California. Combining the Lorenz model, we discuss the earthquake migration to and fro. Moreover, many external causes for earthquake are merely...
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.
Dynamics of a Limit Cycle Oscillator under Time Delayed Linear and Nonlinear Feedbacks
D. V. Ramana Reddy; A. Sen; G. L. Johnston
1999-01-01
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos. Such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle
Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks
D. V. Ramana Reddy; A. Sen; G. L. Johnston
2000-01-01
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips, frequency suppression, multiple periodic states and chaos. Such phenomena are frequently observed in the collective behavior of a large number of coupled limit cycle
Nonlinear Analysis of the Light Curve of the Variable Star R Scuti
J. R. Buchler; Z. Kollath; T. Serre; J. Mattei
1996-01-01
It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multiperiodic and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time series analysis, the global flow reconstruction technique,
Modeling of chaotic DC-DC converters by iterated nonlinear mappings
David C. Hamill; Jonathan H. B. Deane; David J. Jefferies
1992-01-01
In parameter ranges where conventional methods break down, DC-DC converters may be described by iterated mappings, a nonlinear discrete modeling technique. The underlying principles are explained and are applied to the example of a PWM-controlled buck converter. Stable behavior and bifurcations to chaos are predicted by numerical evaluation of the governing mapping and are confirmed by experiment
Adaptive anti control of chaos for robot manipulators with experimental evaluations
NASA Astrophysics Data System (ADS)
Moreno-Valenzuela, Javier
2013-01-01
Roughly speaking, anti control of chaos consists in injecting a chaotic behavior to a system by means of a control scheme. This note introduces a new scheme to solve the anti control of chaos for robot manipulators. The proposed controller uses an adaption law to estimate the robot parameters on line. Thus, the controller does not require any knowledge of the physical parameters of the manipulator, such as masses, lengths of the links, moments of inertia, etc. The new scheme is based in the velocity field control paradigm, hence the specification of a chaotic system to define a desired velocity field is required. Experimental results in a two degrees-of-freedom direct-drive robot illustrate the practical feasibility of the introduced theory. In order to achieve anti control of chaos of our experimental system, two different chaotic attractors are used: the Genesio-Tesi system and a Jerk-type system. Results showed that the controller is able to inject the chaotic behavior to the robot while the robot parameters are estimated on line.
Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation
NASA Technical Reports Server (NTRS)
Moon, H. T.; Goldman, M. V.
1984-01-01
The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.
Complexity in the nonlinear Dieterich-Ruina friction law
Brittany Angela Erickson
2010-01-01
We investigate the emergent dynamics when the nonlinear Dieterich-Ruina rate and state friction law is attached to a Burridge-Knopoff spring-block model. For a single block with this friction law, the system undergoes a transition to chaos in the numerical solution when a specific parameter is increased and we discuss the model's ability to capture 1-dimensional earthquake motion. Taking this study
Maxwell on Chaos Brian R. Hunt and James A. Yorke*
Yorke, James
. I Maxwell on Chaos Brian R. Hunt and James A. Yorke* James Clerk Maxwell (1831-1879) is perhaps. They can be reached by eleclronic mail aliwIII@ipSI.umd.edu. James Clerk'Maxwell. Courtesy of American Articles in this issue... Scientific Article Maxwell on Chaos Brian R. Hunt and James A. Yorke Feature
Diagnostics of the generalized synchronization in microwave generators of chaos
A. V. Starodubov; A. A. Koronovskii; A. E. Khramov; Yu. D. Zharkov; B. S. Dmitriev; V. N. Skorokhodov
2010-01-01
The generalized synchronization of chaos in a system of microwave generators based on klystron amplifiers with delayed feedback\\u000a has been studied. A modification of the nearest neighbors method for diagnostics of generalized synchronization of chaos in\\u000a systems with delayed feedback is developed. The efficiency of the modified method for processing experimental data is shown.
Controlling chaos in a Lorenz-like system using feedback
G. Kociuba; N. R. Heckenberg
2003-01-01
We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or
Analysis of Chaos-Based Coded Modulations under Intersymbol Interference
Rey Juan Carlos, Universidad
Analysis of Chaos-Based Coded Modulations under Intersymbol Interference Francisco J. Escribano's) in channels with time-invariant intersymbol interference (ISI). We use the ISI distance spectrum of the CCM are of potential interest in this kind of distorting environment. Index Terms--Chaos, Intersymbol interference
Analysis of Discovery of Chaos: Social and Cognitive Aspects.
ERIC Educational Resources Information Center
Kim, J. B.
The purpose of this study was to examine Edward Lorenz's psychological processes and other environmental aspects in the discovery of chaos at that time. The general concept of chaos is discussed based on relations with previous scientific theories such as Newtonian physics and quantum mechanics. The constraints of discovery in terms of available…
Quantum Chaos Fundamental Problems an Application to Material Science
Katsuhiro Nakamura
1989-01-01
We investigate quantum mechanics of nonintegrable and chaotic systems. Two realistic examples of quantum chaos in magnetic phenomena are given: (1) Quantum billiard in a magnetic field; (2) quantum dynamics of a pulsed spin system. In these examples, we discuss salient aspects of irregular energy spectra and complicated quantum diffusion. Then, fundamental problems of quantum chaos are examined from a
Chaos: A Topic for Interdisciplinary Education in Physics
ERIC Educational Resources Information Center
Bae, Saebyok
2009-01-01
Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…
Master Teachers: Making a Difference on the Edge of Chaos
ERIC Educational Resources Information Center
Chapin, Dexter
2008-01-01
The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…
The Chaos Theory of Careers: A User's Guide
ERIC Educational Resources Information Center
Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…
The Origin of Chaos in the Outer Solar System
Murray, Norman
responsible for the acceptance of Newton's theory of gravitation. Despite this, Newton doubted the longThe Origin of Chaos in the Outer Solar System N. Murray1 and M. Holman2 Classical analytic theories. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the jovian planets
Uncertainty Propagation in CFD Using Polynomial Chaos Decomposition
O. M. Knio
2005-01-01
Uncertainty quantication (UQ) in CFD computations is receiving increased in- terest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent applica- tion of Polynomial Chaos (PC) methods for uncertainty representation and propa- gation in CFD computations. The fundamental concept on which Polynomial Chaos (PC) representations
Chaos-pass filtering in injection-locked semiconductor lasers
Atsushi Murakami; K. Alan Shore
2005-01-01
Chaos-pass filtering (CPF) of semiconductor lasers has been studied theoretically. CPF is a phenomenon which occurs in laser chaos synchronization by injection locking and is a fundamental technique for the extraction of messages at the receiver laser in chaotic communications systems. We employ a simple theory based on driven damped oscillators to clarify the physical background of CPF. The receiver
Communication using Synchronization of Chaos in Semiconductor Lasers with optoelectronic
Illing, Lucas
Communication using Synchronization of Chaos in Semiconductor Lasers with optoelectronic feedback S scheme based on the synchronization of two chaotic semiconductor lasers is experimentally tested. The Chaos in the single-mode semiconductor lasers is generated by means of an optoelectronic feedback
Determinisme, Chaos en Toeval Instituut voor Wiskunde en Informatica
Broer, H.W.
://www.math.rug.nl/~broer Chaos p.2 #12;Newton en Laplace Isaac Newton Pierre-Simon Laplace (1642-1727) (1749-1827) Zonnestelsel Groningen Chaos p.1 #12;Helden - Newton en Laplace - Leibniz en Voltaire - Poincaré en Kolmogorov - Lorenz
Universality in dynamical formation of entanglement for quantum chaos
Kubotani, Hiroto; Toda, Mikito; Adachi, Satoshi [Institute of Physics, Faculty of Engineering, Kanagawa University, Yokohama 221-8686 (Japan); Department of Physics, Faculty of Science, Nara Women's University, Nara 630-8506 (Japan); Department of Physics, Faculty of Science, Tokyo Institute of Technology, Meguro 152-8550 (Japan)
2006-09-15
Dynamical formation of entanglement is studied for quantum chaotic biparticle systems. We find that statistical properties of the Schmidt eigenvalues for strong chaos are well described by the random matrix theory of the Laguerre unitary ensemble. This implies that entanglement formation for quantum chaos has universal properties, and does not depend on specific aspects of the systems.
Chaos and cryptography: block encryption ciphers based on chaotic maps
Goce Jakimoski; Ljupco Kocarev
2001-01-01
This paper is devoted to the analysis of the impact of chaos-based techniques on block encryption ciphers. We present several chaos based ciphers. Using the well-known principles in the cryptanalysis we show that these ciphers do not behave worse than the standard ones, opening in this way a novel approach to the design of block encryption ciphers
Topics in Quantum Chaos and Thermoelectricity A thesis presented
Heller, Eric
Topics in Quantum Chaos and Thermoelectricity A thesis presented by William Edward Bies Bies All rights reserved #12; Abstract Topics in Quantum Chaos and Thermoelectricity William Edward of semiclassical theory. In Part II we study thermoelectric e#11;ects in anisotropic materials. As a direct
Using a quantum computer to investigate quantum chaos
Ruediger Schack
1997-05-10
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Large fluctuations and nonlinear dynamics of birhythmicity
NASA Astrophysics Data System (ADS)
Kar, S.; Ray, D. S.
2004-07-01
Birhythmicity, which arises due to the simultaneous existence of two stable limit cycles, has been shown to be an interesting dynamical scenario in chemical reactions and biology. Here we present an extension of the Decroly-Goldbeter model for birhythmicity in glycolysis within a Hamiltonian structure incorporating the stochastic substrate injection rate, the critical controlling factor in glycolytic oscillations. Our analysis reveals several generic features of nonlinear dynamics of birhythmicity in the weak-noise limit, e.g., crossover of birhythmicity to monorhythmic behaviour, period-doubling bifurcations leading to chaos and noise-induced transition between attractors.
Nonlinearity of TCP and instability with RED
NASA Astrophysics Data System (ADS)
La, Richard J.; Ranjan, Priya; Abed, Eyad H.
2002-07-01
Recently researchers have proposed active queue management (AQM) mechanisms as a means of better managing congestion at the bottlenecks inside the network. Random Early Detection (RED) mechanism has been proposed to control the average queue size at the congested routers. It has been shown that the interaction between an RED gateway and TCP connections can lead to period doubling bifurcation and chaos. In this paper we extend this model and study the interaction of the RED gateway with TCP and UDP connections, using a discrete-time model. First, we show that the presence of UDP traffic does much more than simply taking away the available capacity from the TCP connections. In fact it fundamentally changes the dynamics of the system. Second, with the help of bifurcation diagrams, we demonstrate the existence of nonlinear phenomena, such as oscillations and chaos, as the parameters of the RED mechanism are varied. Further, the presence of UDP traffic tends to stabilize the system in the sense that bifurcations and chaos are delayed in the parameter region. We investigate the impact of various system parameters on the stability of the system, present numerical results, and validate our analysis through ns-2 simulation.
Boyer, Edmond
@edu.univ-fcomte.fr Abstract--A new framework for information hiding security, called chaos-security, has been proposed of security, as stego-security, are more linked to information leaks. It has been proven that spread- spectrum that the new framework for security tends to improve the ability to compare data hiding scheme. Keywords-Information
Jones, Antonia J.
DRACOPOULOS AND JONES: ADAPTIVE NEURO-GENETIC CONTROL OF CHAOS 1 Adaptive Neuro-Genetic Control supported by SERC grant 90800355. #12;DRACOPOULOS AND JONES: ADAPTIVE NEURO-GENETIC CONTROL OF CHAOS 2, the neuro-genetic controller may use large control adjustments and proves capable of effectively attaining
Hyperlabyrinth chaos: From chaotic walks to spatiotemporal chaos Konstantinos E. Chlouverakis
Sprott, Julien Clinton
ordinary differential equations CODEs in a ring architecture that was originally proposed by Thomas et al.8 September 2007; published online 21 May 2007 In this paper we examine a very simple and elegant example of high-dimensional chaos in a coupled array of flows in ring architecture that is cyclically symmetric
nonlinearity G-perfect nonlinearity
Poinsot, Laurent
nonlinearity Bent functions Difference sets Application of bent functions 3 Group action based perfect on cryptanalysis 2 Traditional Approach Perfect nonlinearity Bent functions Difference sets Application of bent Basics on cryptography Basics on cryptanalysis 2 Traditional Approach Perfect nonlinearity Bent functions
NSDL National Science Digital Library
Springer-Verlag Heidelberg.
Springer-Verlag Journals Preview Service (discussed in the September 17, 1997 issue of the Scout Report for Science & Engineering) has been integrated into Springer-Verlag's LINK service. This free service provides users with the most recent tables of contents and abstracts from more than 200 journals retrievable via LINK. Each new table of contents, with links to respective abstracts, is sent automatically to you via e-mail as soon as it becomes available electronically. To subscribe, users select one or more journals from an alphabetical list or click on an area of interest. Once an email address is entered, subscribers receive a confirmation message. Note that LINK Alert replaces SVJPS.
Exploring Information Chaos in Community Pharmacy Handoffs
Chui, Michelle A; Stone, Jamie A
2013-01-01
Background A handoff is the process of conveying necessary information in order to transfer primary responsibility for providing safe and effective drug therapy to a patient from one community pharmacist to another, typically during a shift change. The handoff information conveyed in pharmacies has been shown to be unstructured and variable, leading to pharmacist stress and frustration, prescription delays, and medication errors. Objective The purpose of this study was to describe and categorize the information hazards present in handoffs in community pharmacies. Methods A qualitative research approach was used to elicit the subjective experiences of community pharmacists. Community pharmacists who float or work in busy community pharmacies were recruited and participated in a face to face semi-structured interview. Using a systematic content data analysis, the study identified five categories of information hazards that can lead to information chaos, a framework grounded in human factors and ergonomics. Results Information hazards including erroneous information and information overload, underload, scatter, and conflict, are experienced routinely by community pharmacists during handoff communication and can result in information chaos. The consequences of information chaos include increased mental workload, which can precipitate problematic prescriptions “falling between the cracks”. This can ultimately impact patient care and pharmacist quality of working life. Conclusions The results suggest that handoffs in community pharmacies result in information hazards. These information hazards can distract pharmacists from their primary work of assessing prescriptions and educating their patients. Further research on how handoffs are conducted can produce information on how hazards in the system can be eliminated. PMID:23665076
NASA Astrophysics Data System (ADS)
Zavrazhina, T. V.
2007-10-01
A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ?2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.
Controlling chaos in ecology: from deterministic to individual-based models.
Solé, R V; Gamarra, J G; Ginovart, M; López, D
1999-11-01
The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested. PMID:17879875
NSDL National Science Digital Library
Charnine, Michael
This compiled site contains titles and links to over 40 sites, journal articles, course and tutorial materials, simulations, batteries, and other resources. Definitions of chemistry, theoretical chemistry, organic, physical and nuclear chemistry are integrated with the links to outside materials. A number of useful keywords are included to help users navigate the materials.
Beyond Benford's Law: Distinguishing Noise from Chaos
Li, Qinglei; Fu, Zuntao; Yuan, Naiming
2015-01-01
Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly. PMID:26030809
Classical and Quantum Chaos in Atom Optics
Farhan Saif
2006-04-10
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.
Deconstructing spatiotemporal chaos using local symbolic dynamics.
Pethel, Shawn D; Corron, Ned J; Bollt, Erik
2007-11-23
We find that the global symbolic dynamics of a diffusively coupled map lattice is well approximated by a very small local model for weak to moderate coupling strengths. A local symbolic model is a truncation of the full symbolic model to one that considers only a single element and a few neighbors. Using interval analysis, we give rigorous results for a range of coupling strengths and different local model widths. Examples are presented of extracting a local symbolic model from data and of controlling spatiotemporal chaos. PMID:18233220
Chaos and the Shapes of Elliptical Galaxies
David Merritt
1996-01-17
Hubble Space Telescope (HST) observations reveal that the density of stars in most elliptical galaxies rises toward the center in a power-law cusp. Many of these galaxies also contain central dark objects,possibly supermassive black holes. The gravitational force from a steep cusp or black hole will destroy most of the box orbits that constitute the ``backbone'' of a triaxial stellar system. Detailed modelling demonstrates that the resulting chaos can preclude a self-consistent, strongly triaxial equilibrium. Most elliptical galaxies may therefore be nearly axisymmetric, either oblate or prolate.
Beyond Benford's Law: Distinguishing Noise from Chaos.
Li, Qinglei; Fu, Zuntao; Yuan, Naiming
2015-01-01
Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly. PMID:26030809
Chaos and microbial systems. Final project report, July 1989--July 1992
Kot, M.
1992-10-01
The field of nonlinear dynamics has generated a variety of new techniques for identifying order in seemingly chaotic systems. These techniques have led to new insights for several ecological and epidemiological systems, most notably childhood disease epidemics. To better test the efficacy and relevance of these new techniques to population biology research with two components namely a mathematical analysis of some simple microbial models with chaotic dynamics; and experimental (chemostat) population studies to evaluate the accuracy of these models. I have completed a thorough analysis of the forced double-Monod model and of the phase-locking route to chaos that it exhibits. I have also analyzed a simpler pulsed system with mass action kinetics and a period-doubling route to chaos. This research also motivated detailed analyses of discrete-time predator-prey and dispersal models, and a fast new method for computing fractal dimension. My colleagues and I have assembled a complete laboratory system to determine the appropriateness of the forced double-Monod model. We have tested assays for concentration and density and have performed a variety of diagnostic tests on this system. We have measured growth parameters for bacteria and for protozoa in chemostat.
Chaos in a semiclassical model of multiphoton excitation of spherical top molecules
Galbraith, H.W.; Ackerhalt, J.R.; Milonni, P.W.
1983-01-01
We study the dynamical effects of vibration-rotation coupling in multiple photon excitation at lowest order. Our molecular model is the simplest possible: that of an oscillator (triply degenerate) and uncoupled rigid rotor. The molecule-field interactions introduce a vibration-rotation nonlinearity which gives rise to nonconservation of the molecular angular momentum and in some instances consequent chaotic dynamics. The chaos leads to incoherence (widely seen in experiments) in the time dependence of the photon absorption and is not treatable in an additive way as inhomogeneous broadening. The nonconservation of the molecular angular momentum is due to the development with time of the molecular vibrational angular momentum. The degree of chaotic behavior is found to depend upon the relative size of the vibrational to pure rotational angular momenta as the excitation progresses, i.e., when vibrational angular momentum exceeds the pure rotational angular momentum we find chaos, conversely when J/sub 0/ is quite large the motion is gyroscopically stabilized and quasiperiodic. Therefore the suggested cold experiments are perhaps not so desirable.
Quantum Chaos in Physical Systems: from Super Conductors to Quarks
Elmar Bittner; Harald Markum; Rainer Pullirsch
2001-10-31
This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.
Theory of the nucleus as applied to quantum chaos
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University, Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute (Russian Federation)
2014-12-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.
Tse, Chi K. "Michael"
Channel Equalization for Chaos-based Communication Systems Jiu-chao Feng, Chi K. Tse and Francis C, the performance of chaos-based communication systems can be enhanced. In this paper, we study the equalization of the channel for chaotic communication systems. A channel equalizer is designed and realized by a modified
RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM
Deck, Katherine M.; Winn, Joshua N. [Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Agol, Eric [Department of Astronomy, Box 351580, University of Washington, Seattle, WA 98195 (United States); Lissauer, Jack J. [NASA Ames Research Center, Moffet Field, CA 94035 (United States)
2012-08-10
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only {approx}10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first-order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for {approx}4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large-scale orbital instabilities on the timescale of our integrations ({approx}200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.
Chaos and scaling in daily river flow
M. De Domenico; M. Ali Ghorbani
2011-04-07
Adequate knowledge of the nature of river flow process is crucial for proper planning and management of our water resources and environment. This study attempts to detect the salient characteristics of flow dynamics of the Karoon River in Iran. Daily discharge series observed over a period of six years (1999-2004) is analyzed to examine the chaotic and scaling characteristics of the flow dynamics. The presence of chaos is investigated through the correlation dimension and Lyapunov exponent methods, while the Hurst exponent and R\\'enyi dimension analyses are performed to explore the scaling characteristics. The low correlation dimension ($2.60 \\pm 0.07$) and the positive largest Lyapunov exponent ($0.014 \\pm 0.001$) suggest the presence of low-dimensional chaos; they also imply that the flow dynamics are dominantly governed by three variables and can be reliably predicted up to 48 days (i.e. prediction horizon). Results from the Hurst exponent and R\\'enyi dimension analyses reveal the multifractal character of the flow dynamics, with persistent and anti-persistent behaviors observed at different time scales.
Chaos and structure of level densities
Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenholt, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN
2008-01-01
The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.
Joint Entropy Coding and Encryption using Robust Chaos
Nithin Nagaraj; Prabhakar G Vaidya; Kishor G Bhat
2006-08-22
We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the dynamical system, we could back-iterate and encode the message as the initial condition of the dynamical system. We show that such an encoding achieves Shannon's entropy and hence optimal for compression. It turns out that the appropriate discrete dynamical system to achieve optimality is the piecewise-linear Generalized Luroth Series (GLS) and further that such an entropy coding technique is exactly equivalent to the popular Arithmetic Coding algorithm. GLS is a generalization of Arithmetic Coding with different modes of operation. GLS preserves the Lebesgue measure and is ergodic. We show that these properties of GLS enable a framework for joint compression and encryption and thus give a justification of the recent work of Grangetto et al. and Wen et al. Both these methods have the obvious disadvantage of the key length being equal to the message length for strong security. We derive measure preserving piece-wise non-linear GLS (nGLS) and their skewed cousins, which exhibit Robust Chaos. We propose a joint entropy coding and encryption framework using skewed-nGLS and demonstrate Shannon's desired sensitivity to the key parameter. Potentially, our method could improve the security and key efficiency over Grangetto's method while still maintaining the total compression ratio. This is a new area of research with promising applications in communications.
ERIC Educational Resources Information Center
Nelson, Mary
1975-01-01
At Moraine Valley Community College (Illinois), a chain of events, programs, activities, and services has linked the college and community in such areas as fine arts, ethnic groups, public services, community action, community service, and community education. (Author/NHM)
Zeeman catastrophe machines as a toolkit for teaching chaos
NASA Astrophysics Data System (ADS)
Nagy, Péter; Tasnádi, Péter
2014-01-01
The investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics in the basic course of mechanics taught to engineering students. In this paper, it will be demonstrated that the Zeeman machine can be a versatile and motivating tool for students to acquire introductory knowledge about chaotic motion via interactive simulations. The Zeeman catastrophe machine is a typical example of a quasi-static system with hysteresis. 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 the 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, Lyapunov exponents and so on. This paper is organically linked to our website (http://csodafizika.hu/zeeman) where the discussed simulation programs can be downloaded. In a second paper, the novel construction of a network of Zeeman machines will be presented to study the properties of cooperative systems.
Detecting nonlinear structure in time series
Theiler, J.
1991-01-01
We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs.
Generalized spectral decomposition for stochastic nonlinear problems
NASA Astrophysics Data System (ADS)
Nouy, Anthony; Le Ma?ˆtre, Olivier P.
2009-01-01
We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.
Aytac Arikoglu; Ibrahim Ozkol
2008-01-01
In this note, we would like to point some similarities between the study [Erturk VS, Momani S, Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlinear Sci Numer Simul. doi:10.1016\\/j.cnsns.2007.02.006] with the already existing one [Arikoglu A, Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Soliton Fract. 10.1016\\/j.chaos.2006.09.004].
NASA Astrophysics Data System (ADS)
Chen, Dalin; Yang, Yiren; Fan, Chenguang
2008-02-01
The problem of nonlinear aerothermoelasticity of a two-dimension thin plate in supersonic airflow is examined. The strain-displacement relation of the von Karman’s large deflection theory is employed to describe the geometric non-linearity and the aerodynamic piston theory is employed to account for the effects of the aerodynamic force. A new method, the differential quadrature method (DQM), is used to obtain the discrete form of the motion equations. Then the Runge-Kutta numerical method is applied to solve the nonlinear equations and the nonlinear response of the plate is obtained numerically. The results indicate that due to the aerodynamic heating, the plate stability is degenerated, and in a specific region of system parameters the chaos motion occurs, and the route to chaos motion is via doubling-period bifurcations.
Anlage, Steven
on the damped driven non- linear oscillator formed by a resistor, inductor, and varactor diode RLD circuitUnified model and reverse recovery nonlinearities of the driven diode resonator Renato Mariz de study the origins of period doubling and chaos in the driven series resistor-inductor-varactor diode
A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes
NASA Astrophysics Data System (ADS)
Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2013-07-01
We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.
Exact invariant measures: How the strength of measure settles the intensity of chaos
NASA Astrophysics Data System (ADS)
Venegeroles, Roberto
2015-06-01
The aim of this paper is to show how to extract dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of finding nonlinear interval maps from a given invariant measure. Then we show how to identify ergodic properties by means of transitions along the phase space via exact measures. On the other hand, we discuss quantitatively how infinite measures imply maps having subexponential Lyapunov instability (weakly chaotic), as opposed to finite measure ergodic maps, which are fully chaotic. In addition, we provide general solutions of maps for which infinite invariant measures are exactly known throughout the interval (a demand from this field). Finally, we give a simple proof that infinite measure implies universal Mittag-Leffler statistics of observables, rather than narrow distributions typically observed in finite measure ergodic maps.
Takagi-Sugeno fuzzy modeling and chaos control of partial differential systems
NASA Astrophysics Data System (ADS)
Vasegh, Nastaran; Khellat, Farhad
2013-12-01
In this paper a unified approach is presented for controlling chaos in nonlinear partial differential systems by a fuzzy control design. First almost all known chaotic partial differential equation systems are represented by Takagi-Sugeno fuzzy model. For investigating design procedure, Kuramoto-Sivashinsky (K-S) equation is selected. Then, all linear subsystems of K-S equation are transformed to ordinary differential equation (ODE) systems by truncated Fourier series of sine-cosine functions. By solving Riccati equation for each ODE systems, parallel stabilizing feedback controllers are determined. Finally, a distributed fuzzy feedback for K-S equation is designed. Numerical simulations are given to show that the distributed fuzzy controller is very easy to design, efficient, and capable to extend.
A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes
Choi, Minseok [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)] [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Sapsis, Themistoklis P. [Courant Institute of Mathematical Sciences, New York University, NY 10012 (United States)] [Courant Institute of Mathematical Sciences, New York University, NY 10012 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2013-07-15
We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.
Nonlinear Magnetohydrodynamics
Dieter Biskamp
1997-01-01
This book provides a self-contained introduction to magnetohydrodynamics (MHD), with emphasis on nonlinear processes. The book outlines the conventional aspects of MHD theory, magnetostatic equilibrium and linear stability theory. It concentrates on nonlinear theory, starting with the evolution and saturation of individual ideal and resistive instabilities, continuing with a detailed analysis of magnetic reconnection and concluding with a study of
Controlling chaos in the presence of noise
Dorning
1991-01-01
Although the presence of nonlinearity in real-world complex engineering systems is hardly a revelation, only recently has it been realized how ubiquitous and far-reaching its effects are. Important examples of oscillatory and chaotic behavior of complex, and even simple, nonlinear engineering systems abound. These are supplemented by an immense number of related scientific examples from pioneering laboratory experiments. Naturally, interest
Parallel Computation Using Generalized Models of Exactly Solvable Chaos
Ken Umeno
1996-10-03
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be used for some complex computations, while the precise information of initial conditions which vanishes in the course of iterations deos not matter for this kind of computations. The key observation of the present study is that computation using ergordicity of dynamical systems can be thought of as massively parallel Monte Carlo simulations. Here, to avoid difficulty in elucidating the ergordicity of dynamical systems, we propose computational schemes using the generalized class of one-dimensional chaos with explicit invariant measures. The validity of our results which connect chaos with parallel computation is checked by the precision computations of some transcendental numbers like \\pi.
Filtering with Marked Point Process Observations via Poisson Chaos Expansion
Sun Wei, E-mail: wsun@mathstat.concordia.ca [Concordia University, Department of Mathematics and Statistics (Canada); Zeng Yong, E-mail: zengy@umkc.edu [University of Missouri at Kansas City, Department of Mathematics and Statistics (United States); Zhang Shu, E-mail: zhangshuisme@hotmail.com [Concordia University, Department of Mathematics and Statistics (Canada)
2013-06-15
We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.
The Perturbing Worldview of Chaos: Implications for Public Relations.
ERIC Educational Resources Information Center
Cottone, Laura Perkins
1993-01-01
Argues that the traditional scientific worldview provides an insufficient foundation for public relations theory development. Proposes reformulating public relations theory based on a model informed by the dynamic worldview of chaos. (HB)
Randomness, Dynamics and Risk From Quantum Theory and Chaos
Brigo, Damiano
No randomness: Clockwork universe? 3 Chaos Extreme sensitivity to initial conditions: practical unpredictability universally agreed upon Prof. D. Brigo (Imperial College London) Randomness, Dynamics and Risk 29 Jan 2014 6
Suppression of quantum chaos in a quantum computer hardware.
Lages, J; Shepelyansky, D L
2006-08-01
We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos. PMID:17025526
Global Spectral Structures of Type III Intermittent Chaos
Hisao Okamoto; Hazime Mori; Shoichi Kuroki
1988-01-01
Power spectra of type III intermittent chaos near its onset point are investigated by developing a statistical-physical theory of power spectra of intermittent chaos due to Mori et al. It is shown that the power spectra exhibit eminent peaks at selected frequencies m omega_{0} with m = 0, 1\\/2, 1, 3\\/2, 2, *s, where omega_{0} is an eigenfrequency of laminar
Generalized synchronization of chaos in electronic circuit experiments
A. Kittel; J. Parisi; K. Pyragas
1998-01-01
Two examples of one-way coupled electronic circuits displaying generalized synchronization of chaos are considered. In one of them, the dynamics of both the response and the driving systems represent a double-scroll chaos oscillator. In another example, the double-scroll oscillator is driven by an electronic analog of the Mackey-Glass system. To detect the generalized synchronization, an auxiliary response system that is
Controlling chaos using Takagi Sugeno fuzzy model and adaptive adjustment
NASA Astrophysics Data System (ADS)
Zheng, Yong-Ai
2006-11-01
In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno (TS) fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rössler's system verify the effectiveness of the proposed methods.
Philosophical perspectives on quantum chaos: Models and interpretations
NASA Astrophysics Data System (ADS)
Bokulich, Alisa Nicole
2001-09-01
The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.
Chaos suppression in a spin-torque nano-oscillator
NASA Astrophysics Data System (ADS)
Xu, H. Z.; Chen, X.; Liu, J.-M.
2008-11-01
We propose a novel practicable self-control scheme to suppress chaos in a spin-torque nano-oscillator in the presence of spin-polarized dc and ac. The magnetization dynamics is investigated by performing micromagnetic simulation. A complete chaos control diagram is obtained, indicating that employment of this proper self-control scheme over a broad frequency range of the ac can greatly reduce the degree of chaoticity in the oscillator.
Chaos in the general relativistic three-body problem
NASA Astrophysics Data System (ADS)
Neilsen, David; Jay, Jared; Morgan, Taylor
2014-03-01
The three-body problem in classical gravity is known to have chaotic solutions. We are investigating chaos in the three-body problem in general relativity using post Newtonian equations. We model a binary system that interacts with an incoming star. We solve the post-Newtonian evolution equations in the Hamiltonian formalism to order 2.5. We present results of these interactions that display features of chaos, such as sensitivity to initial conditions and scale invariance.
EEG and chaos: Description of underlying dynamics and its relation to dissociative states
NASA Technical Reports Server (NTRS)
Ray, William J.
1994-01-01
The goal of this work is the identification of states especially as related to the process of error production and lapses of awareness as might be experienced during aviation. Given the need for further articulation of the characteristics of 'error prone state' or 'hazardous state of awareness,' this NASA grant focused on basic ground work for the study of the psychophysiology of these states. In specific, the purpose of this grant was to establish the necessary methodology for addressing three broad questions. The first is how the error prone state should be conceptualized, and whether it is similar to a dissociative state, a hypnotic state, or absent mindedness. Over 1200 subjects completed a variety of psychometric measures reflecting internal states and proneness to mental lapses and absent mindedness; the study suggests that there exists a consistency of patterns displayed by individuals who self-report dissociative experiences such that those individuals who score high on measures of dissociation also score high on measures of absent mindedness, errors, and absorption, but not on scales of hypnotizability. The second broad question is whether some individuals are more prone to enter these states than others. A study of 14 young adults who scored either high or low on the dissociation experiences scale performed a series of six tasks. This study suggests that high and low dissociative individuals arrive at the experiment in similar electrocortical states and perform cognitive tasks (e.g., mental math) in a similar manner; it is in the processing of internal emotional states that differences begin to emerge. The third question to be answered is whether recent research in nonlinear dynamics, i.e., chaos, offer an addition and/or alternative to traditional signal processing methods, i.e., fast Fourier transforms, and whether chaos procedures can be modified to offer additional information useful in identifying brain states. A preliminary review suggests that current nonlinear dynamical techniques such as dimensional analysis can be successfully applied to electrocortical activity. Using the data set developed in the study of the young adults, chaos analyses using the Farmer algorithm were performed; it is concluded that dimensionality measures reflect information not contained in traditional EEG Fourier analysis.
ERIC Educational Resources Information Center
Association of Research Libraries, Washington, DC.
Three papers are compiled here for research library directors: (1) "Background: Open Systems Interconnection," in which David F. Bishop provides fundamental background information to explain the concept of the emerging technology of linked systems and open systems interconnection--i.e., an agreed upon standard set of conventions or rules that,…
Synchronization of Chaos in Fully Developed Turbulence
NASA Astrophysics Data System (ADS)
Lalescu, Cristian C.; Meneveau, Charles; Eyink, Gregory L.
2013-02-01
We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.
Food chain chaos due to Shilnikov's orbit.
Deng, Bo; Hines, Gwendolen
2002-09-01
Assume that the reproduction rate ratio zeta of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit zeta=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio epsilon of the top-predator over the predator is greater than a modest value epsilon(0). The additional conditions under which such a singular orbit may occur are also explicitly given. (c) 2002 American Institute of Physics. PMID:12779583
A pseudo-matched filter for chaos
Seth D. Cohen; Daniel J. Gauthier
2012-04-05
A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these results, we describe a pseudo-matched filter, which removes noise from the same chaotic signal. It consists of a notch filter followed by a first-order, low-pass filter. We compare quantitatively the matched filter's performance to that of our pseudo-matched filter using correlation functions in a simulated radar application. On average, the pseudo-matched filter performs with a correlation signal-to-noise ratio that is 2.0 dB below that of the matched filter. Our pseudo-matched filter, though somewhat inferior in comparison to the matched filter, is easily realizable at high speed (> 1 GHz) for potential radar applications.
NASA Astrophysics Data System (ADS)
Chatterjee, Monish R.; Mohamed, Fathi H. A.
2014-10-01
In recent research, propagation of plane electromagnetic (EM) waves through a turbulent medium with modified von Karman phase characteristics was modeled and numerically simulated using transverse planar apertures representing narrow phase turbulence along the propagation path. The case for extended turbulence was also studied by repeating the planar phase screens multiple times over the propagation path and incorporating diffractive effects via a split-step algorithm. The goal of the research reported here is to examine two random phenomena: (a) atmospheric turbulence due to von Karman-type phase fluctuations, and (b) chaos generated in an acousto-optic (A-O) Bragg cell under hybrid feedback. The latter problem has been thoroughly examined for its nonlinear dynamics and applications in secure communications. However, the statistical characteristics (such as the power spectral density (PSD)) of the chaos have not been estimated in recent work. To that end, treating the chaos phenomena as a random process, the time waveforms of the chaos intensity and their spectra are numerically evaluated over a (large) number of time iterations. These spectra are then averaged to derive the equivalent PSD of the A-O chaos. For the turbulence problem, an optical beam passing through an input pinhole is propagated through a random phase screen (placed at different locations) to a desired distance (typically near-field) under different levels of turbulence strength. The resulting spatial intensity profile is then averaged and the process repeated over a (large) number of pre-specified time intervals. From this data, once again, the turbulence PSD is calculated via the Fourier spectra of the average intensity snapshots. The results for the two systems are compared.
The Application of Chaos Theory to the Career-Plateaued Worker.
ERIC Educational Resources Information Center
Duffy, Jean Ann
2000-01-01
Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)
Federal Register 2010, 2011, 2012, 2013, 2014
2010-08-30
...Determinations: ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936'' SUMMARY: Notice is hereby given...in the exhibition ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936,'' imported from abroad for...
Comparison Between Terrestrial Explosion Crater Morphology in Floating Ice and Europan Chaos
NASA Technical Reports Server (NTRS)
Billings, S. E.; Kattenhorn, S. A.
2003-01-01
Craters created by explosives have been found to serve as valuable analogs to impact craters, within limits. Explosion craters have been created in floating terrestrial ice in experiments related to clearing ice from waterways. Features called chaos occur on the surface of Europa s floating ice shell. Chaos is defined as a region in which the background plains have been disrupted. Common features of chaos include rafted blocks of pre-existing terrain suspended in a matrix of smooth or hummocky material; low surface albedo; and structural control on chaos outline shape by pre-existing lineaments. All published models of chaos formation call on endogenic processes whereby chaos forms through thermal processes. Nonetheless, we note morphological similarities between terrestrial explosion craters and Europan chaos at a range of scales and consider whether some chaos may have formed by impact. We explore these similarities through geologic and morphologic mapping.
Straus, Christian; Samara, Ziyad; Fiamma, Marie-Noëlle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darré, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas
2011-05-01
Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P < 0.0001). It also increased with acidosis, but in postmetamorphic tadpoles only (P < 0.05). The noise-titration technique evidenced low-dimensional nonlinearities in all the postmetamorphic brainstems, at both pH. Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P < 0.01). In contrast, linear models best fitted the ventilatory rhythm in all but one of the premetamorphic preparations at pH 7.8 (P < 0.005 vs. postmetamorphic) and in four at pH 7.4 (not significant vs. postmetamorphic). Therefore, in a lower vertebrate model, the brainstem respiratory central rhythm generator accounts for ventilatory chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals. PMID:21325645
Analog Chaos-based Secure Communications and Cryptanalysis: A Brief Survey
Shujun Li; Gonzalo Álvarez; Zhong Li; Wolfgang A. Halang
2007-01-01
A large number of analog chaos-based secure communication systems have been proposed since the early 1990s exploiting the technique of chaos synchronization. A brief survey of these chaos-based cryptosystems and of related cryptanalytic results is given. Some recently proposed counter- measures against known attacks are also introduced. I. INTRODUCTION Since the late 1980s, chaos-based cryptography has at- tracted more and
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
California at Los Angles, University of
Generality of Deterministic Chaos, Exponential Spectra, and Lorentzian Pulses in Magnetically) The dynamics of transport at the edge of magnetized plasmas is deterministic chaos. The connection is made is the signature of deterministic chaos. The exponential character arises from Lorentzian pulses. The results
Chaos in the Composition Classroom: Why Do Some Classes Fail To Function?
ERIC Educational Resources Information Center
Salmon, Vickie
1999-01-01
The author asserts that through chaos theory, she began to view the failures and successes of one particular semester in a different light. Describes chaos theory in layman's terms and provides recommendations for teaching in this new paradigm. Asserts that understanding chaos theory will allow instructors to celebrate diversity, disorder, and…
A General Noncoherent Chaos-Shift-Keying Communication System and its Performance
Tse, Chi K. "Michael"
A General Noncoherent Chaos-Shift-Keying Communication System and its Performance Analysis Hongbin@polyu.edu.hk Abstract-- A general noncoherent chaos-shift-keying (CSK) communication system with adjustable weights has triggered some interest in the development of chaos-based communication systems in the past decade
An Improved Chaos-Based Stream Cipher Algorithm and its VLSI Implementation
Shubo Liu; Jing Sun; Zhengquan Xu; Zhaohui Cai
2008-01-01
Recently, the growing numbers of cryptosystems based on chaos have been proposed; many of them have good statistical properties and security but low efficiency. To increase operating efficiency of cryptosystems, an improved chaos-based stream cipher algorithm based on discrete chaotic maps is presented. The algorithm improves the complexity of chaos by randomly changing chaotic control parameter. In the proposed algorithm,
Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case
ERIC Educational Resources Information Center
Akmansoy, Vesile; Kartal, Sadik
2014-01-01
Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…
Towards a computer-assisted proof for chaos in a forced damped pendulum equation
Csendes, Tibor
Towards a computer-assisted proof for chaos in a forced damped pendulum equation Tibor Csendes the computational proof of the chaotic behavior of the forced damped pendulum. Although, chaos for this pendulum properties necessary for complicate chaotic behaviour. Key words: Differential equations, Chaos, Pendulum
FOOD CHAIN CHAOS DUE TO SHILNIKOV'S ORBIT BO DENG AND GWENDOLEN HINES
Deng, Bo
FOOD CHAIN CHAOS DUE TO SHILNIKOV'S ORBIT BO DENG AND GWENDOLEN HINES Abstract. Assume that the reproduction rate ratio # of the predator over the prey is su#ciently small in a basic tritrophic food chain understood without understanding the role chaos plays in food chains. Yet chaos generating mechanisms have
Laser Chaos Induced by Delayed-Feedback and External Modulation Cheng JUANG, Shu-Ming CHANG1
Lin, Wen-Wei
Laser Chaos Induced by Delayed-Feedback and External Modulation Cheng JUANG, Shu-Ming CHANG1 , Nien, 2005; published November 9, 2005) Electronic-controlled routes to chaos in a quantum-well laser diode to chaos, intermittency routes to chaos, quantum-well laser diodes, delayed-feedback 1. Introduction
Topographic variations in chaos on Europa: Implications for diapiric formation
NASA Astrophysics Data System (ADS)
Schenk, Paul M.; Pappalardo, Robert T.
2004-08-01
Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Carr et al., 1998; Greenberg et al., 1999], or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 2000]. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.
J. Leuthold; C. Koos; W. Freude
2010-01-01
The nonlinearities in silicon are diverse. This Review covers the wealth of nonlinear effects in silicon and highlights the important applications and technological solutions in nonlinear silicon photonics.
NSDL National Science Digital Library
Hopley, Phil.
The JFK Link is an archive of documents relevant to the "life, administration, death, and legacy" of John Fitzgerald Kennedy. Understanding and experiencing the annoyance of trying to locate political speeches, Phil Hopley has produced a Web site that makes JFK's career speeches free and easily accessible to anyone. In its nascent stages, the site currently contains materials of the 1960 Presidential Campaign for then Senator John F. Kennedy and Vice President Richard Nixon. These materials include speeches, remarks, press conferences, study papers, and statements given by both candidates from August 1 - November 7, 1960. Forthcoming are public messages, speeches, and statements of JFK from the dates January 20, 1961 to November 22, 1963; he also plans to offer select speeches made by JFK from 1947 to 1960.
NSDL National Science Digital Library
Herzler, Roger
The mission of the Astronomy Links Web site is to provide an index of thebest astronomy and space related Web sites found around the world on theInternet. As a service of the AstroPages.com and run by Roger Herzler, the page gives those interested a wealth of resources related to astronomy including a site search engine as well as organized andinformative browsing features. The main page contains over twenty categoriesincluding astrophysics, observatories, satellites, the solar system, telescopes,and history. Each of these contain subcategories and individual linksthat contain a description, the date it was added, the number of times thesite has been clicked, and even a rating. Other features of the welldesigned site include astronomy news, popular and new site categories, andmuch more. [JAB
NASA Astrophysics Data System (ADS)
(left) European Geophysical Society (EGS) President Rolf Meissner at AGU Headquarters with (center) Executive Director Fred Spilhaus and (right) Foreign Secretary Juan Roederer. Meissner attended the meeting of AGU's Committee on International Participation (CIP) on February 26, 1988. At that meeting, specific ways of fostering close links between AGU and EGS were discussed.A few weeks later, Roederer and AGU staff, working with EGS Secretary-General Arne Richter at the EGS meeting in Bologna, Italy, March 21-25, planned details of the establishment of an AGU office in Europe. The Copernicus Gesellschaft, a new entity located on the premises of the Max Planck Institute for Aeronomy in Lindau, Federal Republic of Germany, will provide the administrative staff and handle logistics.
NSDL National Science Digital Library
Hosted by the Yerkes Regional Primate Research Center at Emory University, the Living Links site specializes in "comparisons of the social life, ecology, cognition, neurology, and molecular genetics of apes and humans." With an emphasis on the four extant great apes (bonobos, chimpanzees, gorillas, and orangutans), this educational site attempts "1) to reconstruct human evolution, 2) pinpoint the differences and similarities between humans and apes, and 3) educate the public about apes, and promote their well-being and conservation." The Info section provides a long (hyperlinked) list of general information on apes, from Allogrooming to Wooly spider monkeys. The Research section gives a brief overview of the Yerkes Center's research questions (and their evolutionary context), and Animals describes the Center's study animals -- three main social groups of chimpanzees -- with a special vocalizations feature. For those interested in learning more about apes and how our ancestry is intertwined with theirs, this site will be of interest.
Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation
Moon, Songky; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon
2015-01-01
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of $0.41\\dot{6}\\eta^2$ for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of $\\eta$ much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained...
NASA Astrophysics Data System (ADS)
Guallini, Luca; Gilmore, Martha; Marinangeli, Lucia; Thomas, Nicolas
2015-04-01
Iani Chaos is a ~30,000 square kilometers region that lies at the head of the Ares Vallis outflow channel system. Mapping of Ares Vallis reveals multiple episodes of erosion, probably linked to several discharge events from the Iani Chaos aquifer. We present the first detailed geomorphological map of the Iani region. Five chaos units have been distinguished with varying degrees of modification (primarily by erosion and fracturing), starting from a common terrain (Noachian highlands). We observe a general progressive decrease of their mean elevation from the Mesas, Mesas & Knobs and Hummocky (Hy) terrains to the Knobs and Knobby morphologies. This trend is consistent with an initial collapse of the original surface with an increase of the fracturing and/or of the erosion. Light-toned Layered Deposits (LLD) have been also mapped and described in Iani Chaos. These terrains are clearly distinguished by a marked light-toned albedo, high thermal inertia and a pervasively fractured morphology. LLD both fill the basins made by the collapsed chaotic terrains and are found to be partially modified by the chaos formation. LLD also overlap chaos mounds or are themselves eroded into mounds after deposition. These stratigraphic relationships demonstrate that LLD deposition occurred episodically in the Iani region and throughout the history of the development of the chaos. Water seems to have had an active role in the geological history of Iani. The composition and morphologies of the LLD are consistent with deposition in an evaporitic environment and with erosion by outflows, requiring stable water on the surface. For the first time, we have also mapped and analyzed potential fluvial features (i.e., channels, streamlined islands, terraces, grooved surfaces) on the surface of the LLD. These landforms describe a fluvial system that can be traced from central Iani and linked northward to Ares Vallis. Using topographic data, we have compared the elevation of the LLD and channel units and find that their altitudes are remarkably similar to the altitude of the floors of the major Ares Vallis channels. This is decisive evidence of 1) a possible fluvial system within Iani linked to the Ares Vallis outflow system, characterized by five episodes of outflow at least (S1 to S5), and 2) of the existence of the LLD within Iani during the occurrence of the outflows (i.e., the LLD are coeval with or postdate the Ares Vallis outflow channels). On the basis of our analysis, we propose the following formation model for Iani Chaos: 1) Initial fracturing and tectonic subsidence of the pristine Noachian materials and subsequent outflow erosion of the bedrock (Ares Vallis S1 channel origin); 2) Evaporitic deposition of older LLD units on top and between chaotic terrains. Layering suggests cyclic wetting and drying; 3) Tectonic subsidence and fluvial erosion of chaos and LLD (Ares Vallis S2 to S3 channels); 4) Deposition of younger LLD units in central and northern Iani; 5) Tectonic subsidence and outflows, erosion of chaos and LLD (Ares Vallis S4 to S5 channel origin and subsequent downdropping of NW and N(e) Iani).
Self-regulated homoclinic chaos in neural networks activity
NASA Astrophysics Data System (ADS)
Volman, Vladislav; Baruchi, Itay; Ben-Jacob, Eshel
2004-12-01
We compare the recorded activity of cultured neuronal networks with hybridized model simulations, in which the model neurons are driven by the recorded activity of special neurons. The latter, named `spiker' neurons, that exhibit fast firing with homoclinic chaos like characteristics, are expected to play an important role in the networks' self regulation. The cultured networks are grown from dissociated mixtures of cortical neurons and glia cells. Despite the artificial manner of their construction, the spontaneous activity of these networks exhibits rich dynamical behavior, marked by the formation of temporal sequences of synchronized bursting events (SBEs), and additional features which seemingly reflect the action of underlying regulating mechanism, rather than arbitrary causes and effects. Our model neurons are composed of soma described by the two Morris-Lecar dynamical variables (voltage and fraction of open potassium channels), with dynamical synapses described by the Tsodyks-Markram three variables dynamics. To study the recorded and simulated activities we evaluated the inter-neuron correlation matrices, and analyzed them utilizing the functional holography approach: the correlations are re-normalized by the correlation distances — Euclidean distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of re-normalized correlations, or correlation affinities, onto a corresponding 3-D causal manifold (3-D Cartesian space constructed by the 3 leading principal vectors of the N-dimensional space. The neurons are located by their principal eigenvalues and linked by their original (not-normalized) correlations. This reveals hidden causal motifs: the neuron locations and their links form simple structures. Similar causal motifs are exhibited by the model simulations when feeded by the recorded activity of the spiker neurons. We illustrate that the homoclinic chaotic behavior of the spiker neurons can be generated by glia-regulated self-synapses. Since in real networks the glia are regulated back by the networks' neuronal activity, our findings hint that the structure of the causal manifolds in the affinity space is self-regulated via collective regulation of the homoclinic behavior of the spiker neurons. We further propose that the existence of such simple causal motifs in the complex activity of stand-alone cultured networks calls for a new view of the neuro-glia interactions, where linked neurons and glia cells function as a hybridized fabric by which information is co-processed.
Downloaded 09 Sep 2008 to 132.77.4.43. Redistribution subject to AIP license or copyright; see http://chaos.aip.org/chaos/copyright.jsp #12;Downloaded 09 Sep 2008 to 132.77.4.43. Redistribution subject to AIP license or copyright; see subject to AIP license or copyright; see http://chaos.aip.org/chaos/copyright.jsp #12;Downloaded 09 Sep
Planck's quantum-driven integer quantum Hall effect in chaos
Yu Chen; Chushun Tian
2014-09-18
The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of critical $h_e$-values, but otherwise bounded ('insulating' phase). The latter phase is topological in nature and characterized by a quantum number ('quantized Hall conductance'). The number jumps by unity whenever $h_e$ decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.
Turbulence transition and the edge of chaos in pipe flow
Tobias M Schneider; Bruno Eckhardt; James A Yorke
2007-03-30
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \\emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.
Symbolic dynamics and chaos in plane Couette flow
Li, Y Charles
2015-01-01
According to a recent theory \\cite{Li14}, when the Reynolds number is large, fully developed turbulence is caused by short term unpredictability (rough dependence upon initial data); when the Reynolds number is moderate, often transient turbulence is caused by chaos (long term unpredictability). This article aims at studying chaos in plane Couette flow at moderate Reynolds number. Based upon the work of L. van Veen and G. Kawahara \\cite{VK11} on a transversal homoclinic orbit asymptotic to a limit cycle in plane Couette flow, we explore symbolic dynamics and chaos near the homoclinic orbit. Mathematical analysis shows that there is a collection of orbits in the neighborhood of the homoclinic orbit, which is in one-to-one correspondence with the collection of binary sequences. The Bernoulli shift on the binary sequences corresponds to a chaotic dynamics of a properly defined return map.
Frequency assortativity can induce chaos in oscillator networks
NASA Astrophysics Data System (ADS)
Skardal, Per Sebastian; Restrepo, Juan G.; Ott, Edward
2015-06-01
We investigate the effect of preferentially connecting oscillators with similar frequency to each other in networks of coupled phase oscillators (i.e., frequency assortativity). Using the network Kuramoto model as an example, we find that frequency assortativity can induce chaos in the macroscopic dynamics. By applying a mean-field approximation in combination with the dimension reduction method of Ott and Antonsen, we show that the dynamics can be described by a low dimensional system of equations. We use the reduced system to characterize the macroscopic chaos using Lyapunov exponents, bifurcation diagrams, and time-delay embeddings. Finally, we show that the emergence of chaos stems from the formation of multiple groups of synchronized oscillators, i.e., meta-oscillators.
Genotoxicity of drinking water from Chao Lake
Liu, Q.; Jiao, Q.C. [Nanjing Univ. (China). Dept. of Biological Science and Technology] [Nanjing Univ. (China). Dept. of Biological Science and Technology; Huang, X.M.; Jiang, J.P.; Cui, S.Q.; Yao, G.H.; Jiang, Z.R.; Zhao, H.K.; Wang, N.Y. [Anhui Antiepidemic Station, Hefei (China)] [Anhui Antiepidemic Station, Hefei (China)
1999-02-01
Genotoxic activity appears to originate primarily from reactions of chlorine with humic substances in the source waters. Comparisons of extracts of settled versus chlorinated water have confirmed that chlorinating during water treatment produces mutagenic activity in the mutagenicity tests. Present work on XAD-2 extracts of raw, chlorinated (treated), and settled water from the Chao Lake region of China has involved a battery of mutagenicity assays for various genetic endpoints: the Salmonella test, the sister-chromatid exchange (SCE) induction in Chinese hamster lung (CHL) cells, and the micronucleus (MN) induction in the peripheral blood erythrocytes of silver carp. Extracts of raw and treated water but not the settled water are mutagenic in the Salmonella assay. On the other hand, extracts of three water samples show activity in the SCE and MN assays, especially the raw and treated water. These data show that contamination and chlorinating contribute mutagens to drinking water and suggest that the mammalian assays may be more sensitive for detecting mutagenicity in aquatic environment than the Salmonella test.
Synchronized chaos in networks of simple units
Frank Bauer; Fatihcan M. Atay; Juergen Jost
2010-01-25
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that, in contrast to diffusively coupled networks, the synchronous behavior of a non-diffusively coupled network can be dramatically different from the behavior of its constituent units. In particular, we show that chaos can emerge as synchronized behavior although the dynamics of individual units are very simple. Conversely, individually chaotic units can display simple behavior when the network synchronizes. We give a synchronization criterion that depends on the spectrum of the generalized graph Laplacian, as well as the dynamical properties of the individual units and the interaction function. This general result will be applied to coupled systems of tent and logistic maps and to two models of neuronal dynamics. Our approach yields an analytical understanding of how simple model neurons can produce complex collective behavior through the coordination of their actions.
Quantum chaos using delta kicked systems
NASA Astrophysics Data System (ADS)
Ramareddy, Vijayashankar
Scope and Method of Study. The purpose of this research was to experimentally study quantum dynamics of systems whose classical dynamics are chaotic. Quantum delta-kicked systems such as kicked rotor and kicked accelerator were used. The cold non condensed atoms were kicked first to realize the kicked accelerator. Among the objectives were the realization of resonances of the kicked accelerator and associated phenomena of quantum accelerator modes using a Bose-Einstein Condensation (BEC). One of the major achievements of the work in this thesis was the creation of the quantum delta-kicked rotor and its associated resonances to realize a quantum ratchet. The properties of the ratchet were studied in detail. Findings and Conclusions. The Quantum Accelerator Modes (QAM) were realized using both thermal samples of atoms and a BEC. Multiple micro optical traps were accidentally observed and in order to understand their behavior a theory was developed using spherical aberration of a lens. The maps produced by an effective classical theory were studied using the QAM. The resonances of the delta-kicked accelerator were observed for the first time and the theory was developed. One of the models that describes the QAM using rephasing of momentum states was observed in the experiments. The ratchet was realized using the resonances of the kicked rotor and accelerator where the diffusion in the case of classical ratchets was replaced by chaos in the quantum ratchet mechanism.
NSDL National Science Digital Library
Mr. Teitelbaum
2010-11-18
Here are some links to Astronomy applets, animations, and movies. Celestial and Terrestrial Motions Sky and telescope Interactive Sky Chart Rotating Sky Explorer Ecliptic (Zodiac) Simulator Seasonal Solar Motions Antarctica Time Lapse: A Year on Ice Aurora Australis: The Southern Lights [Daylight Hours Explorer Season as viewed from Space Animation Sun Position and Season animation Paths of the Sun Seasons and Ecliptic Simulator Sun s Rays Simulator Sun Motions Simulator Time-Lapse Seasons Simulator Kepler's Laws of Planetary Motion Kepler s 1st and 2nd laws Applet Orbit Applet Planetary Orbit Simulator Gravity Simulator Moon Phases and Satellite Motions Lunar and Solar Eclipse Information Moon Phase Animation What Causes Tides Lunar Phase Quizzer Eclipse Shadow Simulator Moon Phases and the Horizon Diagram Synodic Lag The Solar System Solar and Heliospheric Observatory (SOHO) Images Planetary Photo Journal Planetary Configuration Simulator Geocentric Retrograde Motion Animation Epicycle / Orbit Applet Gravity Simulator Ptolemaic Orbit of Mars The Universe Virtual Reality Milky Way Panorama Interactive H-R Diagram Element Absorption and Emision Lines Doppler Shift Demonstrator Lookback Time Simulator Other: SpaceWeather.com ...
Nonlinear Dynamics, Magnitude-Period Formula and Forecasts on Earthquake
Yi-Fang Chang
2008-02-02
Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold value of rock due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum. From the nonlinear equations of fluid mechanics, a simplified nonlinear solution of momentum corresponding the accumulation of the energy could be derived. Otherwise, a chaos equation could be obtained, in which chaos corresponds to the earthquake, which shows complexity on seismology, and impossibility of exact prediction of earthquakes. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, the magnitude-period formula of the earthquake may be derived approximately, and some results can be calculated quantitatively. For example, we forecast a series of earthquakes of 2004, 2009 and 2014, especially in 2019 in California. Combining the Lorenz model, we discuss the earthquake migration to and fro. Moreover, many external causes for earthquake are merely the initial conditions of this nonlinear system.
The bifurcation threshold value of the chaos detection system for a weak signal
NASA Astrophysics Data System (ADS)
Li, Yue; Yang, Bao-Jun; Du, Li-Zhi; Yuan, Ye
2003-07-01
Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detection system for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detection are correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system for a weak signal is established by using the theory of linear differential equation with periodic coefficients and computing the Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system is defined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of the chaos detection system.
Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model
Gu, Huaguang
2013-01-01
An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern. PMID:24339962
Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions
NASA Technical Reports Server (NTRS)
Rauch, Kevin P.; Holman, Matthew
1999-01-01
We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.
Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables
Sergey V. Lototsky
2003-01-01
\\u000a \\u000a Abstract. An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed\\u000a by the Wiener chaos decomposition. The result is applied to the nonlinear filtering problem for the time-homogeneous diffusion\\u000a model with correlated noise. An algorithm is proposed for computing recursive approximations of the unnormalized filtering\\u000a density and filter, and the errors of
Aronovich, Daniel; Bartal, Guy
2013-02-15
The performance of an optical hyperlens made of metal-dielectric layers can be improved by incorporating self-focusing nonlinearity in the dielectric layers. Using a modified beam propagation method in cylindrical coordinates, we show increased bandwidth and better propagation length, which can improve the spatial and temporal resolution of the device. PMID:23455086
Controlling chaos in a Lorenz-like system using feedback
NASA Astrophysics Data System (ADS)
Kociuba, G.; Heckenberg, N. R.
2003-12-01
We demonstrate that the dynamics of an autonomous chaotic laser can be controlled to a periodic or steady state under self-synchronization. In general, past the chaos threshold the dependence of the laser output on feedback applied to the pump is submerged in the Lorenz-like chaotic pulsation. However there exist specific feedback delays that stabilize the chaos to periodic behavior or even steady state. The range of control depends critically on the feedback delay time and amplitude. Our experimental results are compared with the complex Lorenz equations which show good agreement.
Signatures of chaos in the dynamics of quantum discord.
Madhok, Vaibhav; Gupta, Vibhu; Trottier, Denis-Alexandre; Ghose, Shohini
2015-03-01
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord. PMID:25871171
Structural chaos in reversible spontaneous emission of moving atoms
Prants, Sergei V; Yusupov, V I [V.I. Il'ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)
2000-07-31
t is proved analytically and numerically that, under certain conditions, the reversible spontaneous emission of two-level atoms moving in a high-Q resonator and described quantum-classically can be chaotic in the sense of the exponential sensitivity with respect to the initial conditions. The wavelet analysis of the vacuum Rabi oscillations showed that this chaos is structural. The numerical estimates showed that a Rydberg atom maser with a superconducting microwave resonator operating in a strong coupling mode is a promising device for detecting mani-festations of the dynamic chaos in the reversible spontaneous emission. (laser applications and other topics in quantum electronics)
Is the National Health Service at the edge of chaos?
Papadopoulos, Marios C; Hadjitheodossiou, Michalis; Chrysostomou, Costas; Hardwidge, Carl; Bell, B Anthony
2001-01-01
We used chaos and complexity theory to analyse waiting-list data (1998-2001) pertaining to over 20 000 National Health Service (NHS) patients from general surgical, orthopaedic and neurosurgical units across England. Plots of frequency versus quarter-to-quarter change in waiting times revealed a power relation which seems independent of surgical specialty and hospital location. One interpretation of these findings is that, for the period in question, the NHS was a system at the edge of chaos. This hypothesis might explain why waiting times have resisted attempts at shortening. PMID:11733585
Chaos and the dynamics of biological populations
Robert M. May
1987-01-01
As first emphasized in the early 1970s, the nonlinearities that are inherent in simple models for the regulation of plant nad animal populations can lead to chaotic dynamics. This review deals with a variety of instances where chaotic phenomena can arise, particularly in interactions between prey and predators (including hosts and pathogens, hosts and parasitic insects, and harvested populations). Some
Chaos in an intermittently driven damped oscillator
Manu. P. John; V. M. Nandakumaran
2008-09-05
We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear dynamics. Interchanging roles of determinism and stochasticity is also considered.
Chaos in an intermittently driven damped oscillator
Manu. P. John; V. M. Nandakumaran
2007-01-01
We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear dynamics. Interchanging roles of determinism and stochasticity is also considered.
NASA Astrophysics Data System (ADS)
Miwadinou, C. H.; Monwanou, A. V.; Chabi Orou, J. B.
This paper considers the effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh-Duffing oscillator where pure cubic, unpure cubic, pure quadratic and unpure quadratic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos. Unpure quadratic parameter and parametric excitation amplitude effects are found on the critical Melnikov amplitude ?cr. Finally, the phase space of initial conditions is carefully examined in order to analyze the effect of the nonlinear damping, and particularly how the basin boundaries become fractalized.
NASA Astrophysics Data System (ADS)
Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia
2014-05-01
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy (GMF-SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF-SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.
Zhu, Zhiwen, E-mail: zhuzhiwentju@163.com [Department of Mechanics, Tianjin University, Tianjin 300072 (China); Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072 (China); Zhang, Qingxin, E-mail: zqxfirst@163.com; Xu, Jia, E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, Tianjin 300072 (China)
2014-05-07
Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.
Non-linear dynamic analysis of hemodynamic parameters in an undulation type artificial heart system.
Yambe, Tomoyuki; Abe, Yusuke; Isoyama, Takashi; Tabayashi, Kouichi; Nanka, Shunsuke; Imachi, Kou; Nitta, Shin-ichi
2002-01-01
Undulation pump total artificial heart (UPTAH) is a unique total artificial heart implant (TAH) using an undulation pump that is a continuous blood flow pump. To evaluate the autonomic nerve function mediating the circulation system, we analyzed the hemodynamic parameters during animal experiments with UPTAH using the non-linear mathematical analyzing technique, including chaos and fractal theory. Adult female goats were used for the implantation of UPTAH. The natural heart was replaced with UPTAH under extra-corporal circulation. The conductance- and arterial pressure-based control method (1/R control) was applied on the 5th to 7th post-operative day as the influences of the cardiopulmonary bypass circulation were diagnosed to be terminated. Hemodynamic parameters were recorded on the data recorder, and non-linear mathematical analysis was performed. For the quantitative evaluation of the strange attractor, which was the characteristics of the deterministic chaos, the fractal dimension analysis was carried out. As a result, hemodynamic parameters fluctuated on the time axis and showed fractal characteristics, which were thought to be the characteristics of the deterministic chaos. The reconstructed attractor of the hemodynamics showed various behaviors according to changes in the situation of the goats. These results suggest that non-linear dynamical analysis might be useful in monitoring the circulatory regulatory system in artificial heart circulation. PMID:12653195
Fallacies of composition in nonlinear marketing models
NASA Astrophysics Data System (ADS)
Bischi, Gian Italo; Cerboni Baiardi, Lorenzo
2015-01-01
In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the one-dimensional model of a representative agent, whose dynamics summarize the common behavior of identical interacting agents, may be misleading. In order to discuss these topics some simple methods for the study of local stability and bifurcations are employed, as well as numerical examples where some results taken from the literature on chaos synchronization are applied to two-dimensional marketing models that exhibit riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors.