Harnessing quantum transport by transient chaos.

PubMed

Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M

2013-03-01

Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.

Shape and size distribution of chaos areas on Europa

NASA Astrophysics Data System (ADS)

Mikell, T.; Cox, R.

2008-12-01

Chaos terrain is ubiquitous on Europa's surface, but not randomly distributed. The global distribution of chaos areas shows a significant concentration between 30° N and S latitude, decreasing dramatically at higher latitudes. The low-latitude clustering is not an artifact of recognizability, as there is a greater proportion of images with high solar incidence angle (low light) at higher latitudes. Clustering is especially marked in context of the few but vast regional chaos tracts (>15,000 km2) that occupy a substantial proportion of the equatorial region: i.e. the low latitudes have not only greater numbers but much greater areal chaos coverage. Apex-antapex asymmetry is difficult to evaluate because the Galileo longitudinal coverage is so poor; but comparison of the image swaths that follow great circles across the leading and trailing hemispheres respectively shows greater numbers of chaos areas on the leading side. In spite of the equatorial location of a few vast chaos tracts, there is no apparent relationship between chaos area size and latitude. Chaos area outlines vary from smoothly circular to extremely jagged: the irregularity index ranges from 2- 270% (based on the ratio between measured chaos area perimeter and the circumference of a circle of equal area). There is a range of shapes in all size brackets, but smaller chaos areas on average have simpler, more equidimensional shapes, and edge complexity increases for larger chaos areas. Chaos areas of ~10 km equivalent circle diameter (ECD) have outlines that are 4-90% irregular, ones ~50 km ECD are 15-180% and those >100 km ECD are 35-270% irregular. In general, chaos areas with higher irregularity indices also have a higher raft:matrix ratio. These results, while preliminary, are consistent with experimental evidence suggesting an impact origin for some chaos terrain on Europa. In particular, the relationship between shape and size parallels the results of impact experiments into ice over water, in

Chaos, Complexity and Deterrence

DTIC Science & Technology

2000-04-19

populations of adversary countries but which seldom affect their leadership . Conclusion The jury is still out on the applicability of chaos theory to...Advent of Chaos Chaos theory in the West (considerable work on chaos was also conducted in the Soviet Union) developed from the 1960s work of...predicted by his model over time.1 This discovery, sensitivity to initial conditions, is one of the fundamental characteristics of chaos theory . Lorenz

Effect of smoothing on robust chaos.

PubMed

Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

2010-08-01

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.

PubMed

Gilpin, William; Feldman, Marcus W

2017-07-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

Embrace the Chaos

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…

Chaos in neurons and its application: perspective of chaos engineering.

PubMed

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.

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were

Controlling chaos-assisted directed transport via quantum resonance.

PubMed

Tan, Jintao; Zou, Mingliang; Luo, Yunrong; Hai, Wenhua

2016-06-01

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Controlling chaos-assisted directed transport via quantum resonance

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

Tan, Jintao; Zou, Mingliang; Luo, Yunrong

2016-06-15

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?

PubMed Central

Gelens, Lendert; Huang, Kerwyn Casey; Ferrell, James E.

2015-01-01

Summary Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume, and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration, and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells. PMID:26212326

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)

How to Generate Chaos at Home.

ERIC Educational Resources Information Center

Smith, Douglas

1992-01-01

Describes an electronic circuit that can function as a prototype for chaotic systems. Specific applied voltages produce chaotic signals that can be viewed with an oscilloscope or be made audible with a home stereo system. Provides directions for assembly with typical costs, mathematical basis of chaos theory, and experimental extensions. (JJK)

Defining chaos.

PubMed

Hunt, Brian R; Ott, Edward

2015-09-01

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.

Secure communications of CAP-4 and OOK signals over MMF based on electro-optic chaos.

PubMed

Ai, Jianzhou; Wang, Lulu; Wang, Jian

2017-09-15

Chaos-based secure communication can provide a high level of privacy in data transmission. Here, we experimentally demonstrate secure signal transmission over two kinds of multimode fiber (MMF) based on electro-optic intensity chaos. High-quality synchronization is achieved in an electro-optic feedback configuration. Both 5  Gbit/s carrier-less amplitude/phase (CAP-4) modulation and 10  Gbit/s on-off key (OOK) signals are recovered efficiently in electro-optic chaos-based communication systems. Degradations of chaos synchronization and communication system due to mismatch of various hardware keys are also discussed.

Routes to spatiotemporal chaos in Kerr optical frequency combs.

PubMed

Coillet, Aurélien; Chembo, Yanne K

2014-03-01

We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.

Weak nanoscale chaos and anomalous relaxation in DNA

NASA Astrophysics Data System (ADS)

Mazur, Alexey K.

2017-06-01

Anomalous nonexponential relaxation in hydrated biomolecules is commonly attributed to the complexity of the free-energy landscapes, similarly to polymers and glasses. It was found recently that the hydrogen-bond breathing of terminal DNA base pairs exhibits a slow power-law relaxation attributable to weak Hamiltonian chaos, with parameters similar to experimental data. Here, the relationship is studied between this motion and spectroscopic signals measured in DNA with a small molecular photoprobe inserted into the base-pair stack. To this end, the earlier computational approach in combination with an analytical theory is applied to the experimental DNA fragment. It is found that the intensity of breathing dynamics is strongly increased in the internal base pairs that flank the photoprobe, with anomalous relaxation quantitatively close to that in terminal base pairs. A physical mechanism is proposed to explain the coupling between the relaxation of base-pair breathing and the experimental response signal. It is concluded that the algebraic relaxation observed experimentally is very likely a manifestation of weakly chaotic dynamics of hydrogen-bond breathing in the base pairs stacked to the photoprobe and that the weak nanoscale chaos can represent an ubiquitous hidden source of nonexponential relaxation in ultrafast spectroscopy.

Weak nanoscale chaos and anomalous relaxation in DNA.

PubMed

Mazur, Alexey K

2017-06-01

Anomalous nonexponential relaxation in hydrated biomolecules is commonly attributed to the complexity of the free-energy landscapes, similarly to polymers and glasses. It was found recently that the hydrogen-bond breathing of terminal DNA base pairs exhibits a slow power-law relaxation attributable to weak Hamiltonian chaos, with parameters similar to experimental data. Here, the relationship is studied between this motion and spectroscopic signals measured in DNA with a small molecular photoprobe inserted into the base-pair stack. To this end, the earlier computational approach in combination with an analytical theory is applied to the experimental DNA fragment. It is found that the intensity of breathing dynamics is strongly increased in the internal base pairs that flank the photoprobe, with anomalous relaxation quantitatively close to that in terminal base pairs. A physical mechanism is proposed to explain the coupling between the relaxation of base-pair breathing and the experimental response signal. It is concluded that the algebraic relaxation observed experimentally is very likely a manifestation of weakly chaotic dynamics of hydrogen-bond breathing in the base pairs stacked to the photoprobe and that the weak nanoscale chaos can represent an ubiquitous hidden source of nonexponential relaxation in ultrafast spectroscopy.

Chaos without nonlinear dynamics.

PubMed

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.

Chaos Modeling: An Introduction and Research Application.

ERIC Educational Resources Information Center

Newman, Isadore; And Others

1993-01-01

Introduces the basic concepts of chaos theory and chaos modeling. Relates chaos theory to qualitative research and factor analysis. Describes some current research in education and psychology using chaos theory. Claims that the philosophical implications of chaos theory have been misapplied in practical terms. (KS)

An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers.

PubMed

Zapateiro De la Hoz, Mauricio; Acho, Leonardo; Vidal, Yolanda

2015-01-01

Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes.

An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers

PubMed Central

Zapateiro De la Hoz, Mauricio; Vidal, Yolanda

2015-01-01

Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes. PMID:26413563

Rydberg Atoms in Strong Fields: a Testing Ground for Quantum Chaos.

NASA Astrophysics Data System (ADS)

Courtney, Michael

1995-01-01

Rydberg atoms in strong static electric and magnetic fields provide experimentally accessible systems for studying the connections between classical chaos and quantum mechanics in the semiclassical limit. This experimental accessibility has motivated the development of reliable quantum mechanical solutions. This thesis uses both experimental and computed quantum spectra to test the central approaches to quantum chaos. These central approaches consist mainly of developing methods to compute the spectra of quantum systems in non -perturbative regimes, correlating statistical descriptions of eigenvalues with the classical behavior of the same Hamiltonian, and the development of semiclassical methods such as periodic-orbit theory. Particular emphasis is given to identifying the spectral signature of recurrences --quantum wave packets which follow classical orbits. The new findings include: the breakdown of the connection between energy-level statistics and classical chaos in odd-parity diamagnetic lithium, the discovery of the signature of very long period orbits in atomic spectra, quantitative evidence for the scattering of recurrences by the alkali -metal core, quantitative description of the behavior of recurrences near bifurcations, and a semiclassical interpretation of the evolution of continuum Stark spectra. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Experimental demonstration of the real-time online fault monitoring technique for chaos-based passive optical networks

NASA Astrophysics Data System (ADS)

Dou, Xinyu; Yin, Hongxi; Yue, Hehe; Jin, Yu; Shen, Jing; Li, Lin

2015-09-01

In this paper, a real-time online fault monitoring technique for chaos-based passive optical networks (PONs) is proposed and experimentally demonstrated. The fault monitoring is performed by the chaotic communication signal. The proof-of-concept experiments are demonstrated for two PON structures, i.e., wavelength-division-multiplexing (WDM) PON and Ethernet PON (EPON), respectively. For WDM PON, two monitoring approaches are investigated, one deploying a chaotic optical time domain reflectometry (OTDR) for each transmitter, and the other using only one tunable chaotic OTDR. The experimental results show that the faults at beyond 20 km from the OLT can be detected and located. The spatial resolution of the tunable chaotic OTDR is an order of magnitude of centimeter. Meanwhile, the monitoring process can operate in parallel with the chaotic optical secure communications. The proposed technique has benefits of real-time, online, precise fault location, and simple realization, which will significantly reduce the cost of operation, administration and maintenance (OAM) of PON.

[Shedding light on chaos theory].

PubMed

Chou, Shieu-Ming

2004-06-01

Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.

Death and revival of chaos.

PubMed

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2016-12-01

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.

Noise tolerant spatiotemporal chaos computing.

PubMed

Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L

2014-12-01

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Noise tolerant spatiotemporal chaos computing

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

Kia, Behnam; Kia, Sarvenaz; Ditto, William L.

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Relativistic chaos is coordinate invariant.

PubMed

Motter, Adilson E

2003-12-05

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.

Chaos Criminology: A critical analysis

NASA Astrophysics Data System (ADS)

McCarthy, Adrienne L.

There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.

Teaching as Chaos

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…

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Aram and Iani Chaos

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-344, 28 April 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image mosaic was constructed from data acquired by the MOC red wide angle camera. The large, circular feature in the upper left is Aram Chaos, an ancient impact crater filled with layered sedimentary rock that was later disrupted and eroded to form a blocky, 'chaotic' appearance. To the southeast of Aram Chaos, in the lower right of this picture, is Iani Chaos. The light-toned patches amid the large blocks of Iani Chaos are known from higher-resolution MOC images to be layered, sedimentary rock outcrops. The picture center is near 0.5oN, 20oW. Sunlight illuminates the scene from the left/upper left.

Brownian motion properties of optoelectronic random bit generators based on laser chaos.

PubMed

Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge

2016-07-11

The nondeterministic property of the optoelectronic random bit generator (RBG) based on laser chaos are experimentally analyzed from two aspects of the central limit theorem and law of iterated logarithm. The random bits are extracted from an optical feedback chaotic laser diode using a multi-bit extraction technique in the electrical domain. Our experimental results demonstrate that the generated random bits have no statistical distance from the Brownian motion, besides that they can pass the state-of-the-art industry-benchmark statistical test suite (NIST SP800-22). All of them give a mathematically provable evidence that the ultrafast random bit generator based on laser chaos can be used as a nondeterministic random bit source.

Chaos and noise.

PubMed

He, Temple; Habib, Salman

2013-09-01

Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.

"Chaos Rules" Revisited

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…

A bound on chaos

DOE PAGES

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas

2016-08-17

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Relations between distributional and Devaney chaos.

PubMed

Oprocha, Piotr

2006-09-01

Recently, it was proven that chaos in the sense of Devaney and weak mixing both imply chaos in the sense of Li and Yorke. In this article we give explicit examples that any of these two implications do not hold for distributional chaos.

Chaos synchronization in networks of semiconductor superlattices

NASA Astrophysics Data System (ADS)

Li, Wen; Aviad, Yaara; Reidler, Igor; Song, Helun; Huang, Yuyang; Biermann, Klaus; Rosenbluh, Michael; Zhang, Yaohui; Grahn, Holger T.; Kanter, Ido

2015-11-01

Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.

3D pulsed chaos lidar system.

PubMed

Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi

2018-04-30

We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

PubMed

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Finding Order and Direction from Chaos: A Comparison of Chaos Career Counseling and Trait Matching Counseling

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…

Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity.

PubMed

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.

Quantum Chaos

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

Quantum Chaos

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

The joy of transient chaos.

PubMed

Tél, Tamás

2015-09-01

We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.

Chaos-assisted tunneling in the presence of Anderson localization.

PubMed

Doggen, Elmer V H; Georgeot, Bertrand; Lemarié, Gabriel

2017-10-01

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case, for both a deterministic and a disordered model. We develop a single-parameter scaling description which accurately describes the numerical data. Several possible experimental implementations using cold atoms, photonic lattices, or microwave billiards are discussed.

Using chaos theory: the implications for nursing.

PubMed

Haigh, Carol

2002-03-01

The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.

Quantum chaos in nuclear physics

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators.

PubMed

Kuwamura, Masataka; Chiba, Hayato

2009-12-01

It is shown that the dormancy of predators induces mixed-mode oscillations and chaos in the population dynamics of a prey-predator system under certain conditions. The mixed-mode oscillations and chaos are shown to bifurcate from a coexisting equilibrium by means of the theory of fast-slow systems. These results may help to find experimental conditions under which one can demonstrate chaotic population dynamics in a simple phytoplankton-zooplankton (-resting eggs) community in a microcosm with a short duration.

Effect of correction of aberration dynamics on chaos in human ocular accommodation.

PubMed

Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

2013-11-15

We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

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

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

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

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.

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

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

Chaos and wave propagation regimes

NASA Astrophysics Data System (ADS)

Colosi, John

2003-04-01

Ray chaos theory and parabolic equation numerical modeling were two thrusts of Fred Tappert's research that were perpetually in tension. Fred was interested in the problem of identifying wave propagation regimes, most notably the strong focusing caustic regime and its evolution into the saturation regime. On the one hand, chaos theory held the seed of the complexity Fred believed existed in ocean acoustic wavefields; on the other hand ocean acoustic ray chaos theory (which Fred helped to pioneer) was a disdainful approximation to the full wave treatments offered by parabolic equation calculations. Fred was convinced that the saturation limit could not be obtained using ray theory and therefore he examined a new field of inquiry: a blend of chaotic ray insight and full wave dynamics called wave chaos. This talk will discuss some of Fred's insights on this topic and how they relate to observations from basin scale acoustic transmissions.

Wiener Chaos and Nonlinear Filtering

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

Lototsky, S.V.

2006-11-15

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. Themore » paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.« less

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

Survival and weak chaos.

PubMed

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Survival and weak chaos

PubMed Central

2018-01-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as ‘infant mortality’. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality—sensu engineering—without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy. PMID:29892407

How to test for partially predictable chaos.

PubMed

Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

2017-04-24

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

Chaos and complexity by design

DOE PAGES

Roberts, Daniel A.; Yoshida, Beni

2017-04-20

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We also show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. In addition, we prove that these 2k-point correlators for Pauli operators completely determine the k-foldmore » channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.« less

Outcrops In Aram Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

16 October 2004 Aram Chaos is the name of an approximately 275 km (171 mi) diameter impact crater near Ares Vallis, roughly half way between the Mars Exploration Rover, Opportunity, site in Meridiani Planum and the easternmost troughs of the Valles Marineris. The Aram Chaos crater is partially filled with a thick accumulation of layered rock. Erosion has exposed light- and dark-toned rock materials in the basin. This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a small area exhibiting some of the rock outcrops in Aram Chaos. The light-toned rocks may be sedimentary in origin. This image is located near 4.0oN, 20.6oW, and covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.

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.

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.

Controllable chaos in hybrid electro-optomechanical systems

PubMed Central

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-01-01

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505

Controllable chaos in hybrid electro-optomechanical systems.

PubMed

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-03-07

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.

Relativistic quantum chaos-An emergent interdisciplinary field.

PubMed

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Route to broadband chaos in a chaotic laser diode subject to optical injection.

PubMed

Wang, An-Bang; Wang, Yun-Cai; Wang, Juan-Fen

2009-04-15

We experimentally and numerically demonstrate a route to bandwidth-enhanced chaos that is induced by an additional optical injection for a chaotic laser diode with optical feedback. The measured and calculated optical spectra consistently reveal that the mechanism of bandwidth enhancement is the interaction between the injection and chaotic laser field via beating. The bandwidth can be maximized only when the injected light is detuned into the edge of the optical spectrum of the chaotic laser field and the beating frequency exceeds the original bandwidth. The simulated dynamics maps indicate that 20 GHz broadband chaos can be obtained by commonly used laser diodes.

Quantifying chaos for ecological stoichiometry.

PubMed

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

2010-09-01

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Household chaos and family sleep during infants' first year.

PubMed

Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M

2018-05-21

Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

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…

Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

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

Ghosh, S., E-mail: sabuj.ghosh@saha.ac.in; Kumar Shaw, Pankaj; Sekar Iyengar, A. N.

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noisemore » level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.« less

The information geometry of chaos

NASA Astrophysics Data System (ADS)

Cafaro, Carlo

2008-10-01

In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already

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…

!CHAOS: A cloud of controls

NASA Astrophysics Data System (ADS)

Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.

2016-01-01

The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.

Iani Chaos

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.

Iani Chaos

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.

Meteorite divide points to solar system chaos

NASA Astrophysics Data System (ADS)

Voosen, Paul

2018-03-01

The solar system of today was in turmoil in its first several million years, theorists believe, with giant planets sowing chaos as they strayed far from their current orbits. But corroborating evidence has been thin—until now. Scientists have found a new window into the early dynamics: a curious chemical divide in the dozens of species of meteorites. The picture has emerged over several years, but in work presented last week at the 2018 Lunar and Planetary Science Conference in The Woodlands, Texas, a group of German geochemists reported clinching evidence. Those distinct chemistries imply distinct origin stories for asteroids: One group formed from grist that began near the current location of the asteroid belt. The others coalesced beyond a proto-Jupiter, near where Saturn orbits today. The discovery opens the way to investigations of the solar system's earliest days, and could even set back the clock on the system's age.

Household Chaos--Links with Parenting and Child Behaviour

ERIC Educational Resources Information Center

Coldwell, Joanne; Pike, Alison; Dunn, Judy

2006-01-01

Background: The study aimed to confirm previous findings showing links between household chaos and parenting in addition to examining whether household chaos was predictive of children's behaviour over and above parenting. In addition, we investigated whether household chaos acts as a moderator between parenting and children's behaviour. Method:…

Decrease of cardiac chaos in congestive heart failure

NASA Astrophysics Data System (ADS)

Poon, Chi-Sang; Merrill, Christopher K.

1997-10-01

The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.

Exploiting chaos for applications.

PubMed

Ditto, William L; Sinha, Sudeshna

2015-09-01

We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.

Chaos, Chaos Control and Synchronization of a Gyrostat System

NASA Astrophysics Data System (ADS)

GE, Z.-M.; LIN, T.-N.

2002-03-01

The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.

Applied Chaos: From Oxymoron to Reality.

NASA Astrophysics Data System (ADS)

Ditto, William

1996-11-01

The rapidly emerging field of chaotic dynamics has presented the applied scientist with intriguing new tools to understand and manipulate systems that behave chaotically. An overview will be presented which will answer the questions: What is Chaos? and What can you do with Chaos? Examples of recent applications of chaos theory to the physical and biological sciences will be presented covering applications that range from encryption in communications to control of chaotically beating human hearts. Part A of program listing

The Capabilities of Chaos and Complexity

PubMed Central

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

Detecting nonlinearity and chaos in epidemic data

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

Ellner, S.; Gallant, A.R.; Theiler, J.

1993-08-01

Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude ofmore » epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.« less

Contractility of glycerinated Amoeba proteus and Chaos-chaos.

PubMed

Rinaldi, R; Opas, M; Hrebenda, B

1975-05-01

Immediate contact with large volumes of cold 50% (v/v) buffered glycerol preserved typical ameboid shape of Chaos chaos and Amoeba proteus with no visible distortions. These technics allowed determination of the contraction sites in these glycerinated models upon applications of ATP-Ca-Mg-solutions. The ectoplasmic tube was the main site of contraction. Preliminary EM investigations revealed thick and thin filaments, associated with the ectoplasmic tube near the plasma-lemma, which appeared to be the basis for the contractility of the ectoplasmic tube. There was no predominant contraction of the pseudopodial tips or the endoplasm in these models. The changes of volume were as much as 50%, and in some cases were not accompanied by any change in the length of the ameba; however, lengthwise contractions of the ectoplasmic tube in some amebae occurred to as much as 25%. The data substantiate a basic requirement of the ectoplasmic tube contraction theory of ameboid locomotion.

A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism

NASA Astrophysics Data System (ADS)

Chen, Jun-xin; Zhu, Zhi-liang; Fu, Chong; Yu, Hai; Zhang, Li-bo

2015-03-01

In recent years, a variety of chaos-based image cryptosystems have been investigated to meet the increasing demand for real-time secure image transmission. Most of them are based on permutation-diffusion architecture, in which permutation and diffusion are two independent procedures with fixed control parameters. This property results in two flaws. (1) At least two chaotic state variables are required for encrypting one plain pixel, in permutation and diffusion stages respectively. Chaotic state variables produced with high computation complexity are not sufficiently used. (2) The key stream solely depends on the secret key, and hence the cryptosystem is vulnerable against known/chosen-plaintext attacks. In this paper, a fast chaos-based image encryption scheme with a dynamic state variables selection mechanism is proposed to enhance the security and promote the efficiency of chaos-based image cryptosystems. Experimental simulations and extensive cryptanalysis have been carried out and the results prove the superior security and high efficiency of the scheme.

Chaos-Assisted Quantum Tunneling and Delocalization Caused by Resonance or Near-Resonance

NASA Astrophysics Data System (ADS)

Liang, Danfu; Zhang, Jiawei; Zhang, Xili

2018-05-01

We investigate the quantum transport of a single particle trapped in a tilted optical lattice modulated with periodical delta kicks, and attempt to figure out the relationship between chaos and delocalization or quantum tunneling. We illustrate some resonant parameter lines existing in both chaotic and regular parameter regions, and discover the velocity of delocalization of particle tends to faster in the resonant line as well as the lines in which the lattice tilt is an integral multiple n of tilt driving frequency in chaotic region. While the degree of localization is linked to the distance between parameter points and resonant lines. Those useful results can be experimentally applied to control chaos-assisted transport of single particle held in optical lattices.

Chaos Control of Epileptiform Bursting in the Brain

NASA Astrophysics Data System (ADS)

Slutzky, M. W.; Cvitanovic, P.; Mogul, D. J.

Epilepsy, defined as recurrent seizures, is a pathological state of the brain that afflicts over one percent of the world's population. Seizures occur as populations of neurons in the brain become overly synchronized. Although pharmacological agents are the primary treatment for preventing or reducing the incidence of these seizures, over 30% of epilepsy cases are not adequately helped by standard medical therapies. Several groups are exploring the use of electrical stimulation to terminate or prevent epileptic seizures. One experimental model used to test these algorithms is the brain slice where a select region of the brain is cut and kept viable in a well-oxygenated artificial cerebrospinal fluid. Under certain conditions, such slices may be made to spontaneously and repetitively burst, thereby providing an in vitro model of epilepsy. In this chapter, we discuss our efforts at applying chaos analysis and chaos control algorithms for manipulating this seizure-like behavior in a brain slice model. These techniques may provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain.

Chaos based encryption system for encrypting electroencephalogram signals.

PubMed

Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

2014-05-01

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

Investigating a link between large and small-scale chaos features on Europa

NASA Astrophysics Data System (ADS)

Tognetti, L.; Rhoden, A.; Nelson, D. M.

2017-12-01

Chaos is one of the most recognizable, and studied, features on Europa's surface. Most models of chaos formation invoke liquid water at shallow depths within the ice shell; the liquid destabilizes the overlying ice layer, breaking it into mobile rafts and destroying pre-existing terrain. This class of model has been applied to both large-scale chaos like Conamara and small-scale features (i.e. microchaos), which are typically <10 km in diameter. Currently unknown, however, is whether both large-scale and small-scale features are produced together, e.g. through a network of smaller sills linked to a larger liquid water pocket. If microchaos features do form as satellites of large-scale chaos features, we would expect a drop off in the number density of microchaos with increasing distance from the large chaos feature; the trend should not be observed in regions without large-scale chaos features. Here, we test the hypothesis that large chaos features create "satellite" systems of smaller chaos features. Either outcome will help us better understand the relationship between large-scale chaos and microchaos. We focus first on regions surrounding the large chaos features Conamara and Murias (e.g. the Mitten). We map all chaos features within 90,000 sq km of the main chaos feature and assign each one a ranking (High Confidence, Probable, or Low Confidence) based on the observed characteristics of each feature. In particular, we look for a distinct boundary, loss of preexisting terrain, the existence of rafts or blocks, and the overall smoothness of the feature. We also note features that are chaos-like but lack sufficient characteristics to be classified as chaos. We then apply the same criteria to map microchaos features in regions of similar area ( 90,000 sq km) that lack large chaos features. By plotting the distribution of microchaos with distance from the center point of the large chaos feature or the mapping region (for the cases without a large feature), we

Chaos in the Solar System

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!

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Effortful control and school adjustment: The moderating role of classroom chaos.

PubMed

Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

2017-11-01

Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

Chaos as a Social Determinant of Child Health: Reciprocal Associations?

PubMed Central

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250

Chaos: Choto delat?

NASA Astrophysics Data System (ADS)

Campbell, David

1987-11-01

I provide a brief overview of the current status of the field of deterministic "chaos" stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.

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

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.

Gullies of Gorgonus Chaos

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

Conference: Statistical Physics and Biological Information

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

Gross, David J.; Hwa, Terence

OAK B188 In the spring of 2001, the Institute for Theoretical Physics ran a 6 month scientific program on Statistical Physics and Biological Information. This program was organized by Walter Fitch (UC Irvine), Terence Hwa (UC San Diego), Luca Peliti (University Federico II), Naples Gary Stormo (Washington University School of Medicine) and Chao Tang (NEC). Overall scientific supervision was provided by David Gross, Director, ITP. The ITP has an online conference/program proceeding which consists of audio and transparencies of almost all of the talks held during this program. Over 100 talks are available on the site at http://online.kitp.ucsb.edu/online/infobio01/.

Polynomiography and Chaos

NASA Astrophysics Data System (ADS)

Kalantari, Bahman

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

Collision analysis of one kind of chaos-based hash function

NASA Astrophysics Data System (ADS)

Xiao, Di; Peng, Wenbing; Liao, Xiaofeng; Xiang, Tao

2010-02-01

In the last decade, various chaos-based hash functions have been proposed. Nevertheless, the corresponding analyses of them lag far behind. In this Letter, we firstly take a chaos-based hash function proposed very recently in Amin, Faragallah and Abd El-Latif (2009) [11] as a sample to analyze its computational collision problem, and then generalize the construction method of one kind of chaos-based hash function and summarize some attentions to avoid the collision problem. It is beneficial to the hash function design based on chaos in the future.

Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

PubMed

Adin, Mehmet Emin

2017-10-01

Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.

Low-dimensional chaos in turbulence

NASA Technical Reports Server (NTRS)

Vastano, John A.

1989-01-01

Direct numerical simulations are being performed on two different fluid flows in an attempt to discover the mechanism underlying the transition to turbulence in each. The first system is Taylor-Couette flow; the second, two-dimensional flow over an airfoil. Both flows exhibit a gradual transition to high-dimensional turbulence through low-dimensional chaos. The hope is that the instabilities leading to chaos will be easier to relate to physical processes in this case, and that the understanding of these mechanisms can then be applied to a wider array of turbulent systems.

Asymmetric spatiotemporal chaos induced by a polypoid mass in the excised larynx

PubMed Central

Zhang, Yu; Jiang, Jack J.

2008-01-01

In this paper, asymmetric spatiotemporal chaos induced by a polypoid mass simulating the laryngeal pathology of a vocal polyp is experimentally observed using high-speed imaging in an excised larynx. Spatiotemporal analysis reveals that the normal vocal folds show spatiotemporal correlation and symmetry. Normal vocal fold vibrations are dominated mainly by the first vibratory eigenmode. However, pathological vocal folds with a polypoid mass show broken symmetry and spatiotemporal irregularity. The spatial correlation is decreased. The pathological vocal folds spread vibratory energy across a large number of eigenmodes and induce asymmetric spatiotemporal chaos. High-order eigenmodes show complicated dynamics. Spatiotemporal analysis provides a valuable biomedical application for investigating the spatiotemporal chaotic dynamics of pathological vocal fold systems with a polypoid mass and may represent a valuable clinical tool for the detection of laryngeal mass lesion using high-speed imaging. PMID:19123612

Criticality and Chaos in Systems of Communities

NASA Astrophysics Data System (ADS)

Ostilli, Massimo; Figueiredo, Wagner

2016-01-01

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

The Nature (and Nurture) of Children's Perceptions of Family Chaos

ERIC Educational Resources Information Center

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

2010-01-01

Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…

Chaos Theory as a Model for Managing Issues and Crises.

ERIC Educational Resources Information Center

Murphy, Priscilla

1996-01-01

Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…

God's Stuff: The Constructive Powers of Chaos for Teaching Religion

ERIC Educational Resources Information Center

Willhauck, Susan

2010-01-01

Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…

PREFACE: The International Conference on Science of Friction

NASA Astrophysics Data System (ADS)

Miura, Kouji; Matsukawa, Hiroshi

2007-07-01

The first international conference on the science of friction in Japan was held at Irago, Aichi on 9-13 September 2007. The conference focused on the elementary process of friction phenomena from the atomic and molecular scale view. Topics covered in the conference are shown below.:

Quasiperiodicity route to chaos in cardiac conduction model

NASA Astrophysics Data System (ADS)

Quiroz-Juárez, M. A.; Vázquez-Medina, R.; Ryzhii, E.; Ryzhii, M.; Aragón, J. L.

2017-01-01

It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system proposed in Ref. [Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. Comput Meth Prog Bio 2014;117(1):40-49. doi:10.1016/j.cmpb.2014.04.009.], by including an ectopic pacemaker that stimulates the ventricular muscle to model arrhythmias. With this modification, the transition from normal rhythm to ventricular fibrillation is controlled by a single parameter. We show that this transition follows the so-called torus of quasi-periodic route to chaos, as verified by using numerical tools such as power spectrum and largest Lyapunov exponent.

The Importance of Chaos and Lenticulae on Europa for the JIMO Mission

NASA Technical Reports Server (NTRS)

Spaun, Nicole A.

2003-01-01

The Galileo Solid State Imaging (SSI) experiment provided high-resolution images of Europa's surface allowing identification of surface features barely distinguishable at Voyager's resolution. SSI revealed the visible pitting on Europa's surface to be due to large disrupted features, chaos, and smaller sub-circular patches, lenticulae. Chaos features contain a hummocky matrix material and commonly contain dislocated blocks of ridged plains. Lenticulae are morphologically interrelated and can be divided into three classes: domes, spots, and micro-chaos. Domes are broad, upwarped features that generally do not disrupt the texture of the ridged plains. Spots are areas of low albedo that are generally smooth in texture compared to other units. Micro-chaos are disrupted features with a hummocky matrix material, resembling that observed within chaos regions. Chaos and lenticulae are ubiquitous in the SSI regional map observations, which average approximately 200 meters per pixel (m/pxl) in resolution, and appear in several of the ultra-high resolution, i.e., better than 50 m/pxl, images of Europa as well. SSI also provided a number of multi-spectral observations of chaos and lenticulae. Using this dataset we have undertaken a thorough study of the morphology, size, spacing, stratigraphy, and color of chaos and lenticulae to determine their properties and evaluate models of their formation. Geological mapping indicates that chaos and micro-chaos have a similar internal morphology of in-situ degradation suggesting that a similar process was operating during their formation. The size distribution denotes a dominant size of 4-8 km in diameter for features containing hummocky material (i.e., chaos and micro-chaos). Results indicate a dominant spacing of 15 - 36 km apart. Chaos and lenticulae are generally among the youngest features stratigraphically observed on the surface, suggesting a recent change in resurfacing style. Also, the reddish non-icy materials on Europa

Generic superweak chaos induced by Hall effect

NASA Astrophysics Data System (ADS)

Ben-Harush, Moti; Dana, Itzhack

2016-05-01

We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.

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…

Controlling chaos faster.

PubMed

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

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

PubMed

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

2015-09-01

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

Chaos and the (un)predictability of evolution in a changing environment

PubMed Central

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-01-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. PMID:29235104

Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

PubMed

Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram

2015-04-01

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

Computing with Chaos

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).

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

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

2013-08-01

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

Chaos in learning a simple two-person game

PubMed Central

Sato, Yuzuru; Akiyama, Eizo; Farmer, J. Doyne

2002-01-01

We investigate the problem of learning to play the game of rock–paper–scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy. PMID:11930020

Does chaos theory have major implications for philosophy of medicine?

PubMed

Holm, S

2002-12-01

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.

Biologically inspired rate control of chaos.

PubMed

Olde Scheper, Tjeerd V

2017-10-01

The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

Chaos in charged AdS black hole extended phase space

NASA Astrophysics Data System (ADS)

Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

2018-06-01

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Chaos and Christianity: A Response to Butz and a Biblical Alternative.

ERIC Educational Resources Information Center

Watts, Richard E.; Trusty, Jerry

1997-01-01

M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

Convergent chaos

NASA Astrophysics Data System (ADS)

Pradas, Marc; Pumir, Alain; Huber, Greg; Wilkinson, Michael

2017-07-01

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterize the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the ‘butterfly effect’ needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of convergent chaos, which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

Chaos on the conveyor belt.

PubMed

Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán

2013-04-01

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five).

Dynamic Ice-Water Interactions Form Europa's Chaos Terrains

NASA Astrophysics Data System (ADS)

Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.

2011-12-01

Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

Ikeda-like chaos on a dynamically filtered supercontinuum light source

NASA Astrophysics Data System (ADS)

Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent

2016-08-01

We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

Chaos and the (un)predictability of evolution in a changing environment.

PubMed

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-02-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Noise induced chaos in optically driven colloidal rings.

NASA Astrophysics Data System (ADS)

Roichman, Yael; Zaslavsky, George; Grier, David G.

2007-03-01

Given a constant flux of energy, many driven dissipative systems rapidly organize themselves into configurations that support steady state motion. Examples include swarming of bacterial colonies, convection in shaken sandpiles, and synchronization in flowing traffic. How simple objects interacting in simple ways self-organize generally is not understood, mainly because so few of the available experimental systems afford the necessary access to their microscopic degrees of freedom. This talk introduces a new class of model driven dissipative systems typified by three colloidal spheres circulating around a ring-like optical trap known as an optical vortex. By controlling the interplay between hydrodynamic interactions and fixed disorder we are able to drive a transition from a previously predicted periodic steady state to fully developed chaos. In addition, by tracking both microscopic trajectories and macroscopic collective fluctuations the relation between the onset of microscopic weak chaos and the evolution of space-time self-similarity in macroscopic transport properties is revealed. In a broader scope, several optical vortices can be coupled to create a large dissipative system where each building block has internal degrees of freedom. In such systems the little understood dynamics of processes like frustration and jamming, fluctuation-dissipation relations and the propagation of collective motion can be tracked microscopically.

Li-Yorke Chaos in Hybrid Systems on a Time Scale

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2015-12-01

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

Synchronisation of chaos and its applications

NASA Astrophysics Data System (ADS)

Eroglu, Deniz; Lamb, Jeroen S. W.; Pereira, Tiago

2017-07-01

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.

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.

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

PubMed

Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur

2014-12-01

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

"I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

ERIC Educational Resources Information Center

Pryor, Robert; Bright, Jim

2004-01-01

This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…

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…

Planning in Higher Education and Chaos Theory: A Model, a Method.

ERIC Educational Resources Information Center

Cutright, Marc

This paper proposes a model, based on chaos theory, that explores strategic planning in higher education. It notes that chaos theory was first developed in the physical sciences to explain how apparently random activity was, in fact, complexity patterned. The paper goes on to describe how chaos theory has subsequently been applied to the social…

Conduct problems, IQ, and household chaos: a longitudinal multi-informant study

PubMed Central

Deater-Deckard, Kirby; Mullineaux, Paula Y.; Beekman, Charles; Petrill, Stephen A.; Schatschneider, Chris; Thompson, Lee A.

2010-01-01

Background We tested the hypothesis that household chaos would be associated with lower child IQ and more child conduct problems concurrently and longitudinally over two years while controlling for housing conditions, parent education/IQ, literacy environment, parental warmth/negativity, and stressful events. Methods The sample included 302 families with same-sex twins (58% female) in Kindergarten/1st grade at the first assessment. Parents’ and observers’ ratings were gathered, with some collected over a two-year period. Results Chaos varied widely. There was substantial mother–father agreement and longitudinal stability. Chaos covaried with poorer housing conditions, lower parental education/IQ, poorer home literacy environment, higher stress, higher negativity and lower warmth. Chaos statistically predicted lower IQ and more conduct problems, beyond the effects of other home environment factors. Conclusions Even with other home environment factors controlled, higher levels of chaos were linked concurrently with lower child IQ, and concurrently and longitudinally with more child conduct problems. Parent self-reported chaos represents an important aspect of housing and family functioning, with respect to children’s cognitive and behavioral functioning. PMID:19527431

Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

PubMed

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

Method of controlling chaos in laser equations

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-01-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

PubMed Central

2017-01-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies. PMID:28678792

Torus Breakdown and Homoclinic Chaos in a Glow Discharge Tube

NASA Astrophysics Data System (ADS)

Ginoux, Jean-Marc; Meucci, Riccardo; Euzzor, Stefano

2017-12-01

Starting from historical researches, we used, like Van der Pol and Le Corbeiller, a cubic function for modeling the current-voltage characteristic of a direct current low-pressure plasma discharge tube, i.e. a neon tube. This led us to propose a new four-dimensional autonomous dynamical system allowing to describe the experimentally observed phenomenon. Then, mathematical analysis and detailed numerical investigations of such a fourth-order torus circuit enabled to highlight bifurcation routes from torus breakdown to homoclinic chaos following the Newhouse-Ruelle-Takens scenario.

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…

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

PubMed Central

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

2016-01-01

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

Extension of spatiotemporal chaos in glow discharge-semiconductor systems

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

Akhmet, Marat, E-mail: marat@metu.edu.tr; Fen, Mehmet Onur; Rafatov, Ismail

2014-12-15

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases themore » potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].« less

Home Chaos: Sociodemographic, Parenting, Interactional, and Child Correlates

ERIC Educational Resources Information Center

Dumas, Jean E.; Nissley, Jenelle; Nordstrom, Alicia; Smith, Emilie Phillips; Prinz, Ronald J.; Levine, Douglas W.

2005-01-01

We conducted 2 studies to (a) establish the usefulness of the construct of home chaos, (b) investigate its correlates, and (c) determine the validity of the Confusion, Hubbub, and Order Scale (CHAOS) used to measure the construct in each study. Study 1 relied on a sample of European American preschoolers and their mothers and Study 2 on a sample…

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Technical Reports Server (NTRS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. 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.

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.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Controlling Mackey-Glass chaos.

PubMed

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Controlling Mackey-Glass chaos

NASA Astrophysics Data System (ADS)

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

A Chaos MIMO-OFDM Scheme for Mobile Communication with Physical-Layer Security

NASA Astrophysics Data System (ADS)

Okamoto, Eiji

Chaos communications enable a physical-layer security, which can enhance the transmission security in combining with upper-layer encryption techniques, or can omit the upper-layer secure protocol and enlarges the transmission efficiency. However, the chaos communication usually degrades the error rate performance compared to unencrypted digital modulations. To achieve both physical-layer security and channel coding gain, we have proposed a chaos multiple-input multiple-output (MIMO) scheme in which a rate-one chaos convolution is applied to MIMO multiplexing. However, in the conventional study only flat fading is considered. To apply this scheme to practical mobile environments, i.e., multipath fading channels, we propose a chaos MIMO-orthogonal frequency division multi-plexing (OFDM) scheme and show its effectiveness through computer simulations.

Application of laser chaos control methods to controlling thyroid-catatonic oscillations and burst firing of dopamine neurons

NASA Astrophysics Data System (ADS)

Duong-van, Minh

1993-11-01

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang and Bau. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the lasers equations are isomorphic to the Lorenz equations, we use this new method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential lasers controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills and Hunt. This method of control chaos is now extended to various medical and biological systems.

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)

Atlantis Chaos - False Color

NASA Image and Video Library

2014-12-23

The THEMIS VIS camera contains 5 filters. The data from different filters can be combined in multiple ways to create a false color image. This false color image from NASA 2001 Mars Odyssey spacecraft shows part of Atlantis Chaos.

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Developing Quality Preschool Movement Programs: CHAOS and KinderPlay

ERIC Educational Resources Information Center

Robert, Darren L.; Yongue, Bill

2004-01-01

This article presents two models for creating new developmentally appropriate preschool movement programs: CHAOS (Children Helping Adults Open Senses) at Eastern Connecticut State University and "KinderPlay" at Florida International University. CHAOS and KinderPlay utilize skill themes and movement concepts as their focus and incorporate…

Specifying the Links Between Household Chaos and Preschool Children’s Development

PubMed Central

Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne

2011-01-01

Household chaos has been linked to poorer cognitive, behavioral, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120

[Chaos theory: a fascinating concept for oncologists].

PubMed

Denis, F; Letellier, C

2012-05-01

The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

Fractals and Chaos

DTIC Science & Technology

1991-06-01

22 C. AFFINE TRANSFORMATIONS OF THE PLANE ........................... 25 D. CONTRACTION MAPPINGS OF THE SPACE gi(X...Henri Poincare (1854-1912) knew about chaos in dynamical systems in the late nineteenth century. Additionally, the French mathematicians Pierre Fatou...portion) are presented in the Euclidean plane , with a brief mention of more abstract spaces where applicable. Mathematical proofs that can be

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…

Error function attack of chaos synchronization based encryption schemes.

PubMed

Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

2004-03-01

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

PubMed Central

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

2015-01-01

Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

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)

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

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

Sun Wei, E-mail: wsun@mathstat.concordia.ca; Zeng Yong, E-mail: zengy@umkc.edu; Zhang Shu, E-mail: zhangshuisme@hotmail.com

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 schememore » 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.« less

Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology

NASA Astrophysics Data System (ADS)

Dhamala, Mukeshwar; Lai, Ying-Cheng

1999-02-01

Transient chaos is a common phenomenon in nonlinear dynamics of many physical, biological, and engineering systems. In applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos. We address how to sustain transient chaos in deterministic flows. We utilize a simple and practical method, based on extracting the fundamental dynamics from time series, to maintain chaos. The method can result in control of trajectories from almost all initial conditions in the original basin of the chaotic attractor from which transient chaos is created. We apply our method to three problems: (1) voltage collapse in electrical power systems, (2) species preservation in ecology, and (3) elimination of undesirable bursting behavior in a chemical reaction system.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet.

PubMed

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E; Sols, Fernando; Carr, Lincoln D

2018-06-08

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Dynamical topology and statistical properties of spatiotemporal chaos.

PubMed

Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

2012-12-01

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

Entanglement as a signature of quantum chaos.

PubMed

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

2004-01-01

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

The Nature of Nurture: A Genomewide Association Scan for Family Chaos

PubMed Central

Plomin, Robert

2008-01-01

Widely used measures of the environment, especially the family environment of children, show genetic influence in dozens of twin and adoption studies. This phenomenon is known as gene-environment correlation in which genetically driven influences of individuals affect their environments. We conducted the first genome-wide association (GWA) analysis of an environmental measure. We used a measure called CHAOS which assesses ‘environmental confusion’ in the home, a measure that is more strongly associated with cognitive development in childhood than any other environmental measure. CHAOS was assessed by parental report when the children were 3 years and again when the children were 4 years; a composite CHAOS measure was constructed across the 2 years. We screened 490,041 autosomal single-nucleotide polymorphisms (SNPs) in a two-stage design in which children in low chaos families (N = 469) versus high chaos families (N = 369) from 3,000 families of 4-year-old twins were screened in Stage 1 using pooled DNA. In Stage 2, following SNP quality control procedures, 41 nominated SNPs were tested for association with family chaos by individual genotyping an independent representative sample of 3,529. Despite having 99% power to detect associations that account for more than 0.5% of the variance, none of the 41 nominated SNPs met conservative criteria for replication. Similar to GWA analyses of other complex traits, it is likely that most of the heritable variation in environmental measures such as family chaos is due to many genes of very small effect size. PMID:18360741

The nature of nurture: a genomewide association scan for family chaos.

PubMed

Butcher, Lee M; Plomin, Robert

2008-07-01

Widely used measures of the environment, especially the family environment of children, show genetic influence in dozens of twin and adoption studies. This phenomenon is known as gene-environment correlation in which genetically driven influences of individuals affect their environments. We conducted the first genome-wide association (GWA) analysis of an environmental measure. We used a measure called CHAOS which assesses 'environmental confusion' in the home, a measure that is more strongly associated with cognitive development in childhood than any other environmental measure. CHAOS was assessed by parental report when the children were 3 years and again when the children were 4 years; a composite CHAOS measure was constructed across the 2 years. We screened 490,041 autosomal single-nucleotide polymorphisms (SNPs) in a two-stage design in which children in low chaos families (N = 469) versus high chaos families (N = 369) from 3,000 families of 4-year-old twins were screened in Stage 1 using pooled DNA. In Stage 2, following SNP quality control procedures, 41 nominated SNPs were tested for association with family chaos by individual genotyping an independent representative sample of 3,529. Despite having 99% power to detect associations that account for more than 0.5% of the variance, none of the 41 nominated SNPs met conservative criteria for replication. Similar to GWA analyses of other complex traits, it is likely that most of the heritable variation in environmental measures such as family chaos is due to many genes of very small effect size.

Discretization chaos - Feedback control and transition to chaos

NASA Technical Reports Server (NTRS)

Grantham, Walter J.; Athalye, Amit M.

1990-01-01

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser

NASA Astrophysics Data System (ADS)

Coulibaly, S.; Clerc, M. G.; Selmi, F.; Barbay, S.

2017-02-01

The occurrence of extreme events in a spatially extended microcavity laser has been recently reported [Selmi et al., Phys. Rev. Lett. 116, 013901 (2016), 10.1103/PhysRevLett.116.013901] to be correlated to emergence of spatiotemporal chaos. In this dissipative system, the role of spatial coupling through diffraction is essential to observe the onset of spatiotemporal complexity. We investigate further the formation mechanism of extreme events by comparing the statistical and dynamical analyses. Experimental measurements together with numerical simulations allow us to assign the quasiperiodicity mechanism as the route to spatiotemporal chaos in this system. Moreover, by investigating the fine structure of the maximum Lyapunov exponent, of the Lyapunov spectrum, and of the Kaplan-Yorke dimension of the chaotic attractor, we are able to deduce that intermittency plays a key role in the proportion of extreme events measured. We assign the observed mechanism of generation of extreme events to quasiperiodic extended spatiotemporal intermittency.

The CHAOS-4 geomagnetic field model

NASA Astrophysics Data System (ADS)

Olsen, Nils; Lühr, Hermann; Finlay, Christopher C.; Sabaka, Terence J.; Michaelis, Ingo; Rauberg, Jan; Tøffner-Clausen, Lars

2014-05-01

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly determined. More than 14 yr of data from the satellites Ørsted, CHAMP and SAC-C, augmented with magnetic observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (lithospheric) field is n = 100. The core field is expressed by spherical harmonic expansion coefficients up to n = 20; its time-evolution is described by order six splines, with 6-month knot spacing, spanning the time interval 1997.0-2013.5. The third time derivative of the squared radial magnetic field component is regularized at the core-mantle boundary. No spatial regularization is applied to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its high-degree lithospheric field part is solely determined from low-altitude CHAMP satellite observations taken during the last 2 yr (2008 September-2010 September) of the mission. We obtain a good agreement with other recent lithospheric field models like MF7 for degrees up to n = 85, confirming that lithospheric field structures down to a horizontal wavelength of 500 km are currently robustly determined.

Stochastic Representation of Chaos using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2005-01-01

A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

Chaos Through-Wall Imaging Radar

NASA Astrophysics Data System (ADS)

Xu, Hang; Wang, Bingjie; Zhang, Jianguo; Liu, Li; Li, Ying; Wang, Yuncai; Wang, Anbang

2017-12-01

We experimentally demonstrate a chaos through-wall imaging radar using ultra-wideband chaotic-pulse-position modulation (CPPM) microwave signal. The CPPM signal based on logistic map with 1-ns pulse width and 1-GHz bandwidth is implemented by a field programmable gate array (FPGA) and then up-converted as the radar transmitting signal. Two-dimensional image of human objects behind obstacles is obtained by correlation method and back projection algorithm. Our experiments successfully perform through-wall imaging for single and multiple human objects through 20-cm thick wall. The down-range resolution of the proposed radar is 15 cm. Furthermore, the anti-jamming properties of the proposed radar in CPPM jamming, linear frequency-modulated jamming, and Gaussian noise jamming environments are demonstrated by electromagnetic simulations using the finite-difference time-domain. The simulation results show the CPPM microwave signal possesses excellent jamming immunity to the noise and radio frequency interference, which makes it perform superbly in multiradar environments.

Chaos in brake squeal noise

NASA Astrophysics Data System (ADS)

Oberst, S.; Lai, J. C. S.

2011-02-01

Brake squeal has become an increasing concern to the automotive industry because of warranty costs and the requirement for continued interior vehicle noise reduction. Most research has been directed to either analytical and experimental studies of brake squeal mechanisms or the prediction of brake squeal propensity using finite element methods. By comparison, there is a lack of systematic analysis of brake squeal data obtained from a noise dynamometer. It is well known that brake squeal is a nonlinear transient phenomenon and a number of studies using analytical and experimental models of brake systems (e.g., pin-on-disc) indicate that it could be treated as a chaotic phenomenon. Data obtained from a full brake system on a noise dynamometer were examined with nonlinear analysis techniques. The application of recurrence plots reveals chaotic structures even in noisy data from the squealing events. By separating the time series into different regimes, lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents. Further analysis of the recurrence plot of squealing events by means of recurrence quantification analysis measures reveals different regimes of laminar and random behaviour, periodicity and chaos-forming recurrent transitions. These results help to classify brake squeal mechanisms and to enhance understanding of friction-related noise phenomena.

On chaos synchronization and secure communication.

PubMed

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. This journal is © 2010 The Royal Society

Quasiperiodicity and chaos in cardiac fibrillation.

PubMed

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

1997-01-15

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.

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods.

PubMed

Liu, Boquan; Polce, Evan; Sprott, Julien C; Jiang, Jack J

2018-05-17

The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100 Monte Carlo experiments were applied to analyze the output of jitter, shimmer, correlation dimension, and spectrum convergence ratio. The computational output of the 4 classifiers was then plotted against signal chaos level to investigate the performance of these acoustic analysis methods under varying degrees of signal chaos. A diffusive behavior detection-based chaos level test was used to investigate the performances of different voice classification methods. Voice signals were constructed by varying the signal-to-noise ratio to establish differing signal chaos conditions. Chaos level increased sigmoidally with increasing noise power. Jitter and shimmer performed optimally when the chaos level was less than or equal to 0.01, whereas correlation dimension was capable of analyzing signals with chaos levels of less than or equal to 0.0179. Spectrum convergence ratio demonstrated proficiency in analyzing voice signals with all chaos levels investigated in this study. The results of this study corroborate the performance relationships observed in previous studies and, therefore, demonstrate the validity of the validation test method. The presented chaos level validation test could be broadly utilized to evaluate acoustic analysis methods and establish the most appropriate methodology for objective voice analysis in clinical practice.

Suppression of chaos at slow variables by rapidly mixing fast dynamics

NASA Astrophysics Data System (ADS)

Abramov, R.

2012-04-01

One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

Chaos in quantum channels

DOE PAGES

Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; ...

2016-02-01

For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back upmore » our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.« less

Magnetic field induced dynamical chaos.

PubMed

Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra

2013-12-01

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.

A history of chaos theory.

PubMed

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.

A history of chaos theory

PubMed Central

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

Santa Rita Experimental Range: 100 years (1903 to 2003) of accomplishments and contributions; conference proceedings; 2003 October 30-November 1; Tucson, AZ

Treesearch

Mitchel P. McClaran; Peter F. Ffolliott; Carleton B. Edminster

2003-01-01

The purpose of this conference was to celebrate the 100 years of accomplishments and contributions of the Santa Rita Experimental Range, the longest continuously operating research area dedicated to the sustainable management of North American rangelands. The conference consisted of one-and-a-half days of invited synthesis papers and contributed poster presentations...

Chaos control of Hastings-Powell model by combining chaotic motions

NASA Astrophysics Data System (ADS)

Danca, Marius-F.; Chattopadhyay, Joydev

2016-04-01

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

Chaos in an imperfectly premixed model combustor.

PubMed

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.

Quantum chaos on a critical Fermi surface.

PubMed

Patel, Aavishkar A; Sachdev, Subir

2017-02-21

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of [Formula: see text] species of fermions at nonzero density coupled to a [Formula: see text] gauge field in two spatial dimensions and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters; i.e., the relationship is independent of [Formula: see text], the gauge-coupling constant, the Fermi velocity, the Fermi surface curvature, and high-energy details.

Improved Adaptive LSB Steganography Based on Chaos and Genetic Algorithm

NASA Astrophysics Data System (ADS)

Yu, Lifang; Zhao, Yao; Ni, Rongrong; Li, Ting

2010-12-01

We propose a novel steganographic method in JPEG images with high performance. Firstly, we propose improved adaptive LSB steganography, which can achieve high capacity while preserving the first-order statistics. Secondly, in order to minimize visual degradation of the stego image, we shuffle bits-order of the message based on chaos whose parameters are selected by the genetic algorithm. Shuffling message's bits-order provides us with a new way to improve the performance of steganography. Experimental results show that our method outperforms classical steganographic methods in image quality, while preserving characteristics of histogram and providing high capacity.

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

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

PubMed

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

2012-03-01

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

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

PubMed Central

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

The onset of chaos in orbital pilot-wave dynamics.

PubMed

Tambasco, Lucas D; Harris, Daniel M; Oza, Anand U; Rosales, Rodolfo R; Bush, John W M

2016-10-01

We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario.

Control of Chaos: New Perspectives in Experimental and Theoretical Science. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. Theme Issue. Part 1. Volume 8, Number 8, August 1998.

DTIC Science & Technology

1998-08-01

de Matemdticas, Universidad de Murcia, Murcia, Spain RICARDO CHACON Departamento de Electr6nica e, Ingenieria Electromecdnica, Escuela, de... Ingenierias Industriales, Universidad de Extremadura, 06071, Badajoz, Spain MIGUEL ANGEL LOPEZ Departamento de Matemdticas, Aplicada, Escuela Universitaria de...World Scientific Publishing Company FUZZY CONTROL OF CHAOS OSCAR CALVO* CICpBA, L.E.L C.1, Departamento de Electrotecnia, Facultad de Ingenieria

Specifying the Links between Household Chaos and Preschool Children's Development

ERIC Educational Resources Information Center

Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne

2012-01-01

Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…

Flavors of Chaos in the Asteroid Belt

NASA Astrophysics Data System (ADS)

Tsiganis, Kleomenis

2016-10-01

The asteroid belt is a natural laboratory for studying chaos, as a large fraction of asteroids actually reside on chaotic orbits. Numerous studies over the past 25 years have unveiled a multitude of dynamical chaos-generating mechanisms, operating on different time-scales and dominating over different regions of the belt. In fact, the distribution of chaotic asteroids in orbital space can be largely understood as the outcome of the combined action of resonant gravitational perturbations and the Yarkovsky effect - two topics on which Paolo Farinella has made an outstanding contribution! - notwithstanding the fact that the different "flavors" of chaos can give rise to a wide range of outcomes, from fast escape (e.g. to NEA space) to slow (~100s My) macroscopic diffusion (e.g. spreading of families) and strange, stable-looking, chaotic orbits (ultra-slow diffusion). In this talk I am going to present an overview of these mechanisms, presenting both analytical and numerical results, and their role in understanding the long-term evolution and stability of individual bodies, asteroid groups and families.

DTU candidate field models for IGRF-12 and the CHAOS-5 geomagnetic field model

NASA Astrophysics Data System (ADS)

Finlay, Christopher C.; Olsen, Nils; Tøffner-Clausen, Lars

2015-07-01

We present DTU's candidate field models for IGRF-12 and the parent field model from which they were derived, CHAOS-5. Ten months of magnetic field observations from ESA's Swarm mission, together with up-to-date ground observatory monthly means, were used to supplement the data sources previously used to construct CHAOS-4. The internal field part of CHAOS-5, from which our IGRF-12 candidate models were extracted, is time-dependent up to spherical harmonic degree 20 and involves sixth-order splines with a 0.5 year knot spacing. In CHAOS-5, compared with CHAOS-4, we update only the low-degree internal field model (degrees 1 to 24) and the associated external field model. The high-degree internal field (degrees 25 to 90) is taken from the same model CHAOS-4h, based on low-altitude CHAMP data, which was used in CHAOS-4. We find that CHAOS-5 is able to consistently fit magnetic field data from six independent low Earth orbit satellites: Ørsted, CHAMP, SAC-C and the three Swarm satellites (A, B and C). It also adequately describes the secular variation measured at ground observatories. CHAOS-5 thus contributes to an initial validation of the quality of the Swarm magnetic data, in particular demonstrating that Huber weighted rms model residuals to Swarm vector field data are lower than those to Ørsted and CHAMP vector data (when either one or two star cameras were operating). CHAOS-5 shows three pulses of secular acceleration at the core surface over the past decade; the 2006 and 2009 pulses have previously been documented, but the 2013 pulse has only recently been identified. The spatial signature of the 2013 pulse at the core surface, under the Atlantic sector where it is strongest, is well correlated with the 2006 pulse, but anti-correlated with the 2009 pulse.

Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point.

PubMed

Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong

2015-07-01

The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.

Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point

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

Shao, Chenxi, E-mail: cxshao@ustc.edu.cn; Xue, Yong; Fang, Fang

2015-07-15

The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedbackmore » control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.« less

Quasiperiodicity and chaos in cardiac fibrillation.

PubMed Central

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

Iceberg Ahead: The Effect of Bands and Ridges During Chaos Formation on Europa.

NASA Astrophysics Data System (ADS)

Hedgepeth, J. E.; Schmidt, B. E.

2016-12-01

Europa presents a dynamic and varied surface, but the most enticing component is arguably its chaos structures. With it, the surface and subsurface can interact, but in order to fully understand if this is occurring we have to properly parameterize the surface structural integrity. We consider the Schmidt et al. (2011) method of classifying icebergs by feature type to study what features remained intact in the chaos matrix. In this work we expand on this idea. We hypothesize that the ice that forms ridges and bands exhibit higher structural strengths than plains. Subsequently, this ice is more likely to remain during chaos formation in the form of icebergs. We begin by mapping the surface around Murias chaos and other prominent chaos features. Maps are used to infer what paleo-topographic features existed before chaos formation by using the features surrounding the chaos regions as blueprints for what existed before. We perform a multivariate regression to correlate the amount of icebergs present to the amount of surface that was covered by either bands, plains, or ridges. We find ridges play the biggest role in the production of icebergs with a weighted value of 40%. Bands may play a smaller role (13%), but plains show little to no correlation (5%). Further mapping will better reveal if this trend holds true in other regions. This statistical analysis supports our hypothesis, and further work will better quantify what is occurring. We will address the energy expended in the chaos regions via movement and rotation of icebergs during the formation event and through ice-melt.

Socioeconomic Risk Moderates the Link between Household Chaos and Maternal Executive Function

PubMed Central

Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

2012-01-01

We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for hypothesis 1, and consistent with hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PMID:22563703

Emergence of chaos in a spatially confined reactive system

NASA Astrophysics Data System (ADS)

Voorsluijs, Valérie; De Decker, Yannick

2016-11-01

In spatially restricted media, interactions between particles and local fluctuations of density can lead to important deviations of the dynamics from the unconfined, deterministic picture. In this context, we investigated how molecular crowding can affect the emergence of chaos in small reactive systems. We developed to this end an amended version of the Willamowski-Rössler model, where we account for the impenetrability of the reactive species. We analyzed the deterministic kinetics of this model and studied it with spatially-extended stochastic simulations in which the mobility of particles is included explicitly. We show that homogeneous fluctuations can lead to a destruction of chaos through a fluctuation-induced collision between chaotic trajectories and absorbing states. However, an interplay between the size of the system and the mobility of particles can counterbalance this effect so that chaos can indeed be found when particles diffuse slowly. This unexpected effect can be traced back to the emergence of spatial correlations which strongly affect the dynamics. The mobility of particles effectively acts as a new bifurcation parameter, enabling the system to switch from stationary states to absorbing states, oscillations or chaos.

Staying Innovative and Change-Focused in the New Economy. A Collection of Special Papers Generated for the 2001 International Career Development Conference (Seattle, Washington, November 7-11, 2001).

ERIC Educational Resources Information Center

Walz, Garry R., Ed.; Knowdell, Richard, Ed.; Kirkman, Chris, Ed.

This publication is designed to broaden exposure to the ideas presented at the 2001 International Career Development Conference. It provides authors with an international forum for communicating their current research, proposals, and projects to the international career development community. The articles in this symposium include: (1) "Chaos,…

Chaos as the hub of systems dynamics. The part I-The attitude control of spacecraft by involving in the heteroclinic chaos

NASA Astrophysics Data System (ADS)

Doroshin, Anton V.

2018-06-01

In this work the chaos in dynamical systems is considered as a positive aspect of dynamical behavior which can be applied to change systems dynamical parameters and, moreover, to change systems qualitative properties. From this point of view, the chaos can be characterized as a hub for the system dynamical regimes, because it allows to interconnect separated zones of the phase space of the system, and to fulfill the jump into the desirable phase space zone. The concretized aim of this part of the research is to focus on developing the attitude control method for magnetized gyrostat-satellites, which uses the passage through the intentionally generated heteroclinic chaos. The attitude dynamics of the satellite/spacecraft in this case represents the series of transitions from the initial dynamical regime into the chaotic heteroclinic regime with the subsequent exit to the final target dynamical regime with desirable parameters of the attitude dynamics.

Chaos: A Mathematical Introduction

NASA Astrophysics Data System (ADS)

Banks, John; Dragan, Valentina; Jones, Arthur

2003-06-01

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

Analysis of chaos attractors of MCG-recordings.

PubMed

Jiang, Shiqin; Yang, Fan; Yi, Panke; Chen, Bo; Luo, Ming; Wang, Lemin

2006-01-01

By studying the chaos attractor of cardiac magnetic induction strength B(z) generated by the electrical activity of the heart, we found that its projection in the reconstructed phase space has a similar shape with the map of the total current dipole vector. It is worth noting that the map of the total current dipole vector is computed with MCG recordings measured at 36 locations, whereas the chaos attractor of B(z) is generated by only one cardiac magnetic field recordings on the measured plan. We discuss only two subjects of different ages in this paper.

Signatures of chaos in the Brillouin zone.

PubMed

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Chaos and random matrices in supersymmetric SYK

NASA Astrophysics Data System (ADS)

Hunter-Jones, Nicholas; Liu, Junyu

2018-05-01

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

Analysis of chaos in high-dimensional wind power system.

PubMed

Wang, Cong; Zhang, Hongli; Fan, Wenhui; Ma, Ping

2018-01-01

A comprehensive analysis on the chaos of a high-dimensional wind power system is performed in this study. A high-dimensional wind power system is more complex than most power systems. An 11-dimensional wind power system proposed by Huang, which has not been analyzed in previous studies, is investigated. When the systems are affected by external disturbances including single parameter and periodic disturbance, or its parameters changed, chaotic dynamics of the wind power system is analyzed and chaotic parameters ranges are obtained. Chaos existence is confirmed by calculation and analysis of all state variables' Lyapunov exponents and the state variable sequence diagram. Theoretical analysis and numerical simulations show that the wind power system chaos will occur when parameter variations and external disturbances change to a certain degree.

Chaos, Hubbub, and Order Scale and Health Risk Behaviors in Adolescents in Los Angeles.

PubMed

Chatterjee, Avik; Gillman, Matthew W; Wong, Mitchell D

2015-12-01

To determine the relationship between household chaos and substance use, sexual activity, and violence-related risk behaviors in adolescents. We analyzed cross-sectional data among 929 high-school students in Los Angeles who completed a 90-minute interview that assessed health behaviors and household chaos with the 14-question Chaos, Hubbub, and Order Scale (CHAOS). Using the generalized estimating equation and adjusting for personal, parental, and family covariates, we examined associations of CHAOS score with substance use, sexual activity, and violent behavior outcome variables. We also examined the role of depression and school engagement as mediators. Mean (SD) age of the 929 students was 16.4 (1.3) years, 516 (55%) were female, and 780 (84%) were Latino. After adjustment, compared with students with CHAOS score 0, those students with the greatest scores (5-14) had ORs of 3.1 (95% CI 1.1-8.7) for smoking, 2.6 (95% CI 1.6-4.4) for drinking, 6.1 (95% CI 1.8-21) for substance use at school, and 1.9 (95% CI 1.1-3.3) for fighting in the past 12 months. Associations between CHAOS score and sexual risk and other violent behaviors were not significant. Depression and school engagement attenuated the associations. In this group of adolescents, greatest CHAOS score was associated with increased odds of risky health behaviors, with depression and school engagement as potential mediators. In the future, CHAOS score could be measured to assess risk for such behaviors or be a target for intervention to reduce chances of engaging in these behaviors. Copyright © 2015 Elsevier Inc. All rights reserved.

Detection of Gray Crystalline Hematite in the Aureum and Iani Chaos Layered Terrains

NASA Astrophysics Data System (ADS)

Glotch, T. D.; Rogers, D.; Christensen, P. R.

2005-12-01

Using the TES and THEMIS datasets, small hematite-rich deposits have been discovered in Aureum and Iani Chaos. The newly discovered hematite-rich deposits share several similarities with the deposit in Aram Chaos [1], including the occurrence of hematite in a friable layered unit, and the presence of a light-toned caprock. The presence of these units over a distance of several hundred kilometers in the equatorial latitudes of Mars may point to a preferred global mechanism for hematite formation. However, it is unclear how, if at all, these units are related to the hematite- and sulfate-rich unit in Meridiani Planum, which is substantially larger and older (by as much as 1 Ga) than the layered units seen in the equatorial chaotic terrains. Though the caprock units in Aram Chaos and Aureum Chaos are similar, the corresponding unit in Iani Chaos is morphologically different, exhibiting less of a cliff-forming erosional pattern. The hematite-rich units in Aram and Aureum Chaos lie stratigraphically below the light-toned caprock units. In Iani Chaos, the hematite deposit is coincident with the light-toned unit. Data returned from the Mars Express OMEGA instrument have shown the presence of hydrated sulfates in the hematite-rich units associated with Aram and Iani Chaos, although to date, no sulfate detection has been reported in Aureum Chaos [2]. The sequence of caprock and hematite units in Aram, Aureum, and Iani Chaos probably did not form coincidentally as part of an extensive regional layer, but instead formed by similar, but not identical, processes in their respective chaotic terrains. The presence of these units in chaotic terrains, which have been hypothesized to form by subsidence after the release of subsurface water, indicate that these units may have been deposited in an aqueous environment. By analogy to Meridiani Planum, later subsurface aqueous activity in the region of the chaotic terrains may have provided the necessary diagenetic conditions for the

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

Narrative and Chaos Acknowledging the Novelty of Lives-in-Time

ERIC Educational Resources Information Center

Randall, William L.

2007-01-01

In this paper I propose that interest in "narrative" within the human sciences is comparable to interest in "chaos" within the natural sciences. In their respective ways, theories on narrative and theories on chaos are aimed at appreciating the dynamics of complex, multi-dimensional systems which otherwise resist our attempts to predict, measure,…

Examining the Relationship Between Children's ADHD Symptomatology and Inadequate Parenting: The Role of Household Chaos.

PubMed

Wirth, Andrea; Reinelt, Tilman; Gawrilow, Caterina; Schwenck, Christina; Freitag, Christine M; Rauch, Wolfgang A

2017-02-01

This study examines the interrelations of parenting practices, emotional climate, and household chaos in families with children with and without ADHD. In particular, indirect pathways from children's ADHD symptomatology to inadequate parenting and negative emotional climate via household chaos were investigated. Parenting, emotional climate, and household chaos were assessed using questionnaires and a speech sample of parents of 31 children with and 53 without ADHD, aged 7 to 13 years. Group differences were found for certain parenting dimensions, the parent-child relationship, critical comments, and household chaos. While we found significant indirect effects between children's ADHD and certain parenting dimensions through household chaos, no effects were found for any aspect of emotional climate. Children's ADHD symptoms translate into inadequate parenting through household chaos, which underlines the need for interventions to improve household organization skills in parents of children with ADHD.

Socioeconomic risk moderates the link between household chaos and maternal executive function.

PubMed

Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

2012-06-01

We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for Hypothesis 1, and consistent with Hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PsycINFO Database Record (c) 2012 APA, all rights reserved.

Quantum chaos: An entropy approach

NASA Astrophysics Data System (ADS)

Sl/omczyński, Wojciech; Życzkowski, Karol

1994-11-01

A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II

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…

Aram Chaos Rocks

NASA Technical Reports Server (NTRS)

2005-01-01

8 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcrops of light-toned, sedimentary rock among darker-toned mesas in Aram Chaos. Dark, windblown megaripples -- large ripples -- are also present at this location.

Location near: 3.0oN, 21.6oW Image width: width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Autumn

Chaos, Poverty, and Parenting: Predictors of Early Language Development

PubMed Central

Vernon-Feagans, Lynne; Garrett-Peters, Patricia; Willoughby, Mike; Mills-Koonce, Roger

2011-01-01

Studies have shown that distal family risk factors like poverty and maternal education are strongly related to children's early language development. Yet, few studies have examined these risk factors in combination with more proximal day-to-day experiences of children that might be critical to understanding variation in early language. Young children's exposure to a chronically chaotic household may be one critical experience that is related to poorer language, beyond the contribution of SES and other demographic variables. In addition, it is not clear whether parenting might mediate the relationship between chaos and language. The purpose of this study was to understand how multiple indicators of chaos over children's first three years of life, in a representative sample of children living in low wealth rural communities, were related to child expressive and receptive language at 36 months. Factor analysis of 10 chaos indicators over five time periods suggested two factors that were named household disorganization and instability. Results suggested that after accounting for thirteen covariates like maternal education and poverty, one of two chaos composites (household disorganization) accounted for significant variance in receptive and expressive language. Parenting partially mediated this relationship although household disorganization continued to account for unique variance in predicting early language. PMID:23049162

Direct generation of all-optical random numbers from optical pulse amplitude chaos.

PubMed

Li, Pu; Wang, Yun-Cai; Wang, An-Bang; Yang, Ling-Zhen; Zhang, Ming-Jiang; Zhang, Jian-Zhong

2012-02-13

We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.

Detecting chaos in irregularly sampled time series.

PubMed

Kulp, C W

2013-09-01

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

Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

PubMed

Kwuimy, C A Kitio; Nataraj, C; Litak, G

2011-12-01

We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

Chaos, Complexity, Learning, and the Learning Organization: Towards a Chaordic Enterprise

ERIC Educational Resources Information Center

van Eijnatten, Frans M.; Putnik, Goran D.

2004-01-01

In order to set the stage for this special issue, the prime concepts are defined: i.e. "chaos," "complexity," "learning" (individual and organizational), "learning organization," and "chaordic enterprise". Also, several chaos-and-complexity-related definitions of learning and learning organizations are provided. Next, the guest editors' main…

An introduction to chaos theory in CFD

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

The Chaos Theory of Careers.

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)

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

PubMed

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium

NASA Astrophysics Data System (ADS)

Bittihn, Philip; Berg, Sebastian; Parlitz, Ulrich; Luther, Stefan

2017-09-01

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

DAQ application of PC oscilloscope for chaos fiber-optic fence system based on LabVIEW

NASA Astrophysics Data System (ADS)

Lu, Manman; Fang, Nian; Wang, Lutang; Huang, Zhaoming; Sun, Xiaofei

2011-12-01

In order to obtain simultaneously high sample rate and large buffer in data acquisition (DAQ) for a chaos fiber-optic fence system, we developed a double-channel high-speed DAQ application of a digital oscilloscope of PicoScope 5203 based on LabVIEW. We accomplished it by creating call library function (CLF) nodes to call the DAQ functions in the two dynamic link libraries (DLLs) of PS5000.dll and PS5000wrap.dll provided by Pico Technology Company. The maximum real-time sample rate of the DAQ application can reach 1GS/s. We can control the resolutions of the application at the sample time and data amplitudes by changing their units in the block diagram, and also control the start and end times of the sampling operations. The experimental results show that the application has enough high sample rate and large buffer to meet the demanding DAQ requirements of the chaos fiber-optic fence system.

Chaos synchronization communication using extremely unsymmetrical bidirectional injections.

PubMed

Zhang, Wei Li; Pan, Wei; Luo, Bin; Zou, Xi Hua; Wang, Meng Yao; Zhou, Zhi

2008-02-01

Chaos synchronization and message transmission between two semiconductor lasers with extremely unsymmetrical bidirectional injections (EUBIs) are discussed. By using EUBIs, synchronization is realized through injection locking. Numerical results show that if the laser subjected to strong injection serves as the receiver, chaos pass filtering (CPF) of the system is similar to that of unidirectional coupled systems. Moreover, if the other laser serves as the receiver, a stronger CPF can be obtained. Finally, we demonstrate that messages can be extracted successfully from either of the two transmission directions of the system.

Arsinoes Chaos

NASA Technical Reports Server (NTRS)

2003-01-01

[figure removed for brevity, see original site]

At the easternmost end of Valles Marineris, a rugged, jumbled terrain known as chaos displays a stratigraphy that could be described as precarious. Perched on top of the jumbled blocks is another layer of sedimentary material that is in the process of being eroded off the top. This material is etched by the wind into yardangs before it ultimately is stripped off to reveal the existing chaos.

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.

Image information: VIS instrument. Latitude -7.8, Longitude 19.1 East (340.9 West). 19 meter/pixel resolution.

The design and research of anti-color-noise chaos M-ary communication system

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

Fu, Yongqing, E-mail: fuyongqing@hrbeu.edu.cn; Li, Xingyuan; Li, Yanan

Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are studied. The formula of zone partition demodulator’s boundary in additive white Gaussian noise is derived, besides, the problem about how to determine the boundary of zone partition demodulator in additive color noise is deeply studied; Then an approach on constructingmore » anti-color-noise chaos M-ary communication system is proposed, in which a pre-distortion filter is added after the chaos baseband modulator in the transmitter and whitening filter is added before zone partition demodulator in the receiver. Finally, the chaos M-ary communication system based on Hamilton oscillator is constructed and simulated in different channel noise. The result shows that the proposed method in this paper can improve the anti-color-noise performance of the whole communication system compared with the former system, and it has better anti-fading and resisting disturbance performance than Quadrature Phase Shift Keying system.« less

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos.

PubMed

Mondal, S; Pawar, S A; Sujith, R I

2017-10-01

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Understanding the Role of Chaos Theory in Military Decision Making

DTIC Science & Technology

2009-01-01

Because chaos is bounded, planners can create allowances for system noise. The existence of strange and normal chaotic attractors helps explain why... strange and normal chaotic attractors helps explain why system turbulence is uneven or concentrated around specific solution regions. Finally, the...give better understanding of the implications of chaos: sensitivity to initial conditions, strange attractors , and constants of motion. By showing the

Chaos: Understanding and Controlling Laser Instability

NASA Technical Reports Server (NTRS)

Blass, William E.

1997-01-01

In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.

Arsinoes Chaos Landforms

NASA Technical Reports Server (NTRS)

2004-01-01

23 October 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned rock outcrops, possibly sedimentary rocks, in the Arsinoes Chaos region east of the Valles Marineris trough system. These rocky materials were once below the martian surface. These features are located near 7.2oS, 27.9oW. The image covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.

Poincaré chaos and unpredictable functions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2017-07-01

The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.

Introduction to the focus issue: fifty years of chaos: applied and theoretical.

PubMed

Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

2012-12-01

The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

PubMed

Oprea, Iuliana; Triandaf, Ioana; Dangelmayr, Gerhard; Schwartz, Ira B

2007-06-01

It has been suggested by experimentalists that a weakly nonlinear analysis of the recently introduced equations of motion for the nematic electroconvection by M. Treiber and L. Kramer [Phys. Rev. E 58, 1973 (1998)] has the potential to reproduce the dynamics of the zigzag-type extended spatiotemporal chaos and localized solutions observed near onset in experiments [M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1998); J. T. Gleeson (private communication)]. In this paper, we study a complex spatiotemporal pattern, identified as spatiotemporal chaos, that bifurcates at the onset from a spatially uniform solution of a system of globally coupled complex Ginzburg-Landau equations governing the weakly nonlinear evolution of four traveling wave envelopes. The Ginzburg-Landau system can be derived directly from the weak electrolyte model for electroconvection in nematic liquid crystals when the primary instability is a Hopf bifurcation to oblique traveling rolls. The chaotic nature of the pattern and the resemblance to the observed experimental spatiotemporal chaos in the electroconvection of nematic liquid crystals are confirmed through a combination of techniques including the Karhunen-Loeve decomposition, time-series analysis of the amplitudes of the dominant modes, statistical descriptions, and normal form theory, showing good agreement between theory and experiments.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

Self-organization of chaos in mythology from a scientific point of view

NASA Astrophysics Data System (ADS)

Melker, Alexander I.

2007-04-01

In this contribution ancient Greek myths describing world's creation are analyzed as if they were a scientific paper. The 'paper' divided into the following parts: initial and boundary conditions, self-organization of chaos, world lines of self-organization, conclusion. It is shown that the self-organization of chaos consists of several stages during which two motive forces (attractive and repulsive) are generated, and totally disordered chaos transforms into partially ordered. It is found that there are five world lines of self-organization: water, light, cosmos-weather, water-fire, and State evolution.

Canyons and Mesas of Aureum Chaos

NASA Image and Video Library

2002-06-26

This image from NASA Mars Odyssey shows a portion of Aureum Chaos located just south of the Martian equator. This fractured landscape contains canyons and mesas with two large impact craters in the upper left.

Aram Chaos: a Long Lived Subsurface Aqueous Environment with Strong Water Resources Potential for Human Missions on Mars

NASA Technical Reports Server (NTRS)

Sibille, L.; Mueller, R.; Niles, P. B.; Glotch, T.; Archer, P. D.; Bell, M. S.

2015-01-01

Aram Chaos, Mars is a crater 280 kilometers in diameter with elevations circa. minus 2 to minus 3 kilometers below datum that provides a compelling landing site for future human explorers as it features multiple scientific regions of interest (ROI) paired with a rich extensible Resource ROI that features poly-hydrated sulfates [1]. The geologic history of Aram Chaos suggests several past episodes of groundwater recharge and infilling by liquid water, ice, and other materials [1-3]. The creation of the fractured region with no known terrestrial equivalent may have been caused by melting of deep ice reservoirs that triggered the collapse of terrain followed by catastrophic water outflows over the region. Aram Chaos is of particular scientific interest because it is hypothesized that the chaotic terrain may be the source of water that contributed to the creation of nearby valleys such as Ares Vallis flowing toward Chryse Planitia. The liquid water was likely sourced as groundwater and therefore represents water derived from a protected subsurface environment making it a compelling astrobiological site [2]. The past history of water is also represented by high concentrations of hematite, Fe-oxyhydroxides, mono-hydrated and poly-hydrated sulfates [1, 2]. Poly-hydrated sulfates are likely to contain abundant water that evolves at temperatures below 500 degrees Centigrade thus conferring Aram Chaos a potentially high value for early in-situ resource utilization (ISRU) [4]. The geologic history also calls for future prospecting of deep ice deposits and possibly liquid water via deep drilling. The most recent stratigraphic units in the central part of Aram Chaos are not fractured, and are part of a dome-shaped formation that features bright, poorly-consolidated material that contains both hydrated sulfates and ferric oxides according to OMEGA (Observatoire pour la Minéralogie, l'Eau, les Glaces et l'Activité) data [5]. These surface material characteristics are

Active formation of 'chaos terrain' over shallow subsurface water on Europa.

PubMed

Schmidt, B E; Blankenship, D D; Patterson, G W; Schenk, P M

2011-11-16

Europa, the innermost icy satellite of Jupiter, has a tortured young surface and sustains a liquid water ocean below an ice shell of highly debated thickness. Quasi-circular areas of ice disruption called chaos terrains are unique to Europa, and both their formation and the ice-shell thickness depend on Europa's thermal state. No model so far has been able to explain why features such as Conamara Chaos stand above surrounding terrain and contain matrix domes. Melt-through of a thin (few-kilometre) shell is thermodynamically improbable and cannot raise the ice. The buoyancy of material rising as either plumes of warm, pure ice called diapirs or convective cells in a thick (>10 kilometres) shell is insufficient to produce the observed chaos heights, and no single plume can create matrix domes. Here we report an analysis of archival data from Europa, guided by processes observed within Earth's subglacial volcanoes and ice shelves. The data suggest that chaos terrains form above liquid water lenses perched within the ice shell as shallow as 3 kilometres. Our results suggest that ice-water interactions and freeze-out give rise to the diverse morphologies and topography of chaos terrains. The sunken topography of Thera Macula indicates that Europa is actively resurfacing over a lens comparable in volume to the Great Lakes in North America. ©2011 Macmillan Publishers Limited. All rights reserved

Active formation of `chaos terrain' over shallow subsurface water on Europa

NASA Astrophysics Data System (ADS)

Schmidt, B. E.; Blankenship, D. D.; Patterson, G. W.; Schenk, P. M.

2011-11-01

Europa, the innermost icy satellite of Jupiter, has a tortured young surface and sustains a liquid water ocean below an ice shell of highly debated thickness. Quasi-circular areas of ice disruption called chaos terrains are unique to Europa, and both their formation and the ice-shell thickness depend on Europa's thermal state. No model so far has been able to explain why features such as Conamara Chaos stand above surrounding terrain and contain matrix domes. Melt-through of a thin (few-kilometre) shell is thermodynamically improbable and cannot raise the ice. The buoyancy of material rising as either plumes of warm, pure ice called diapirs or convective cells in a thick (>10 kilometres) shell is insufficient to produce the observed chaos heights, and no single plume can create matrix domes. Here we report an analysis of archival data from Europa, guided by processes observed within Earth's subglacial volcanoes and ice shelves. The data suggest that chaos terrains form above liquid water lenses perched within the ice shell as shallow as 3kilometres. Our results suggest that ice-water interactions and freeze-out give rise to the diverse morphologies and topography of chaos terrains. The sunken topography of Thera Macula indicates that Europa is actively resurfacing over a lens comparable in volume to the Great Lakes in North America.

Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

PubMed

Vahedi, J; Ashouri, A; Mahdavifar, S

2016-10-01

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

The 8th International Conference on Highly Frustrated Magnetism (HFM 2016)

NASA Astrophysics Data System (ADS)

Gardner, J. S.; Kao, Y. J.

2017-04-01

The 8th International Conference on Highly Frustrated Magnetism 2016 (HFM 2016) took place between the 7th and 11th of September 2016 at the GIS Convention Center at National Taiwan University, Taipei, Taiwan. Over 260 participants from all over the world, attended the meeting making it the largest HFM to-date and revealing the impressive growth in the community since the original meeting in Waterloo, Canada where 80 participants attended. Preceding the meeting a school was held at the National Synchrotron Radiation Research Center to help those new to the field understand the material they were likely to see at HFM2016. Our thanks to the international speakers who attended this school John Chalker, Michel Kenzelmann, Philippe Mendels, Luigi Paolasini, Kirrily Rule, Yixi Su, Isao Watanabe and those from Taiwan W. T. Chen, Y-J, Kao, L. J. Chang and C. S. Ku, for their enlightening presentations. The HFM 2016 conference consisted of five plenary talks by H Takagi, B D Gaulin, L Balents, Y Tokura and S T Bramwell, 20 invited and 40 contributed presentations, and about 160 poster presentations from all aspects of theoretical and experimental frustrated magnetism. During the conference period, many stimulating discussions were held both inside and outside the conference room. Excursions to Taipei 101 and the National Palace Museum, as well as several organized dinners and receptions allowed the participants to initiate collaborations and discuss the hottest issues. The subjects covered in the conference included: · Quantum frustrated magnetism and spin liquids · Novel ordering of geometrically frustrated magnets · Frustration effect on the coupling to lattice, orbital and charge degrees of freedom · Exotic phenomena induced by macroscopic degeneracy · Field effect on frustrated magnetism etc. These proceeding represent a very small, but valuable contribution to the community. I hope you enjoy reading them. In view of the rapid growth of the field, it has been

Ariadnes Colles Chaos

NASA Technical Reports Server (NTRS)

2002-01-01

(Released 18 June 2002) Among the many varied landscapes on Mars the term chaos is applied to those places that have a jumbled, blocky appearance. Most of the better known chaotic terrain occurs in the northern hemisphere but there are other occurrences in the southern hemisphere, three of which are centered on 180 degrees west longitude. Ariadnes Colles, Atlantis, and Gorgonum Chaos all share similar features: relatively bright, irregularly shaped knobs and mesas that rise above a dark, sand-covered, hummocky floor. Close inspection of this THEMIS image shows that the darker material tends to lap up to the base of the knobs and stops where the slopes are steep. On some of the lowest knobs, the dark material appears to overtop them. The knobs themselves are highly eroded, many having a pitted appearance. Images from the camera on Mars Global Surveyor clearly show that the dark material is sand, based on its mantling appearance and the presence of dunes. It looks as though the material that composes the knobs was probably a continuous layer that was subsequently heavily eroded. While it is likely that the dark sand is responsible for some of the erosion it is also possible that the this landscape was eroded by some other process and the sand was emplaced at a later time.

Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Cantrell, Sean A.

2015-01-01

The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

NASA Astrophysics Data System (ADS)

Aspelmeier, T.

2008-03-01

The sample-to-sample fluctuations ΔFN of the free-energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods. The replica calculation for bond chaos shows that the exponent μ governing the growth of the fluctuations with system size N, ΔFN˜Nμ, is bounded by μ≤(1)/(4).

At the Edge of Chaos: A New Paradigm for Social Work?

ERIC Educational Resources Information Center

Hudson, Christopher G.

2000-01-01

Reviews key concepts and applications of chaos theory and the broader complex systems theory in the context of general systems theory and the search for a unified conceptual framework for social work. Concludes that chaos theory shows promise as a solution to many problems posed by the now dated general systems approach. (DB)

Effect of the centrifugal force on domain chaos in Rayleigh-Bénard convection.

PubMed

Becker, Nathan; Scheel, J D; Cross, M C; Ahlers, Guenter

2006-06-01

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency f approximately epsilon(mu) with mu approximately equal to 1 as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, mu and the domain size were consistent with experiment.

Shear-induced chaos

NASA Astrophysics Data System (ADS)

Lin, Kevin K.; Young, Lai-Sang

2008-05-01

Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.

Monohydrated Sulfates in Aurorae Chaos

NASA Technical Reports Server (NTRS)

2008-01-01

This image of sulfate-containing deposits in Aurorae Chaos was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0653 UTC (2:53 a.m. EDT) on June 10, 2007, near 7.5 degrees south latitude, 327.25 degrees east longitude. CRISM's image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 40 meters (132 feet) across. The region covered is roughly 12 kilometers (7.5 miles) wide at its narrowest point.

Aurorae Chaos lies east of the Valles Marineris canyon system. Its western edge extends toward Capri and Eos Chasmata, while its eastern edge connects with Aureum Chaos. Some 750 kilometers (466 miles) wide, Aurorae Chaos is most likely the result of collapsed surface material that settled when subsurface ice or water was released.

The top panel in the montage above shows the location of the CRISM image on a mosaic taken by the Mars Odyssey spacecraft's Thermal Emission Imaging System (THEMIS). The CRISM data covers an area featuring several knobs of erosion-resistant material at one end of what appears to be a large teardrop shaped plateau. Similar plateaus occur throughout the interior of Valles Marineris, and they are formed of younger, typically layered rocks that post-date formation of the canyon system. Many of the deposits contain sulfate-rich layers, hinting at ancient saltwater.

The center left image, an infrared false color image, reveals a swath of light-colored material draped over the knobs. The center right image unveils the mineralogical composition of the area, with yellow representing monohydrated sulfates (sulfates with one water molecule incorporated into each molecule of the mineral).

The lower two images are renderings of data draped over topography with 5 times vertical exaggeration. These images provide a view of the topography and reveal how the monohydrated sulfate-containing deposits drape over the knobs and also an outcrop in lower-elevation parts of the

Equilibriumizing all food chain chaos through reproductive efficiency.

PubMed

Deng, Bo

2006-12-01

The intraspecific interference of a top-predator is incorporated into a classical mathematical model for three-trophic food chains. All chaos types known to the classical model are shown to exist for this comprehensive model. It is further demonstrated that if the top-predator reproduces at high efficiency, then all chaotic dynamics will change to a stable coexisting equilibrium, a novel property not found in the classical model. This finding gives a mechanistic explanation to the question of why food chain chaos is rare in the field. It also suggests that high reproductive efficiency of top-predators tends to stabilize food chains.

Suppression of chaos via control of energy flow

NASA Astrophysics Data System (ADS)

Guo, Shengli; Ma, Jun; Alsaedi, Ahmed

2018-03-01

Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz's theorem. The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittent feedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.

The Chaos of Katrina

DTIC Science & Technology

2007-03-01

partners for their mutual benefit. Unfortunately, based on government reports, FEMA did not have adequate control of its supply chain information ...is one attractor . “Edge of chaos” systems have two to eight attractors and in chaotic systems many attractors . Some are called strange attractors ...investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics

Short-term data forecasting based on wavelet transformation and chaos theory

NASA Astrophysics Data System (ADS)

Wang, Yi; Li, Cunbin; Zhang, Liang

2017-09-01

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Multiple Scenarios of Transition to Chaos in the Alternative Splicing Model

NASA Astrophysics Data System (ADS)

Kogai, Vladislav V.; Likhoshvai, Vitaly A.; Fadeev, Stanislav I.; Khlebodarova, Tamara M.

We have investigated the scenarios of transition to chaos in the mathematical model of a genetic system constituted by a single transcription factor-encoding gene, the expression of which is self-regulated by a feedback loop that involves protein isoforms. Alternative splicing results in the synthesis of protein isoforms providing opposite regulatory outcomes — activation or repression. The model is represented by a differential equation with two delayed arguments. The possibility of transition to chaos dynamics via all classical scenarios: a cascade of period-doubling bifurcations, quasiperiodicity and type-I, type-II and type-III intermittencies, has been numerically demonstrated. The parametric features of each type of transition to chaos have been described.

A period-doubling cascade precedes chaos for planar maps.

PubMed

Sander, Evelyn; Yorke, James A

2013-09-01

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

Efficient topological chaos embedded in the blinking vortex system.

PubMed

Kin, Eiko; Sakajo, Takashi

2005-06-01

We consider the particle mixing in the plane by two vortex points appearing one after the other, called the blinking vortex system. Mathematical and numerical studies of the system reveal that the chaotic particle mixing, i.e., the chaotic advection, is observed due to the homoclinic chaos, but the mixing region is restricted locally in the neighborhood of the vortex points. The present article shows that it is possible to realize a global and efficient chaotic advection in the blinking vortex system with the help of the Thurston-Nielsen theory, which classifies periodic orbits for homeomorphisms in the plane into three types: periodic, reducible, and pseudo-Anosov (pA). It is mathematically shown that periodic orbits of pA type generate a complicated dynamics, which is called topological chaos. We show that the combination of the local chaotic mixing due to the topological chaos and the dipole-like return orbits realize an efficient and global particle mixing in the blinking vortex system.

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

PubMed

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Anti-control of chaos of single time-scale brushless DC motor.

PubMed

Ge, Zheng-Ming; Chang, Ching-Ming; Chen, Yen-Sheng

2006-09-15

Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.

Transition to chaos of a vertical collapsible tube conveying air flow

NASA Astrophysics Data System (ADS)

Castillo Flores, F.; Cros, A.

2009-05-01

"Sky dancers", the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.

Transition to Chaos in Random Neuronal Networks

NASA Astrophysics Data System (ADS)

Kadmon, Jonathan; Sompolinsky, Haim

2015-10-01

Firing patterns in the central nervous system often exhibit strong temporal irregularity and considerable heterogeneity in time-averaged response properties. Previous studies suggested that these properties are the outcome of the intrinsic chaotic dynamics of the neural circuits. Indeed, simplified rate-based neuronal networks with synaptic connections drawn from Gaussian distribution and sigmoidal nonlinearity are known to exhibit chaotic dynamics when the synaptic gain (i.e., connection variance) is sufficiently large. In the limit of an infinitely large network, there is a sharp transition from a fixed point to chaos, as the synaptic gain reaches a critical value. Near the onset, chaotic fluctuations are slow, analogous to the ubiquitous, slow irregular fluctuations observed in the firing rates of many cortical circuits. However, the existence of a transition from a fixed point to chaos in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work, we investigate rate-based dynamics of neuronal circuits composed of several subpopulations with randomly diluted connections. Nonzero connections are either positive for excitatory neurons or negative for inhibitory ones, while single neuron output is strictly positive with output rates rising as a power law above threshold, in line with known constraints in many biological systems. Using dynamic mean field theory, we find the phase diagram depicting the regimes of stable fixed-point, unstable-dynamic, and chaotic-rate fluctuations. We focus on the latter and characterize the properties of systems near this transition. We show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as the single population with Gaussian connectivity. In these architectures, the large mean excitatory and inhibitory inputs dynamically balance each other, amplifying the effect of the residual fluctuations. Importantly, the existence of a transition to chaos

The Chaos Theory of Careers

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…

Turbulence transition and the edge of chaos in pipe flow.

PubMed

Schneider, Tobias M; Eckhardt, Bruno; Yorke, James A

2007-07-20

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 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. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic 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.

Spreading Chaos: The Role of Popularizations in the Diffusion of Scientific Ideas

ERIC Educational Resources Information Center

Paul, Danette

2004-01-01

Scientific popularizations are generally considered translations (often dubious ones) of scientific research for a lay audience. This study explores the role popularizations play within scientific discourse, specifically in the development of chaos theory. The methods included a review of the popular and the semipopular books on chaos theory from…

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

PubMed

Guastello, Stephen J

2009-07-01

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

Hydaspis Chaos in Nighttime Infrared

NASA Technical Reports Server (NTRS)

2002-01-01

This nighttime infrared image, taken by the thermal emission imaging system, captures a massively disrupted region on Mars called Hydaspis Chaos, which is located near the equator at two degrees north, 29 degrees west. The total vertical difference from the lowest to highest points in this region is about five kilometers (three miles.)

The steep slopes leading down into the canyon of Hydaspsis Chaos are strewn with rocks, while the plateaus and mesas above are covered in dust. This pattern indicates that processes are at work to prevent the dust from completely covering the surface of these slopes, even over the very long period since these canyons were formed.

The slopes and floor of these canyons show remarkable variability in the distribution of rocks and fine-grained material. Chaotic terrain may have been formed when subsurface ground water or ice was removed, and the overlying ground collapsed. The release of this water or ice (or both)formed the outflow channel Tiu Valles, which flowed across the Mars Pathfinder landing site.

This image captures a region of chaotic terrain about 106 kilometers (65 miles) long and 32 kilometers (20 miles) wide. The channel that feeds into the chaos at the bottom of the image is about 7 kilometers (4.3 miles)wide and 280 meters (930 feet) deep. The image was acquired on February 19, 2002. North is to the right of the image.

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 was provided by Arizona State University, Tempe. Lockheed Martin Astronautics, Denver, is the prime contractor for the 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.

Chaos minimization in DC-DC boost converter using circuit parameter optimization

NASA Astrophysics Data System (ADS)

Sudhakar, N.; Natarajan, Rajasekar; Gourav, Kumar; Padmavathi, P.

2017-11-01

DC-DC converters are prone to several types of nonlinear phenomena including bifurcation, quasi periodicity, intermittency and chaos. These undesirable effects must be controlled for periodic operation of the converter to ensure the stability. In this paper an effective solution to control of chaos in solar fed DC-DC boost converter is proposed. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The obtained results are compared with the operation of traditional boost converter. Further the obtained results with BFA optimized parameter ensures the operations of the converter are within the controllable region. To elaborate the study of bifurcation analysis with optimized and unoptimized parameters are also presented.

Controlling chaotic behavior in CO2 and other lasers

NASA Astrophysics Data System (ADS)

1993-06-01

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

Chaos enhancing tunneling in a coupled Bose-Einstein condensate with a double driving.

PubMed

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhu, Qianquan

2009-09-01

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean

NASA Astrophysics Data System (ADS)

Goodman, J. C.

2013-12-01

Models for the formation of disruptive chaos features on the icy surface of Europa fall into two broad categories: either chaos is formed when basal heating causes localized melting and thinning of the ice shell, or basal heating drives diapiric convection within the ice shell. We argue that in both of these cases, heating of the ice shell from below does not lead to chaos formation at the location of heating. If chaos is formed when a localized oceanic heat source, such as a hydrothermal plume, "melts through" the ice crust, we must consider what happens to the melted liquid. If Europa's ocean is salty, the melt will form a buoyant pool inside the melted cavity, leading to a stable interface between cold fresh meltwater and warm salty seawater. This stable interface acts like an ablative heat shield, protecting the ice from further damage. Some heat can be transferred across the stable layer by double diffusion, but this transfer is very inefficient. We calculate that local ocean heating cannot be balanced by local flux through the stable layer: instead, the warm ocean water must spread laterally until it is delivering heat to the ice base on a regional or global scale (a heating zone hundreds or thousands of km across, for conservative parameters.) If chaos is formed by diapiric solid-state convection within the ice shell, many investigators have assumed that diapirism and chaos should be most prevalent where the basal heat flux is strongest. We argue that this is not the case. In Rayleigh-Benard convection, increasing the heat flux will make convection more vigorous --- if and only if the convecting layer thickness does not change. We argue that increased basal heat flux will thin the ice shell, reducing its Rayleigh number and making convection less likely, not more. This insight allows us to reverse the logic of recent discussions of the relationship between ocean circulation and chaos (for instance, Soderlund et al, 2013 LPSC). We argue that global oceanic

Time-delay signature of chaos in 1550 nm VCSELs with variable-polarization FBG feedback.

PubMed

Li, Yan; Wu, Zheng-Mao; Zhong, Zhu-Qiang; Yang, Xian-Jie; Mao, Song; Xia, Guang-Qiong

2014-08-11

Based on the framework of spin-flip model (SFM), the output characteristics of a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to variable-polarization fiber Bragg grating (FBG) feedback (VPFBGF) have been investigated. With the aid of the self-correlation function (SF) and the permutation entropy (PE) function, the time-delay signature (TDS) of chaos in the VPFBGF-VCSEL is evaluated, and then the influences of the operation parameters on the TDS of chaos are analyzed. The results show that the TDS of chaos can be suppressed efficiently through selecting suitable coupling coefficient and feedback rate of the FBG, and is weaker than that of chaos generated by traditional variable-polarization mirror feedback VCSELs (VPMF-VCSELs) or polarization-preserved FBG feedback VCSELs (PPFBGF-VCSELs).

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods

ERIC Educational Resources Information Center

Liu, Boquan; Polce, Evan; Sprott, Julien C.; Jiang, Jack J.

2018-01-01

Purpose: The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Study Design: Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100…

Learning the Uses of Chaos.

ERIC Educational Resources Information Center

Berthoff, Ann E.

This paper addresses the issue of learning to write and the need for defining a means of teaching the process of composing. Following a description of what kind of process writing is not, the composing process is presented as a continuum of making meaning out of a chaos of images, half-truths, remembrances, and syntactic fragments. The discovery…

Public-channel cryptography based on mutual chaos pass filters.

PubMed

Klein, Einat; Gross, Noam; Kopelowitz, Evi; Rosenbluh, Michael; Khaykovich, Lev; Kinzel, Wolfgang; Kanter, Ido

2006-10-01

We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker, however, fails to recover an errorless message even if he amplifies the coupling signal.

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback.

PubMed

Nazhan, Salam; Ghassemlooy, Zabih; Busawon, Krishna

2016-01-01

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θp. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θp. The maximum value of the cross-correlation coefficient achieved is -0.99 with a zero time delay over a wide range of θp beyond 65° with a poor synchronization dynamic at θp less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θp. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.

Aureum Chaos

NASA Technical Reports Server (NTRS)

2003-01-01

[figure removed for brevity, see original site]

Released 11 November 2003

Aureum Chaos is a large crater that was filled with sediment after its formation. After the infilling of sediment, something occurred that caused the sediment to be broken up into large, slumped blocks and smaller knobs. Currently, it is believed that the blocks and knobs form when material is removed from the subsurface, creating void space. Subsurface ice was probably heated, and the water burst out to the surface, maybe forming a temporary lake. Other areas of chaos terrain have large outflow channels that emanate from them, indicating that a tremendous amount of water was released.

Image information: VIS instrument. Latitude -3.2, Longitude 331 East (29 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.

Family CHAOS is associated with glycaemic control in children and adolescents with type 1 diabetes mellitus.

PubMed

Chae, M; Taylor, B J; Lawrence, J; Healey, D; Reith, D M; Gray, A; Wheeler, B J

2016-02-01

Despite advances in the medical management of type 1 diabetes mellitus (T1DM), for many, glycaemic control remains substandard. Other factors are clearly important in determining success, or lack thereof, with diabetes management. With this in mind, we have investigated whether family CHAOS may provide a novel tool to identify when environmental confusion could impact on diabetes management and subsequent glycaemic control. A case-control study of children and adolescents with established T1DM and age-/sex-matched controls was conducted. Demographic information, both maternal and paternal CHAOS scores, and HbA1c were collected. Statistical analysis was undertaken to explore associations between T1DM and CHAOS and between CHAOS and HbA1c. Data on 65 children with T1DM and 60 age-/sex-matched controls were obtained. There was no evidence of group differences for maternal CHAOS (p = 0.227), but paternal CHAOS scores were higher for the T1DM group (p = 0.041). Greater maternal and paternal CHAOS scores were both associated with higher HbA1c (p ≤ 0.027). The maternal association remained after controlling for diabetes duration, SMBG frequency, and insulin therapy. In children with T1DM, there appears to be a negative association between increased environmental confusion, as rated by CHAOS, and glycaemic control. In addition, when compared to controls, fathers of children and adolescents with T1DM appear to experience CHAOS differently to mothers. These findings contribute to the growing body of literature exploring psychosocial factors in T1DM. Continuing efforts are required to fully understand how the family and psychosocial environment interact with diabetes to impact on long-term health outcomes.

Interactions between neural networks: a mechanism for tuning chaos and oscillations

PubMed Central

2007-01-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability. PMID:19003511

Interactions between neural networks: a mechanism for tuning chaos and oscillations.

PubMed

Wang, Lipo

2007-06-01

We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.

Observation of Hamiltonian chaos and its control in wave particle interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Macor, A.; Aïssi, A.

2007-12-01

Wave-particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a 'devil's staircase' behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

Sleep Quality Estimation based on Chaos Analysis for Heart Rate Variability

NASA Astrophysics Data System (ADS)

Fukuda, Toshio; Wakuda, Yuki; Hasegawa, Yasuhisa; Arai, Fumihito; Kawaguchi, Mitsuo; Noda, Akiko

In this paper, we propose an algorithm to estimate sleep quality based on a heart rate variability using chaos analysis. Polysomnography(PSG) is a conventional and reliable system to diagnose sleep disorder and to evaluate its severity and therapeatic effect, by estimating sleep quality based on multiple channels. However, a recording process requires a lot of time and a controlled environment for measurement and then an analyzing process of PSG data is hard work because the huge sensed data should be manually evaluated. On the other hand, it is focused that some people make a mistake or cause an accident due to lost of regular sleep and of homeostasis these days. Therefore a simple home system for checking own sleep is required and then the estimation algorithm for the system should be developed. Therefore we propose an algorithm to estimate sleep quality based only on a heart rate variability which can be measured by a simple sensor such as a pressure sensor and an infrared sensor in an uncontrolled environment, by experimentally finding the relationship between chaos indices and sleep quality. The system including the estimation algorithm can inform patterns and quality of own daily sleep to a user, and then the user can previously arranges his life schedule, pays more attention based on sleep results and consult with a doctor.

Western Eos Chaos on Mars: A Potential Site for Future Landing and Returning Samples

NASA Astrophysics Data System (ADS)

Asif Iqbal Kakkassery; Rajesh, V. J.

2018-04-01

Introducing Eos Chaos as a potential area for collecting samples. Eos Chaos contains a number of aqueous minerals. We have detected zoisite — a least reported low-grade metamorphic mineral from this area.

Low-temperature physics: Chaos in the cold

NASA Astrophysics Data System (ADS)

Julienne, Paul S.

2014-03-01

A marriage between theory and experiment has shown that ultracold erbium atoms trapped with laser light and subjected to a magnetic field undergo collisions that are characterized by quantum chaos. See Letter p.475

Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption.

PubMed

Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

2012-01-01

This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

Disordered wires and quantum chaos in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Angonga, Jackson; Gadway, Bryce

2017-04-01

We present two topics: topological wires subjected to disorder and quantum chaos in a spin-J model. These studies are experimentally realized through the use of a momentum-space lattice, in which the dynamics of 87Rb atoms are recorded. In topological wires, a transition to a trivial phase is seen when disorder is applied to either the tunneling strengths or site energies. This transition is detected using both charge-pumping and Hamiltonian-quenching techniques. In the spin-J study we observe the effects of both linear and non-linear spin operations by measuring the linear entropy of the system as well as the out-of-time order correlation function. We further probe the chaotic signatures of the paradigmatic kicked top model.

Experimental validation of wireless communication with chaos.

PubMed

Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S; Grebogi, Celso

2016-08-01

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

Experimental validation of wireless communication with chaos

NASA Astrophysics Data System (ADS)

Ren, Hai-Peng; Bai, Chao; Liu, Jian; Baptista, Murilo S.; Grebogi, Celso

2016-08-01

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

Non Linear Dynamics and Chaos (La Dynamique Non-Lineaie et le Chaos)

DTIC Science & Technology

1993-06-01

mention some aspects of non-linear dynamics and/or disorder is independence. All other definitions are merely negative chaos which p,.Laps a,, margin- al ...collection of fixed coefficients and input-output corellation is U1, pp. 1037-1044, 1990, Roger Cerf et al . Among ,ie very slightly modified. If Rl is...des param~tres qui ou la deformation 61astique d’une partie du sol d~finissent le syst~me A contr~ler, et donne lieu, soudainement A un saut

Geology and Origin of Europa's Mitten Feature (Murias Chaos)

NASA Technical Reports Server (NTRS)

Figueredo, P. H.; Chuang, F. C.; Rathbun, J.; Kirk, R. L.; Greeley, R.

2002-01-01

The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

Geology and origin of Europa's "Mitten" feature (Murias Chaos)

USGS Publications Warehouse

Figueredo, P.H.; Chuang, F.C.; Rathbun, J.; Kirk, R.L.; Greeley, R.

2002-01-01

The "Mitten" (provisionally named Murias Chaos by the International Astronomical Union) is a region of elevated chaos-like terrain in the leading hemisphere of Europa. Its origin had been explained under the currently debated theories of melting through a thin lithosphere or convection within a thick one. Galileo observations reveal several characteristics that suggest that the Mitten is distinct from typical chaos terrain and point to a different formational process. Photoclinometric elevation estimates suggest that the Mitten is slightly elevated with respect to the surrounding terrain; geologic relations indicate that it must have raised significantly from the plains in its past, resembling disrupted domes on Europa's trailing hemisphere. Moreover, the Mitten material appears to have extruded onto the plains and flowed for tens of kilometers. The area subsequently subsided as a result of isostatic adjustment, viscous relaxation, and/or plains loading. Using plate flexure models, we estimated the elastic lithosphere in the area to be several kilometers thick. We propose that the Mitten originated by the ascent and extrusion of a large thermal diapir. Thermal-mechanical modeling shows that a Mitten-sized plume would remain sufficiently warm and buoyant to pierce through the crust and flow unconfined on the surface. Such a diapir probably had an initial radius between 5 and 8 km and an initial depth of 20-40 km, consistent with a thick-lithosphere model. In this scenario the Mitten appears to represent the surface expression of the rare ascent of a large diapir, in contrast to lenticulae and chaos terrain, which may form by isolated and clustered small diapirs, respectively.

Tuning quantum measurements to control chaos.

PubMed

Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R

2017-03-20

Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.

Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

PubMed

Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

2013-03-01

Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

Viewing Eye Movements During Reading through the Lens of Chaos Theory: How Reading Is Like the Weather

ERIC Educational Resources Information Center

Paulson, Eric J.

2005-01-01

This theoretical article examines reading processes using chaos theory as an analogy. Three principles of chaos theory are identified and discussed, then related to reading processes as revealed through eye movement research. Used as an analogy, the chaos theory principle of sensitive dependence contributes to understanding the difficulty in…

Stochastic resonance based on modulation instability in spatiotemporal chaos.

PubMed

Han, Jing; Liu, Hongjun; Huang, Nan; Wang, Zhaolu

2017-04-03

A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Dermoscopic 'Chaos and Clues' in the diagnosis of melanoma in situ.

PubMed

Ramji, Rajan; Valdes-Gonzalez, Guillermo; Oakley, Amanda; Rademaker, Marius

2017-11-02

To describe the dermoscopic features of melanoma in situ using the Chaos and Clues method. Histologically proven primary melanoma in situ (MIS) diagnosed through a specialist teledermoscopy clinic were reviewed by three dermatologists. By consensus they agreed on the global dermoscopic pattern, colours, presence of chaos (asymmetry of colour and structure and more than one pattern), and each of the nine clues described for malignancy. One hundred MIS in 92 patients of European ethnicity (45 males) were assessed. Mean age was 67.3 years (range 20-95). The mean dimensions of the lesions were 11.1 × 12.0 mm (range 2.5-31.3 × 2.3-32.3 mm). Using pattern analysis, 82% of the lesions had three or more patterns (multicomponent) and the rest had 2 patterns. Colours included light brown (100%), dark brown (98%) and grey (75%). All MIS demonstrated chaos. The most prevalent clues were thick lines (88%), eccentric structureless areas (88%), and grey or blue structures (75%). Dermoscopy can be very helpful in the early diagnosis of melanoma and MIS. The Chaos and Clues method is simple to use. Its unambiguous descriptors can be successfully used to describe MIS. The presence of chaos and clues to malignancy (including thick lines, eccentric structureless areas, and blue/grey structures) should raise a red flag and lead to referral or excision. © 2017 The Australasian College of Dermatologists.

The Simple Map for Single-null Divertor Tokamak : How to Find Chaos

NASA Astrophysics Data System (ADS)

Martinez, Ilissa; Ali, Halima; Punjabi, Alkesh

2000-10-01

The Simple Map^1 represents the magnetic field inside a single-null divertor tokamak. The Simple map is given by the equations X_n+1=X_n-KYn (1-Y_n) and Y_n+1=Y_n+KX_n+1. We fix k at 0.6 and X0 at 0. We choose two different starting values of Y_0. These two values are very close together. These values of Y0 represent two field lines which start out very close together. We calculate the distance between two field lines as n is increased. This distance is given by d_n. For both equations given by the distance formula (d_n=[Y_n,2-Y_n,1)^2+(X_n,2-X_n,1)^2]. If dn increases exponentially as n is increased we find chaos, if dn does not increase exponentially then you have not found chaos. We have found chaos, Y0 must be less than one, but higher than 0.9971 for chaos. For Y0 between 0 and 0.9971, there is no chaos. This work is supported by US DOE OFES. Ms. Ilissa Martinez is a HU CFRT Summer Fusion High School Workshop Scholar from the Blanca Malaret High School in Puerto Rico. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Booze A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

Probability Simulations by Non-Lipschitz Chaos

NASA Technical Reports Server (NTRS)

Zak, Michail

1996-01-01

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Erotism and chaos.

PubMed

Giovacchini, P L

1990-01-01

There is a continuum from primitive, undifferentiated feelings that are simply the manifestations of homeostatic balance and imbalance to highly differentiated, pleasurable erotic feelings that characterize mature, intimate love relationships. Sensory reactions are elevated from simple reflex levels to highly complex, sophisticated affects that involve wide areas of the psyche. Thus, affects are associated with integration and organized psychic structure. Consequently they may function in various ways. Freud developed a continuum for anxiety as initially functioning as a conversion reaction enabling sexual feelings that cannot reach mentational levels or be consummated in erotic activity to be discharged. It reaches a final level of organization where it serves as a signal calling various defenses into play as emerging instinctual impulses threaten to upset psychodynamic equilibrium. I have focused on how affects, erotic feelings in particular, have an organizing function that binds a primitive inner agitation that occurs during what is called a prementational stage of the neonatal period. This is a stage that precedes psychological processes. Sexual feelings are generated as an attempt to bind inner chaos that stems from an amorphous, inchoate psychic state. Erotic feelings are experienced in order to smoothe inner tension. The patient tries but seldom achieves calm because the affective binding and structuralizing process, in itself, becomes painful and disruptive. I present several clinical incidents and also refer to so-called treatment relationships where the therapist absorbs the patient's chaos and then acts out sexually which leads to a total breakdown of the therapeutic setting.

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond

NASA Astrophysics Data System (ADS)

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E. G. D.

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

Weak and strong chaos in Fermi-Pasta-Ulam models and beyond.

PubMed

Pettini, Marco; Casetti, Lapo; Cerruti-Sola, Monica; Franzosi, Roberto; Cohen, E G D

2005-03-01

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. The first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: (i) A stochasticity threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. (ii) A strong stochasticity threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weak and strong chaotic regimes. It is stable with N. The second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. Starting this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, the third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

PubMed

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

NASA Astrophysics Data System (ADS)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 21345. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

Information processing in echo state networks at the edge of chaos.

PubMed

Boedecker, Joschka; Obst, Oliver; Lizier, Joseph T; Mayer, N Michael; Asada, Minoru

2012-09-01

We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.

Chaos and The Changing Nature of Science and Medicine. Proceedings

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

Herbert, D.E.; Croft, P.; Silver, D.S.

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)

Chaos-based wireless communication resisting multipath effects

NASA Astrophysics Data System (ADS)

Yao, Jun-Liang; Li, Chen; Ren, Hai-Peng; Grebogi, Celso

2017-09-01

In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

Chaos-based wireless communication resisting multipath effects.

PubMed

Yao, Jun-Liang; Li, Chen; Ren, Hai-Peng; Grebogi, Celso

2017-09-01

In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

Experimental validation of wireless communication with chaos

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

Ren, Hai-Peng; Bai, Chao; Liu, Jian

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and anmore » integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.« less

Subharmonics, chaos and beyond

NASA Astrophysics Data System (ADS)

Adler, Laszlo; Yost, William T.; Cantrell, John H.

2012-05-01

While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed (1,2) in addition to the expected harmonic structure. Subsequently, it was realized that the system was one of the many examples of parametric resonance in which the observed subharmonics are parametrically generated. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the focus of this paper. An ultrasonic interferometer with optical precision was built. The transducers were compressional, undamped quartz and Lithium Niobate crystals ranging from 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system and a receiver transducer attached to an aligned reflector were used to observe the generated frequency components in the cavity. There are at least 5 regions of excitation that were identified. It is shown that from a region of oscillation stability into an unstable region leads to a cascade of bifurcations (subharmonics) culminating in chaotic oscillations. A further increase in the amplitude results in a reversion of the chaos into a second region of stability. A first-principle based explanation of the experimental findings is presented.

Invoking the muse: Dada's chaos.

PubMed

Rosen, Diane

2014-07-01

Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.

Hybrid electronic/optical synchronized chaos communication system.

PubMed

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

2009-04-27

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

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2006-01-01

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

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.

Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars

USGS Publications Warehouse

Rodriguez, J.A.P.; Sasaki, S.; Kuzmin, R.O.; Dohm, J.M.; Tanaka, K.L.; Miyamoto, H.; Kurita, K.; Komatsu, G.; Fairen, A.G.; Ferris, J.C.

2005-01-01

The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that

Chaos control by electric current in an enzymatic reaction.

PubMed

Lekebusch, A; Förster, A; Schneider, F W

1996-09-01

We apply the continuous delayed feedback method of Pyragas to control chaos in the enzymatic Peroxidase-Oxidase (PO) reaction, using the electric current as the control parameter. At each data point in the time series, a time delayed feedback function applies a small amplitude perturbation to inert platinum electrodes, which causes redox processes on the surface of the electrodes. These perturbations are calculated as the difference between the previous (time delayed) signal and the actual signal. Unstable periodic P1, 1(1), and 1(2) orbits (UPOs) were stabilized in the CSTR (continuous stirred tank reactor) experiments. The stabilization is demonstrated by at least three conditions: A minimum in the experimental dispersion function, the equality of the delay time with the period of the stabilized attractor and the embedment of the stabilized periodic attractor in the chaotic attractor.

Route to chaos in porous-medium thermal convection

NASA Astrophysics Data System (ADS)

Kimura, S.; Schubert, G.; Straus, J. M.

1986-05-01

The transition to chaos in two-dimensional single-cell time-dependent convection in a square cross section of porous material saturated with fluid and heated from below is investigated theoretically by means of pseudospectral numerical simulations. The results are presented graphically and discussed in terms of the time-averaged Nusselt number, the oscillation mechanism, and similarities to Hele-Shaw convection. As the Rayleigh number (R) increases, the system is found to proceed from the steady state to a simply periodic state, a quasi-periodic state with two basic frequencies, a second simply periodic state, and finally to chaos. The transitions occur at R = 4 pi squared, 380-400, 500-520, 560-570, and 850-1000. The intermediate and chaotic regimes are characterized in detail.

Integrability and Chaos: The Classical Uncertainty

ERIC Educational Resources Information Center

Masoliver, Jaume; Ros, Ana

2011-01-01

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical…

Blessing and curse of chaos in numerical turbulence simulations

NASA Astrophysics Data System (ADS)

Lee, Jon

1994-03-01

Because of the trajectory instability, time reversal is not possible beyond a certain evolution time and hence the time irreversibility prevails under the finite-accuracy trajectory computation. This therefore provides a practical reconciliation of the dynamic reversibility and macroscopic irreversibility (blessing of chaos). On the other hand, the trajectory instability is also responsible for a limited evolution time, so that finite-accuracy computation would yield a pseudo-orbit which is totally unrelated to the true trajectory (curse of chaos). For the inviscid 2D flow, however, we can accurately compute the long- time average of flow quantities with a pseudo-orbit by invoking the ergodic theorem.

Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Elskens, Y.; Ruzzon, A.

2010-11-01

Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step. This contribution reviews : presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm. The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-03-01

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Multilocation Video Conference By Optical Fiber

NASA Astrophysics Data System (ADS)

Gray, Donald J.

1982-10-01

An experimental system that permits interconnection of many offices in a single video conference is described. Video images transmitted to conference participants are selected by the conference chairman and switched by a microprocessor-controlled video switch. Speakers can, at their choice, transmit their own images or images of graphics they wish to display. Users are connected to the Switching Center by optical fiber subscriber loops that carry analog video, digitized telephone, data and signaling. The same system also provides user-selectable distribution of video program and video library material. Experience in the operation of the conference system is discussed.

Quantum chaos: an introduction via chains of interacting spins-1/2

NASA Astrophysics Data System (ADS)

Gubin, Aviva; Santos, Lea

2012-02-01

We discuss aspects of quantum chaos by focusing on spectral statistical properties and structures of eigenstates of quantum many-body systems. Quantum systems whose classical counterparts are chaotic have properties that differ from those of quantum systems whose classical counterparts are regular. One of the main signatures of what became known as quantum chaos is a spectrum showing repulsion of the energy levels. We show how level repulsion may develop in one-dimensional systems of interacting spins-1/2 which are devoid of random elements and involve only two-body interactions. We present a simple recipe to unfold the spectrum and emphasize the importance of taking into account the symmetries of the system. In addition to the statistics of eigenvalues, we analyze also how the structure of the eigenstates may indicate chaos. This is done by computing quantities that measure the level of delocalization of the eigenstates.

Household chaos moderates the link between maternal attribution bias and parenting

PubMed Central

Wang, Z.; Deater-Deckard, K.; Bell, M.A.

2013-01-01

Objective Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. Design The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers’ ratings. Results The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. Conclusions The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability. PMID:24358017

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

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

2017-10-01

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

Polynomial chaos representation of databases on manifolds

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. Themore » method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.« less

Chaos theory perspective for industry clusters development

NASA Astrophysics Data System (ADS)

Yu, Haiying; Jiang, Minghui; Li, Chengzhang

2016-03-01

Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.

Bifurcation and chaos in the simple passive dynamic walking model with upper body.

PubMed

Li, Qingdu; Guo, Jianli; Yang, Xiao-Song

2014-09-01

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

Bifurcation and chaos in the simple passive dynamic walking model with upper body

NASA Astrophysics Data System (ADS)

Li, Qingdu; Guo, Jianli; Yang, Xiao-Song

2014-09-01

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

Bounding the space of holographic CFTs with chaos

DOE PAGES

Perlmutter, Eric

2016-10-13

In this study, thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ L ≤ 2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ L = 2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge andmore » a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS 3 higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W ∞[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ L = 0. Independently, we show that such theories violate unitarity for |λ| > 2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.« less

Volcanic cones in Hydraotes chaos : implications for the chaotic terrains formation

NASA Astrophysics Data System (ADS)

Meresse, S.; Costard, F.; Mangold, N.; Masson, P.; Neukum, G.

2006-12-01

Numerous geologic scenarios have been proposed for the chaotic terrains formation. They include (1) sub-ice volcanism and other magma-ice interactions and (2) catastrophic release of groundwater from confined aquifers. The lack of volcanic morphology in the chaos was an handicap for the hypothesis of magma-ice interactions but the HRSC (High Resolution Stereo Camera) images have recently revealed possible volcanic cones inside the Hydraotes chaos. About thirty cones lie on the lowest parts of the chaos at elevation between -4300 and -5100 meters. They have basal diameters of 500-1900 m and heights exceeding 100 m. They are observed on young surface: the south smooth floor and inside the narrow valleys separating the mesas. The cones are relatively fresh. Similar morphologies of small cone-shaped structures have been previously identified in the northern lowlands of Mars (Chryse, Acidalia, Amazonis, Isidis and Elysuim Planitia) but their origin remains uncertain. A number of volcanic or cold climate landforms were proposed as potential terrestrial analogues : Icelandic pseudocraters (or rootless cones), cinder cones, tuff cones, pingos and spatter cones. The morphologic measurements made on the Hydraotes cones argue rather for a volcanic origin in comparison with terrestrial analogues. These first volcanic cones observed in Hydraotes chaos suggest that volcanic or subvolcanic activity might have played an important part in the chaotic terrains formation and outflow channels genesis.

Fault detection and isolation in GPS receiver autonomous integrity monitoring based on chaos particle swarm optimization-particle filter algorithm

NASA Astrophysics Data System (ADS)

Wang, Ershen; Jia, Chaoying; Tong, Gang; Qu, Pingping; Lan, Xiaoyu; Pang, Tao

2018-03-01

The receiver autonomous integrity monitoring (RAIM) is one of the most important parts in an avionic navigation system. Two problems need to be addressed to improve this system, namely, the degeneracy phenomenon and lack of samples for the standard particle filter (PF). However, the number of samples cannot adequately express the real distribution of the probability density function (i.e., sample impoverishment). This study presents a GPS receiver autonomous integrity monitoring (RAIM) method based on a chaos particle swarm optimization particle filter (CPSO-PF) algorithm with a log likelihood ratio. The chaos sequence generates a set of chaotic variables, which are mapped to the interval of optimization variables to improve particle quality. This chaos perturbation overcomes the potential for the search to become trapped in a local optimum in the particle swarm optimization (PSO) algorithm. Test statistics are configured based on a likelihood ratio, and satellite fault detection is then conducted by checking the consistency between the state estimate of the main PF and those of the auxiliary PFs. Based on GPS data, the experimental results demonstrate that the proposed algorithm can effectively detect and isolate satellite faults under conditions of non-Gaussian measurement noise. Moreover, the performance of the proposed novel method is better than that of RAIM based on the PF or PSO-PF algorithm.

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

PubMed

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

2014-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

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

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

2014-09-01

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

Sedimentary Rocks of Aram Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

10 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcroppings of light-toned, layered, sedimentary rock within Aram Chaos, an ancient, partly-filled impact crater located near 3.2oN, 19.9oW. This 1.5 meters (5 feet) per pixel picture is illuminated by sunlight from the left and covers an area about 3 km (1.9 mi) across.

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback

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

Nazhan, Salam; Ghassemlooy, Zabih; Busawon, Krishna

2016-01-15

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θ{sub p}. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θ{sub p}. The maximum value of the cross-correlation coefficient achievedmore » is −0.99 with a zero time delay over a wide range of θ{sub p} beyond 65° with a poor synchronization dynamic at θ{sub p} less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θ{sub p}. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.« less

Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

ERIC Educational Resources Information Center

Gilstrap, Donald L.

2013-01-01

In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and…

Chaos Theory as a Planning Tool for Community-Based Educational Experiences for Health Students.

ERIC Educational Resources Information Center

Velde, Beth P.; Greer, Annette G.; Lynch, Deirdre C.; Escott-Stump, Sylvia

2002-01-01

Chaos theory, which attempts to understand underlying order where none is apparent, was applied to an interdisciplinary rural health training program for health professionals. Similar programs should anticipate systemic flux between order and chaos and pay attention to information flow, degree of diversity, richness of connectivity, contained…

Features in Aureum Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

12 November 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, sedimentary rock outcrops in the Aureum Chaos region of Mars. On the brightest and steepest slope in this scene, dry talus shed from the outcrop has formed a series of dark fans along its base. These outcrops are located near 3.4oS, 27.5oW. The image covers an area approximately 3 km (1.9 mi) across and sunlight illuminates the scene from the upper left.

A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

NASA Astrophysics Data System (ADS)

Kewlani, Gaurav; Crawford, Justin; Iagnemma, Karl

2012-05-01

The ability of ground vehicles to quickly and accurately analyse their dynamic response to a given input is critical to their safety and efficient autonomous operation. In field conditions, significant uncertainty is associated with terrain and/or vehicle parameter estimates, and this uncertainty must be considered in the analysis of vehicle motion dynamics. Here, polynomial chaos approaches that explicitly consider parametric uncertainty during modelling of vehicle dynamics are presented. They are shown to be computationally more efficient than the standard Monte Carlo scheme, and experimental results compared with the simulation results performed on ANVEL (a vehicle simulator) indicate that the method can be utilised for efficient and accurate prediction of vehicle motion in realistic scenarios.

Generation of flat wideband chaos with suppressed time delay signature by using optical time lens.

PubMed

Jiang, Ning; Wang, Chao; Xue, Chenpeng; Li, Guilan; Lin, Shuqing; Qiu, Kun

2017-06-26

We propose a flat wideband chaos generation scheme that shows excellent time delay signature suppression effect, by injecting the chaotic output of general external cavity semiconductor laser into an optical time lens module composed of a phase modulator and two dispersive units. The numerical results demonstrate that by properly setting the parameters of the driving signal of phase modulator and the accumulated dispersion of dispersive units, the relaxation oscillation in chaos can be eliminated, wideband chaos generation with an efficient bandwidth up to several tens of GHz can be achieved, and the RF spectrum of generated chaotic signal is nearly as flat as uniform distribution. Moreover, the periodicity of chaos induced by the external cavity modes can be simultaneously destructed by the optical time lens module, based on this the time delay signature can be completely suppressed.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10

Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

PubMed

Wang, Hongli; Ouyang, Qi

2007-11-23

The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.

The edge of chaos: A nonlinear view of psychoanalytic technique.

PubMed

Galatzer-Levy, Robert M

2016-04-01

The field of nonlinear dynamics (or chaos theory) provides ways to expand concepts of psychoanalytic process that have implications for the technique of psychoanalysis. This paper describes how concepts of "the edge of chaos," emergence, attractors, and coupled oscillators can help shape analytic technique resulting in an approach to doing analysis which is at the same time freer and more firmly based in an enlarged understanding of the ways in which psychoanalysis works than some current recommendation about technique. Illustrations from a lengthy analysis of an analysand with obsessive-compulsive disorder show this approach in action. Copyright © 2016 Institute of Psychoanalysis.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

NASA Astrophysics Data System (ADS)

Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.; Balaz, Antun

2016-03-01

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

The Terrain of Margaritifer Chaos

NASA Technical Reports Server (NTRS)

1999-01-01

The jumbled and broken terrain in the picture on the left is known as chaotic terrain. Chaotic terrain was first observed in Mariner 6 and 7 images of Mars more than 30 years ago, and is thought to result from collapse after material--perhaps water or ice--was removed from the subsurface by events such as the formation of giant flood channels. The region shown here is named 'Margaritifer Chaos'. The left picture is a Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) red wide angle camera context frame that covers an area 115 km (71 miles) across. The small white box is centered at 10.3oS, 21.4oW and indicates the location of the high-resolution view on the right. The high resolution view (right) covers a small portion of the Margaritifer Chaos at 1.8 meters (6 feet) per pixel. The area shown is 3 km (1.9 miles) across. Uplands are lumpy with small bright outcrops of bedrock. Lowlands or valleys in the chaotic terrain have floors covered by light-toned windblown d rifts. This image is typical of the very highest-resolution views of the equatorial latitudes of Mars. Both pictures are illuminated from the left/upper left, north is toward the top.

On fractality and chaos in Moroccan family business stock returns and volatility

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-05-01

The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

PubMed

Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J

2013-06-01

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

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…

Complexity and chaos control in a discrete-time prey-predator model

NASA Astrophysics Data System (ADS)

Din, Qamar

2017-08-01

We investigate the complex behavior and chaos control in a discrete-time prey-predator model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete-time prey-predator system with predator partially dependent on prey and investigate the boundedness, existence and uniqueness of positive equilibrium and bifurcation analysis of the system by using center manifold theorem and bifurcation theory. Various feedback control strategies are implemented for controlling the bifurcation and chaos in the system. Numerical simulations are provided to illustrate theoretical discussion.

Landslide in Aureum Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.

Synthesizing folded band chaos.

PubMed

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.

Firefly algorithm with chaos

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

Collective diffusion and quantum chaos in holography

NASA Astrophysics Data System (ADS)

Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu

2018-05-01

We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

Discovery of Dozy Chaos and Discovery of Quanta: Analogy Being in Science and Perhaps in Human Progress

NASA Astrophysics Data System (ADS)

Egorov, Vladimir V.

The concept of a dozy chaos in the theory of quantum transitions and its applications are discussed in a historical context. Conjectured that dozy chaos is of primary importance to the dynamic self-organization of any living organism and concentrated in its brain. A hypothesis of the physical origin of cancer is put forward. Surmised that dozy chaos is the physical origin of life and driving force of its evolution.

The Simple Map for a Single-null Divertor Tokamak: How to Look for Self-Similarity in Chaos

NASA Astrophysics Data System (ADS)

Nguyen, Christina; Ali, Halima; Punjabi, Alkesh

2000-10-01

The movement of magnetic field lines inside a single-null divertor tokamak can be described by the Simple Map^1. The Simple Map in the Poincaré Surface of Section is given by the equations: X_1=X_0-KY_0(1-Y_0) and Y_1=Y_0+KX_1. In these equations, K remains constant at 0.60. However, the values for X0 and Y0 are changed. These values are changed so that we can zoom into chaos. Chaos lies between the region (0,0.997) and (0,1). In chaos, there lies order. As we zoom into chaos, we again find chaos and order that looks like the original good surfaces and chaos. This phenomenon is called self-similarity. Self-similarity can occur for an infinite number of times if one magnifies into the chaotic region. For this work, we write a program in a computer language called Fortran 77 and Gnuplot. This work is supported by US DOE OFES. Ms. Christina Nguyen is a HU CFRT Summer Fusion High School Workshop Scholar from Andrew Hill High School in California. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Boozer A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

Catastrophic ice lake collapse in Aram Chaos, Mars

NASA Astrophysics Data System (ADS)

Roda, Manuel; Kleinhans, Maarten G.; Zegers, Tanja E.; Oosthoek, Jelmer H. P.

2014-07-01

Hesperian chaotic terrains have been recognized as the source of outflow channels formed by catastrophic outflows. Four main scenarios have been proposed for the formation of chaotic terrains that involve different amounts of water and single or multiple outflow events. Here, we test these scenarios with morphological and structural analyses of imagery and elevation data for Aram Chaos in conjunction with numerical modeling of the morphological evolution of the catastrophic carving of the outflow valley. The morphological and geological analyses of Aram Chaos suggest large-scale collapse and subsidence (1500 m) of the entire area, which is consistent with a massive expulsion of liquid water from the subsurface in one single event. The combined observations suggest a complex process starting with the outflow of water from two small channels, followed by continuous groundwater sapping and headward erosion and ending with a catastrophic lake rim collapse and carving of the Aram Valley, which is synchronous with the 2.5 Ga stage of the Ares Vallis formation. The water volume and formative time scale required to carve the Aram channels indicate that a single, rapid (maximum tens of days) and catastrophic (flood volume of 9.3 × 104 km3) event carved the outflow channel. We conclude that a sub-ice lake collapse model can best explain the features of the Aram Chaos Valley system as well as the time scale required for its formation.

75 FR 53013 - Culturally Significant Objects Imported for Exhibition Determinations: “Chaos and Classicism: Art...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-30

... DEPARTMENT OF STATE [Public Notice 7137] Culturally Significant Objects Imported for Exhibition Determinations: ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936'' SUMMARY: Notice is hereby... hereby determine that the objects to be included in the exhibition ``Chaos and Classicism: Art in France...

Numerical proof for chemostat chaos of Shilnikov's type.

PubMed

Deng, Bo; Han, Maoan; Hsu, Sze-Bi

2017-03-01

A classical chemostat model is considered that models the cycling of one essential abiotic element or nutrient through a food chain of three trophic levels. The long-time behavior of the model was known to exhibit complex dynamics more than 20 years ago. It is still an open problem to prove the existence of chaos analytically. In this paper, we aim to solve the problem numerically. In our approach, we introduce an artificial singular parameter to the model and construct singular homoclinic orbits of the saddle-focus type which is known for chaos generation. From the configuration of the nullclines of the equations that generates the singular homoclinic orbits, a shooting algorithm is devised to find such Shilnikov saddle-focus homoclinic orbits numerically which in turn imply the existence of chaotic dynamics for the original chemostat model.

Large-Scale Chaos and Fluctuations in Active Nematics

NASA Astrophysics Data System (ADS)

Ngo, Sandrine; Peshkov, Anton; Aranson, Igor S.; Bertin, Eric; Ginelli, Francesco; Chaté, Hugues

2014-07-01

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Generating macroscopic chaos in a network of globally coupled phase oscillators

PubMed Central

So, Paul; Barreto, Ernest

2011-01-01

We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662

Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread

NASA Astrophysics Data System (ADS)

Billings, Lora; Bollt, Erik M.; Schwartz, Ira B.

2002-06-01

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

Chaos in Magnetic Flux Ropes

NASA Astrophysics Data System (ADS)

Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

2013-12-01

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 using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope 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. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2

Life Chaos and Perceived Social Support Among Methamphetamine-Using Men Who Have Sex With Men Engaging in Transactional Sexual Encounters.

PubMed

Viswanath, Humsini; Wilkerson, J Michael; Breckenridge, Ellen; Selwyn, Beatrice J

2017-01-02

Social support and life chaos have been inversely associated with increased risk of HIV infection. The purpose of this study was to explore among a sample of HIV-negative methamphetamine-using men who have sex with men (MSM) the association between engaging in transactional sex, life chaos, and low social support. HIV-negative methamphetamine-using MSM completed an online questionnaire between July and October 2012 about recent substance use and sexual behavior. Bivariate and multivariate tests were used to obtain statistically significant associations between demographic characteristics, engaging in transactional sex, life chaos, and the participants' perception of their social support. Of the 325 participants, 23.7% reported engaging in transactional sex, 45.2% reported high life chaos, and 53.5% reported low perceived social support. Participants who engaged in transactional sex were more likely to have high life chaos than participants who did not (aOR = 1.70, 95% CI = [1.01, 2.84]); transactional sex was not associated with social support. Participants with high life chaos were more out about their sexual orientation (aOR = 2.29, 95% CI = [1.18, 4.42]) and more likely to perceive they had low social support (aOR = 3.78, 95% CI = [2.31, 6.22]) than participants with low life chaos. Non-Latinos perceived they had less social support than Latinos (aOR = 0.48, 95% CI = [0.25, 0.92]). Methamphetamine-using MSM engaging in transactional sex experience more life chaos than those who do not engage in transactional sex. Outness, perceived social support, and ethnicity are associated with life chaos.

Eos Chaos Rocks

NASA Technical Reports Server (NTRS)

2006-01-01

11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region.

Location near: 12.9oS, 49.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Southern Summer

Chaos and Localization in Dieterich-Ruina Friction

NASA Astrophysics Data System (ADS)

Erickson, B. A.; Birnir, B.; Lavallee, D.

2009-12-01

We consider two models derived from a 1-D Burridge-Knopoff chain of spring connected blocks subject to the Dieterich-Ruina (D-R) friction law. We analyze both the discrete ordinary differential equations, as well as the continuum model. Preliminary investigation into the ODEs shows evidence of the Dieterich-Ruina law exhibiting chaos, dependent on the size of the system. Periodic behavior occurs when considering chains of 3 or 5 blocks, while a chain of 10 blocks with the same parameter values results in chaotic motion. The continuum model (PDE) undergoes a transition to chaos when a specific parameter is increased and the chaotic regime is reached for smaller critical values than in the case of a single block (see Erickson et. al. 2008). This parameter, epsilon is the ratio of the stress parameters (B-A) and A in the D-R friction law. The parameter A is a measure of the direct velocity dependence (sometimes called the "direct effect") while (A-B) is a measure of the steady-state velocity dependence. When compared to the slip weakening friction law, the parameter (B-A) plays a role of a stress drop while A corresponds to the strength excess. In the case of a single block, transitions to chaos occur when epsilon = 11, a value too high for applications in seismology. For the continuum model however, the chaotic regime is reached for epsilon = 1. That the transition to chaos ensues for smaller parameter values than in the case of a single block may also be an indication that a careful rescaling of the friction law is necessary, similar to the conclusions made by Schmittbuhl et. al. (1996) who studied a "hierarchical array of blocks" and found that velocity weakening friction was scale dependent. We also observe solutions to both the discrete and the continuous model where the slip remains localized in space, suggesting the presence of solitonic behavior. Initial data in the form of a gaussian pulse tends to remain localized under certain parameter values and we

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

PubMed

Liu, Huijie; Li, Nianqiang; Zhao, Qingchun

2015-05-10

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

Secure free-space communication, turbulence mitigation, and other applications using acousto-optic chaos.

PubMed

Chatterjee, Monish R; Mohamed, Ali; Almehmadi, Fares S

2018-04-01

Use of acousto-optic (A-O) chaos via the feedback loop in a Bragg cell for signal encryption began as a conceptual demonstration around 2008. Radio frequency (RF) chaos from a hybrid A-O feedback device may be used for secure communications of analog and digital signals. In this paper, modulation of RF chaos via first-order feedback is discussed with results corroborated by nonlinear dynamics, bifurcation maps, and Lyapunov analyses. Applications based on encryption with profiled optical beams, and extended to medical and embedded steganographic data, and video signals are discussed. It is shown that the resulting encryption is significantly robust with key tolerances potentially less than 0.1%. Results are also presented for the use of chaotic encryption for image restoration during propagation through atmospheric turbulence.

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

PubMed

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

2018-03-01

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

Impulse-induced localized control of chaos in starlike networks.

PubMed

Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

2016-06-01

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

Transient chaos in the Lorenz-type map with periodic forcing

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Creating CHAOS for Smart, Troubled High-Riskers

ERIC Educational Resources Information Center

Grimes, Rich

2006-01-01

The acronym CHAOS (Caring, Honesty, Accountability, Ownership, and Success), provides the foundation, structure, and relational components for an environment with all school community members focused on one essential goal--the success of all students. In this article, the author discusses the plight of "troubled" students and discusses the need to…

A Framework for Chaos Theory Career Counselling

ERIC Educational Resources Information Center

Pryor, Robert G. L.

2010-01-01

Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems.

PubMed

Lithwick, Yoram; Wu, Yanqin

2014-09-02

In the inner solar system, the planets' orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. However, in the case of the hot Jupiter, the innermost planet was Jupiter (rather than Mercury) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present results comparing the inclinations of hot Jupiters thus produced with observations.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

PubMed Central

Lithwick, Yoram; Wu, Yanqin

2014-01-01

In the inner solar system, the planets’ orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. However, in the case of the hot Jupiter, the innermost planet was Jupiter (rather than Mercury) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present results comparing the inclinations of hot Jupiters thus produced with observations. PMID:24367108

2017 Gordon Conference on Superconductivity

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

Chubukov, Andrey

The DOE award was for a 2017 Gordon Research conference on Superconductivity (GRC). The objective of GRC is to interchange the information about the latest theoretical and experimental developments in the area of superconductivity and to select most perspective directions for future research in this area.The goal of the Gordon Conference on Superconductivity is to present and discuss the latest results in the field of modern superconductivity, discuss new ideas and new directions of research in the area. It is a long-standing tradition of the Gordon conference on Superconductivity that the vast majority of participants are junior scientists. Funding formore » the conference would primarily be used to support junior researchers, particularly from under-represented groups. We had more 10 female speakers, some of them junior researchers, and some funding was used to support these speakers. The conference was held together with Gordon Research Seminar on Superconductivity, where almost all speakers and participants were junior scientists.« less

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

NASA Astrophysics Data System (ADS)

Mangiarotti, S.

2016-12-01

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

A novel image encryption algorithm based on chaos maps with Markov properties

NASA Astrophysics Data System (ADS)

Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang

2015-02-01

In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.

Chaos-on-a-chip secures data transmission in optical fiber links.

PubMed

Argyris, Apostolos; Grivas, Evangellos; Hamacher, Michael; Bogris, Adonis; Syvridis, Dimitris

2010-03-01

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3).

Ultra-Wideband Chaos Life-Detection Radar with Sinusoidal Wave Modulation

NASA Astrophysics Data System (ADS)

Xu, Hang; Li, Ying; Zhang, Jianguo; Han, Hong; Zhang, Bing; Wang, Longsheng; Wang, Yuncai; Wang, Anbang

2017-12-01

We propose and experimentally demonstrate an ultra-wideband (UWB) chaos life-detection radar. The proposed radar transmits a wideband chaotic-pulse-position modulation (CPPM) signal modulated by a single-tone sinusoidal wave. A narrow-band split ring sensor is used to collect the reflected sinusoidal wave, and a lock-in amplifier is utilized to identify frequencies of respiration and heartbeat by detecting the phase change of the sinusoidal echo signal. Meanwhile, human location is realized by correlating the CPPM echo signal with its delayed duplicate and combining the synthetic aperture technology. Experimental results demonstrate that the human target can be located accurately and his vital signs can be detected in a large dynamic range through a 20-cm-thick wall using our radar system. The down-range resolution is 15cm, benefiting from the 1-GHz bandwidth of the CPPM signal. The dynamic range for human location is 50dB, and the dynamic ranges for heartbeat and respiration detection respectively are 20dB and 60dB in our radar system. In addition, the bandwidth of the CPPM signal can be adjusted from 620MHz to 1.56GHz to adapt to different requirements.

The Sheperd equation and chaos identification.

PubMed

Gregson, Robert A M

2010-04-01

An equation created by Sheperd (1982) to model stability in exploited fish populations has been found to have a wider application, and it exhibits complicated internal dynamics, including phases of strict periodicity and of chaos. It may be potentially applicable to other psychophysiological contexts. The problems of determining goodness-of fit, and the comparative performance of alternative models including the Shephed model, are briefly addressed.

Moriond QCD 2013 Experimental Summary

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

Denisov, Dmitri

2013-06-28

The article presents experimental highlights of Moriond 2013 QCD conference. This was fantastic conference and the first Moriond QCD since the discovery of the Higgs boson. Many new results about its properties have been presented at the conference with Higgs-like particle becoming a Higgs as it properties match expected for the Higgs boson pretty well. There were many new results presented in all experimental areas including QCD, elecroweak, studies of the top, bottom and charm quarks, searches for physics beyond Standard Model as well as studies of the heavy ion collisions. 56 experimental talks have been presented at the conferencemore » and it is impossible to cover each result in the summary, so highlights are limited to what I was able to present in my summary talk presented on March 16 2013. The proceedings of the conference cover in depth all talks presented and I urge you to get familiar with all of them. Theoretical Summary of the conference was given by Michelangelo Mangano, so theory talks are not covered in the article.« less

Topological chaos, braiding and bifurcation of almost-cyclic sets.

PubMed

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Life Chaos and Perceived Social Support Among Methamphetamine-Using Men Who Have Sex with Men Engaging in Transactional Sexual Encounters

PubMed Central

Viswanath, Humsini; Wilkerson, J. Michael; Breckenridge, Ellen; Selwyn, Beatrice J.

2017-01-01

Objective Social support and life chaos have been inversely associated with increased risk of HIV infection. The purpose of this study was to explore among a sample of HIV-negative methamphetamine-using men who have sex with men (MSM) the association between engaging in transactional sex, life chaos, and low social support. Methods HIV-negative methamphetamine-using MSM completed an online questionnaire between July and October 2012 about recent substance use and sexual behavior. Bivariate and multivariate tests were used to obtain statistically significant associations between demographic characteristics, engaging in transactional sex, life chaos, and the participants’ perception of their social support. Results Of the 325 participants, 23.7% reported engaging in transactional sex, 45.2% reported high life chaos, and 53.5% reported low perceived social support. Participants who engaged in transactional sex were more likely to have high life chaos than participants who did not (aOR = 1.70, 95% CI = [1.01, 2.84]); transactional sex was not associated with social support. Participants with high life chaos were more out about their sexual orientation (aOR = 2.29, 95% CI = [1.18, 4.42]) and more likely to perceive they had low social support (aOR = 3.78, 95% CI = [2.31, 6.22]) than participants with low life chaos. Non-Latinos perceived they had less social support than Latinos (aOR = 0.48, 95% CI = [0.25, 0.92]). Conclusions Methamphetamine-using MSM engaging in transactional sex experience more life chaos than those who do not engage in transactional sex. Outness, perceived social support, and ethnicity are associated with life chaos. PMID:27679931

A Resonance Overlap Criterion for the Onset of Chaos in Systems of Two Eccentric Planets

NASA Astrophysics Data System (ADS)

Hadden, Sam; Lithwick, Yoram

2018-04-01

I will desrcribe a new analytic criterion to predict the onset of chaos in systems consisting of two massive, eccentric planets. Given a planet pair's spacing and masses, the criterion predicts the eccentricities at which the onset of large-scale chaos occurs. The onset of chaos is predicted based on overlap of mean motion resonances as in Wisdom (1980)'s pioneering work. Whereas Wisdom's work was limited to the overlap of first-order resonance and therefore to nearly circular planets, we account for resonances of all orders. This allows us to consider resonance overlap for planets with arbitrary eccentricities (up to orbit-crossing). Our results show excellent agreement with numerical simulations.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

PubMed

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

2015-12-01

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Chaotic Feedback Loops within Decision Making Groups: Towards an Integration of Chaos Theory and Cybernetics.

ERIC Educational Resources Information Center

Keaten, James A.

This paper offers a model that integrates chaos theory and cybernetics, which can be used to describe the structure of decision making within small groups. The paper begins with an overview of cybernetics and chaos. Definitional characteristics of cybernetics are reviewed along with salient constructs, such as goal-seeking, feedback, feedback…

Chaos and the Marketing of Computing Services on Campus.

ERIC Educational Resources Information Center

May, James H.

1989-01-01

In an age of chaos and uncertainty in computing services delivery, the best marketing strategy that can be adopted is concern for user constituencies and the long range solutions to their problems. (MLW)

Thermal diffusivity and chaos in metals without quasiparticles

NASA Astrophysics Data System (ADS)

Blake, Mike; Davison, Richard A.; Sachdev, Subir

2017-11-01

We study the thermal diffusivity DT in models of metals without quasiparticle excitations ("strange metals"). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infrared fixed points DT is always related to parameters characterizing many-body quantum chaos: the butterfly velocity vB and Lyapunov time τL through DT˜vB2τL. The relationship holds independently of the charge density, periodic potential strength, or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime and is otherwise insensitive to the profile of any matter fields.

Polynomial chaos expansion with random and fuzzy variables

NASA Astrophysics Data System (ADS)

Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.

2016-06-01

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Using simplified Chaos Theory to manage nursing services.

PubMed

Haigh, Carol A

2008-04-01

The purpose of this study was to evaluate the part simplified chaos theory could play in the management of nursing services. As nursing care becomes more complex, practitioners need to become familiar with business planning and objective time management. There are many time-limited methods that facilitate this type of planning but few that can help practitioners to forecast the end-point outcome of the service they deliver. A growth model was applied to a specialist service to plot service trajectory. Components of chaos theory can play a role in forecasting service outcomes and consequently the impact upon the management of such services. The ability to (1) track the trajectory of a service and (2) manipulate that trajectory by introducing new variables can allow managers to forward plan for service development and to evaluate the effectiveness of a service by plotting its end-point state.

Nonlinear Dynamics and Chaos in Astrophysics: A Festschrift in Honor of George Contopoulos

NASA Astrophysics Data System (ADS)

Buchler, J. Robert; Gottesman, Stephen T.; Kandrup, Henry E.

1998-12-01

The annals of the New York Academy of Sciences is a compilation of work in the area of nonlinear dynamics and chaos in Astrophysics. Sections included are: From Quasars to Extraordinary N-body Problems; Dynamical Spectra and the Onset of Chaos; Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systems; Bifurcations of Periodic Orbits in Axisymmetric Scalefree Potentials; Irregular Period-Tripling Bifurcations in Axisymmetric Scalefree Potentials; Negative Energy Modes and Gravitational Instability of Interpenetrating Fluids; Invariants and Labels in Lie-Poisson Systems; From Jupiter's Great Red Spot to the Structure of Galaxies: Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems; N-Body Simulations of Galaxies and Groups of Galaxies with the Marseille GRAPE Systems; On Nonlinear Dynamics of Three-Dimensional Astrophysical Disks; Satellites as Probes of the Masses of Spiral Galaxies; Chaos in the Centers of Galaxies; Counterrotating Galaxies and Accretion Disks; Global Spiral Patterns in Galaxies: Complexity and Simplicity; Candidates for Abundance Gradients at Intermediate Red-Shift Clusters; Scaling Regimes in the Distribution of Galaxies; Recent Progress in the Study of One-Dimensional Gravitating Systems; Modeling the Time Variability of Black Hole Candidates; Stellar Oscillons; Chaos in Cosmological Hamiltonians; and Phase Space Transport in Noisy Hamiltonian Systems.

Dark Mesas of Aram Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

6 July 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows several dark-toned mesas surrounded by light-toned sedimentary rock outcrops in Aram Chaos, a large impact basin -- over 200 km (more than 125 mi) across. These mesas are remnants of a once more extensive rock unit. The image is located near 2.0oN, 20.2oW, and covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the left.

Chaos Theory and International Relations

DTIC Science & Technology

2016-12-01

two. If we further confine ourselves to directed piercings of the plane , we are left with only a single point. Such a Poincare section reduces our...During the 20th century, Henri Poincare , Yoshisuke Ueda, and Edward Lorenz were the pioneers of the study of CT, although they never used the term Chaos...difference between linear and nonlinear in Chapter I, section C.1, first paragraph. 2 knowledge of them was poor; that is, until the work of Poincare . What

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Distinguishing Error from Chaos in Ecological Time Series

NASA Astrophysics Data System (ADS)

Sugihara, George; Grenfell, Bryan; May, Robert M.

1990-11-01

Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional)noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

NASA Astrophysics Data System (ADS)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Chaos theory for clinical manifestations in multiple sclerosis.

PubMed

Akaishi, Tetsuya; Takahashi, Toshiyuki; Nakashima, Ichiro

2018-06-01

Multiple sclerosis (MS) is a demyelinating disease which characteristically shows repeated relapses and remissions irregularly in the central nervous system. At present, the pathological mechanism of MS is unknown and we do not have any theories or mathematical models to explain its disseminated patterns in time and space. In this paper, we present a new theoretical model from a viewpoint of complex system with chaos model to reproduce and explain the non-linear clinical and pathological manifestations in MS. First, we adopted a discrete logistic equation with non-linear dynamics to prepare a scalar quantity for the strength of pathogenic factor at a specific location of the central nervous system at a specific time to reflect the negative feedback in immunity. Then, we set distinct minimum thresholds in the above-mentioned scalar quantity for demyelination possibly causing clinical relapses and for cerebral atrophy. With this simple model, we could theoretically reproduce all the subtypes of relapsing-remitting MS, primary progressive MS, and secondary progressive MS. With the sensitivity to initial conditions and sensitivity to minute change in parameters of the chaos theory, we could also reproduce the spatial dissemination. Such chaotic behavior could be reproduced with other similar upward-convex functions with appropriate set of initial conditions and parameters. In conclusion, by applying chaos theory to the three-dimensional scalar field of the central nervous system, we can reproduce the non-linear outcome of the clinical course and explain the unsolved disseminations in time and space of the MS patients. Copyright © 2018 Elsevier Ltd. All rights reserved.

Relation of Home Chaos to Cognitive Performance and Behavioral Adjustment of Pakistani Primary School Children

ERIC Educational Resources Information Center

Shamama-tus-Sabah, Syeda; Gilani, Nighat; Wachs, Theodore D.

2011-01-01

Recent findings from Western developed countries have linked home chaos to children's cognitive performance and behavioral problems. In the present paper we test whether the same pattern of associations can be replicated in a non-Western developing country. Our sample was 203 Pakistani primary school children. To assess home chaos the Confusion,…

Hybrid Chaos Synchronization of Four-Scroll Systems via Active Control

NASA Astrophysics Data System (ADS)

Karthikeyan, Rajagopal; Sundarapandian, Vaidyanathan

2014-03-01

This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

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

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

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

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Preface to the Focus Issue: chaos detection methods and predictability.

PubMed

Gottwald, Georg A; Skokos, Charalampos

2014-06-01

This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17-21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue.

Control of complex dynamics and chaos in distributed parameter systems

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

Chakravarti, S.; Marek, M.; Ray, W.H.

This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in themore » complex quasi-periodic or chaotic spatiotemporal patterns.« less

13th International Conference on Chlamydomonas

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

Silflow, Carolyn D.

2014-03-11

The 13th International Conference on Chlamydomonas (EMBO Workshop on the Cell and Molecular Biology of Chlamydomonas) was held May 27 to June 1, 2008 in Hyeres, France. The conference was the biennial meeting for all researchers studying the green algal systems Chlamydomonas and Volvox. The conference brought together approximately 200 investigators from around the world (North America, Asia, Europe and Australia) representing different fields and disciplines (cell biology, genetics, biochemistry, biophysics, plant physiology, genomics). It provided an opportunity for investigators from different countries to share methodologies and to discuss recent results with a focus on the Chlamydomonas experimental system.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

NASA Astrophysics Data System (ADS)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.

PubMed

Zausner, Tobi

2011-04-01

Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation.

Is case-chaos methodology an appropriate alternative to conventional case-control studies for investigating outbreaks?

PubMed

Edelstein, Michael; Wallensten, Anders; Kühlmann-Berenzon, Sharon

2014-08-15

Case-chaos methodology is a proposed alternative to case-control studies that simulates controls by randomly reshuffling the exposures of cases. We evaluated the method using data on outbreaks in Sweden. We identified 5 case-control studies from foodborne illness outbreaks that occurred between 2005 and 2012. Using case-chaos methodology, we calculated odds ratios 1,000 times for each exposure. We used the median as the point estimate and the 2.5th and 97.5th percentiles as the confidence interval. We compared case-chaos matched odds ratios with their respective case-control odds ratios in terms of statistical significance. Using Spearman's correlation, we estimated the correlation between matched odds ratios and the proportion of cases exposed to each exposure and quantified the relationship between the 2 using a normal linear mixed model. Each case-control study identified an outbreak vehicle (odds ratios = 4.9-45). Case-chaos methodology identified the outbreak vehicle 3 out of 5 times. It identified significant associations in 22 of 113 exposures that were not associated with outcome and 5 of 18 exposures that were significantly associated with outcome. Log matched odds ratios correlated with their respective proportion of cases exposed (Spearman ρ = 0.91) and increased significantly with the proportion of cases exposed (b = 0.054). Case-chaos methodology missed the outbreak source 2 of 5 times and identified spurious associations between a number of exposures and outcome. Measures of association correlated with the proportion of cases exposed. We recommended against using case-chaos analysis during outbreak investigations. © The Author 2014. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Deterministic chaos in entangled eigenstates

NASA Astrophysics Data System (ADS)

Schlegel, K. G.; Förster, S.

2008-05-01

We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

Applying Chaos Theory to Careers: Attraction and Attractors

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim E. H.

2007-01-01

This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…

Stability and chaos of Rulkov map-based neuron network with electrical synapse

NASA Astrophysics Data System (ADS)

Wang, Caixia; Cao, Hongjun

2015-02-01

In this paper, stability and chaos of a simple system consisting of two identical Rulkov map-based neurons with the bidirectional electrical synapse are investigated in detail. On the one hand, as a function of control parameters and electrical coupling strengthes, the conditions for stability of fixed points of this system are obtained by using the qualitative analysis. On the other hand, chaos in the sense of Marotto is proved by a strict mathematical way. These results could be useful for building-up large-scale neurons networks with specific dynamics and rich biophysical phenomena.

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

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

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

Radical Lessons: Thoughts on Emma Goldman, Chaos, Grief, and Political Violence Post-9/11/01

ERIC Educational Resources Information Center

Kensinger, Loretta

2009-01-01

Since that fateful day in September 2001, and in its terrible aftermath, the author has often sought inspiration from a wider community of humans seeking to create a different, less terrifying, world. In concluding her 1912 article, "The New Year," Emma Goldman boldly asserted, "Out of the chaos the future emerges in harmony and beauty." Chaos is…

Adaptation to the edge of chaos in a self-starting Kerr-lens mode-locked laser

NASA Astrophysics Data System (ADS)

Hsu, C. C.; Lin, J. H.; Hsieh, W. F.

2009-08-01

We experimentally and numerically demonstrated that self-focusing acts as a slow-varying control parameter that suppresses the transient chaos to reach a stable mode-locking (ML) state in a self-starting Kerr-lens mode-locked Ti:sapphire laser without external modulation and feedback control. Based on Fox-Li’s approach, including the self-focusing effect, the theoretical simulation reveals that the self-focusing effect is responsible for the self-adaptation. The self-adaptation occurs at the boundary between the chaotic and continuous output regions in which the laser system begins with a transient chaotic state with fractal correlation dimension, and then evolves with reducing dimension into the stable ML state.

Canyons and Mesas of Aureum Chaos

NASA Technical Reports Server (NTRS)

2002-01-01

(Released 17 June 2002) This image contains a portion of Aureum Chaos located just south of the Martian equator. This fractured landscape contains canyons and mesas with two large impact craters in the upper left. The largest crater is older than the one above it. This is readily evident because a landslide deposit created by the smaller crater's impact is seen on the larger crater's floor. The overall scene has a rather muted appearance due to mantling by dust. Some small dark streaks can also be seen in this scene. These small dark streaks suggest that the materials covering this area occasionally become unstable and slide. Ridges of resistant material also can be observed in the walls of the canyons. The wall rock seen in the upper part of the cliffs appears to be layered. Classic spur and gully topography created by differing amounts of erosion and possibly different rock types is also visible here. One important observation to be made in this region is that there are no gullies apparent on the slopes such as those seen in Gorgonum Chaos (June 11th daily image). Latitude appears to play a major role in gully occurrence and distribution, with the gullies being predominately found pole ward of 30o.

XVII International Conference on Hadron Spectroscopy and Structure

NASA Astrophysics Data System (ADS)

2017-09-01

The Hadron 2017 Conference is the seventeenth of a series of biennial conferences started in 1985 at Maryland, USA. Its official name, XVII International Conference on Hadron Spectroscopy and Structure, includes for the first time the term structure to emphasize the importance that this issue has acquired in recent editions of the series. The aim of the conference is to provide an overview of the present status and progress in hadron structure and dynamics, as well as a preview of the forthcoming investigations. It will cover lectures on both experimental and theoretical aspects, including in particular the presentation of new results.

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.

Strategic leadership: a view from quantum and chaos theories.

PubMed

McDaniel, R R

1997-01-01

Viewing health care from the perspective of chaos and quantum theories offers new insights into management techniques for effective and efficient delivery of health care services. This article introduces these concepts and gives specific prescriptions for managerial action.

Competitive coexistence in stoichiometric chaos.

PubMed

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.

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

PubMed Central

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

2015-01-01

Behavioral regulation is an important school readiness skill that has been linked to early executive function (EF) and later success in learning and school achievement. Although poverty and related risks as well as negative parenting have been associated with poorer EF and behavioral regulation, chaotic home environments may also play a role in understanding both early EF and later behavioral regulation at school age. To explore these relationships, a unique longitudinal and representative sample was used of 1292 children born to mothers who lived in low wealth rural America who were followed from birth into early elementary school. This study examined whether household chaos, which was measured across the first three years of life, predicted behavioral regulation in kindergarten above and beyond poverty related variables. In addition, this study tested whether parent responsivity and acceptance behaviors, measured during the first three years of life, as well as EF skills, which were measured when children were three to five years of age, mediated the relationship between early household chaos and kindergarten behavioral regulation. Results suggested that household chaos disorganization indirectly predicted kindergarten behavioral regulation through intermediate impacts on parenting behaviors and children's early EF skills. These findings suggest the importance of early household chaos disorganization, the parenting environment and early EF skills in understanding behavioral regulation, above and beyond poverty related risks. PMID:26751500

Quasiperiodic instability and chaos in the bad-cavity laser with modulated inversion: Numerical analysis of a Toda oscillator system

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

Ogawa, T.

The exact equivalence between a bad-cavity laser with modulated inversion and a nonlinear oscillator in a Toda potential driven by an external modulation is presented. The dynamical properties of the laser system are investigated in detail by analyzing a Toda oscillator system. The temporal characteristics of the bad-cavity laser under strong modulation are analyzed extensively by numerically investigating the simpler Toda system as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. The system exhibits two kinds of optical chaos: One is the quasiperiodic chaos in the region of the intermediate modulationmore » amplitude and the other is the intermittent kicked chaos in the region of strong modulation and large dc component of the pumping. The former is well described by a one-dimensional discrete map with a singular invariant probability measure. There are two types of onset of the chaos: quasiperiodic instability (continuous path to chaos) and catastrophic crisis (discontinuous path). The period-doubling cascade of bifurcation is also observed. The simple discrete model of the Toda system is presented to obtain analytically the one-dimensional map function and to understand the effect of the asymmetric potential curvature on yielding chaos.« less

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

PubMed

Shinbrot, Troy

2015-09-01

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

Sedimentary Rocks of Aram Chaos

NASA Technical Reports Server (NTRS)

2004-01-01

4 February 2004 Aram Chaos is a large meteor impact crater that was nearly filled with sediment. Over time, this sediment was hardened to form sedimentary rock. Today, much of the eastern half of the crater has exposures of light-toned sedimentary rock, such as the outcrops shown in this Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image. The picture is located near 2.0oN, 20.3oW, and covers an area 3 km (1.9 mi) wide. Sunlight illuminates the scene from the left.

Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection

NASA Astrophysics Data System (ADS)

Xie, Yi-Yuan; Li, Jia-Chao; He, Chao; Zhang, Zhen-Dong; Song, Ting-Ting; Xu, Chang-Jun; Wang, Gui-Jin

2016-10-01

A novel long-distance multi-channel bidirectional chaos communication system over multiple paths based on two synchronized 1550 nm vertical-cavity surface-emitting lasers (VCSELs) is proposed and studied theoretically. These two responding VCSELs (R-VCSELs) can output similar chaotic signals served as chaotic carrier in two linear polarization (LP) modes with identical signal injection from a driving VCSEL (D-VCSEL), which is subject to optical feedback and optical injection, simultaneously. Through the numerical simulations, high quality chaos synchronization between the two R-VCSELs can be obtained. Besides, the effects of varied qualities of chaos synchronization on communication performances in 20 km single mode fiber (SMF) channels are investigated by regulating different internal parameters mismatch after adopting chaos masking (CMS) technique. With the decrease of the maximum cross correlation coefficient (Max-C) between the two R-VCSELs, the bit error rate (BER) of decoded message increase. Meanwhile, the BER can still be less than 10-9 when the Max-C degrades to 0.982. Based on high quality synchronization, when the dispersion compensating fiber (DCF) links are introduced, 4n messages of 10 Gbit/s can transmit in 180 km SMF channels over n coupling paths, bidirectionally and simultaneously. Thorough tests are carried out with detailed analysis, demonstrating long-distance, multi-channel, bidirectional chaos communication based on VCSELs with chaotic signal injection.

ICCK Conference Final Report

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

Green, William H.

2013-05-28

The 7th International Conference on Chemical Kinetics (ICCK) was held July 10-14, 2011, at Massachusetts Institute of Technology (MIT), in Cambridge, MA, hosted by Prof. William H. Green of MIT's Chemical Engineering department. This cross-disciplinary meeting highlighted the importance of fundamental understanding of elementary reactions to the full range of chemical investigations. The specific conference focus was on elementary-step kinetics in both the gas phase and in condensed phase. The meeting provided a unique opportunity to discuss how the same reactive species and reaction motifs manifest under very different reaction conditions (e.g. atmospheric, aqueous, combustion, plasma, in nonaqueous solvents, onmore » surfaces.). The conference featured special sessions on new/improved experimental techniques, improved models and data analysis for interpreting complicated kinetics, computational kinetics (especially rate estimates for large kinetic models), and a panel discussion on how the community should document/archive kinetic data. In the past, this conference had been limited to homogeneous gas-phase and liquid-phase systems. This conference included studies of heterogeneous kinetics which provide rate constants for, or insight into, elementary reaction steps. This Grant from DOE BES covered about half of the subsidies we provided to students and postdocs who attended the conference, by charging them reduced-rate registration fees. The complete list of subsidies provided are listed in Table 1 below. This DOE funding was essential to making the conference affordable to graduate students, and indeed the attendance at this conference was higher than at previous conferences in this series. Donations made by companies provided additional subsidies, leveraging the DOE funding. The conference was very effective in educating graduate students and important in fostering scientific interactions, particularly between scientists studying gas phase and liquid phase

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…

Chaos control of Hastings-Powell model by combining chaotic motions.

PubMed

Danca, Marius-F; Chattopadhyay, Joydev

2016-04-01

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

[Online-conference using JGN.].

PubMed

Nakayama, Kazuya; Kojima, Kazuhiko; Suzuki, Masayuki; Kikuchi, Yuzo; Iwahara, Masayoshi; Matsui, Osamu; Noguchi, Masato

2004-01-01

Telemedicine and online conference systems have some benefits so that equalizing medical level, improving efficiency of medical care and improving service for patients. It is possible to give advice and to support its medical projects stationed in other facility and to provide the same quality treatments for patients. In this paper, we set up an experimental network system to teleconference using JGN (Japan Gigabit Network) and tried to discussion alternatively for case study between Kanazawa university and Fukui red cross hospital, 70 km away. The JGN used in this study is an ultra-high-speed network for the purpose of research and development. Kanazawa university, and Fukui red cross hospital are connected by a 10 Mbps communication link of the JGN. We tried online conference on the experimental network using video chat system. In result, using video chat system, the average transmission rate of MRI images (256 X 256pixel, 16bit) is 0.2 s/frame.

Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

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

Lu, Fei; Department of Mathematics, University of California, Berkeley; Morzfeld, Matthias, E-mail: mmo@math.lbl.gov

2015-02-01

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Relationships of family conflict, cohesion, and chaos in the home environment on maternal and child food-related behaviours.

PubMed

Martin-Biggers, Jennifer; Quick, Virginia; Zhang, Man; Jin, Yanhong; Byrd-Bredbenner, Carol

2018-04-01

This study examined how food-related behaviours differed in mothers and their preschool children by levels of family functioning (cohesion and conflict) and household disorganization (chaos). A nationally representative sample of mothers of preschoolers completed an online survey assessing food-related behaviours of themselves and their children. Maternal and child diet, eating behaviours, and health status; household availability of fruits/vegetables, salty/fatty snacks, and sugar-sweetened beverages; family mealtime atmosphere; and family conflict, cohesion, and household chaos were assessed with valid, reliable scales. Cluster analyses assigned families into low, middle, and high conflict, cohesion, and chaos groups. Participants (n = 550) were 72% White, and 82% had some post-secondary education. Regression analysis examining the association of cluster grouping levels on diet-related behaviour measures revealed that positive home environments (i.e., low family conflict, high family cohesion, and low household chaos) were associated with healthier food-related behaviours (e.g., increased fruits/vegetables intake), whereas negative home environments (i.e., high family conflict, low family cohesion, and high household chaos) were associated with unhealthy food-related behaviours (e.g., greater % total calories from fat) even after controlling for sociodemographic and related behavioural factors. Findings suggest family functioning and household chaos are associated with food-related behaviours. This frequently overlooked component of family interaction may affect intervention outcomes and objectives of educational and interventional initiatives. © 2017 John Wiley & Sons Ltd.

HIV-Related Stress and Life Chaos Mediate the Association Between Poverty and Medication Adherence Among People Living with HIV/AIDS.

PubMed

Kalichman, Seth C; Kalichman, Moira O

2016-12-01

HIV treatment depends on high-levels of antiretroviral therapy (ART) adherence, which is severely impeded by poverty. Men and women living with HIV infection (N = 92) completed computerized interviews of demographic and health characteristics, poverty markers, stressful life events, and life chaos, as well as unannounced pill counts to determine prospective medication adherence and medical record chart abstractions for HIV viral load. Poverty markers were associated with both stressors and chaos, and the direct effects of all three factors predicted ART non-adherence. The multiple mediation model showed that accounting for stressors and chaos resulted in a non-significant association between poverty markers and ART adherence. The indirect effect of poverty markers on adherence through life chaos was significant, whereas the indirect effect of poverty markers on adherence through stressors was not significant. Factors that render HIV-related stress and create chaos offer intervention targets that are more amenable to change than poverty itself.

Fisher information at the edge of chaos in random Boolean networks.

PubMed

Wang, X Rosalind; Lizier, Joseph T; Prokopenko, Mikhail

2011-01-01

We study the order-chaos phase transition in random Boolean networks (RBNs), which have been used as models of gene regulatory networks. In particular we seek to characterize the phase diagram in information-theoretic terms, focusing on the effect of the control parameters (activity level and connectivity). Fisher information, which measures how much system dynamics can reveal about the control parameters, offers a natural interpretation of the phase diagram in RBNs. We report that this measure is maximized near the order-chaos phase transitions in RBNs, since this is the region where the system is most sensitive to its parameters. Furthermore, we use this study of RBNs to clarify the relationship between Shannon and Fisher information measures.

PREFACE: 10th Joint Conference on Chemistry

NASA Astrophysics Data System (ADS)

2016-02-01

The 10th Joint Conference on Chemistry is an international conference organized by 4 chemistry departments of 4 universities in central Java, Indonesia. The universities are Sebelas Maret University, Diponegoro University, Semarang State University and Soedirman University. The venue was at Solo, Indonesia, at September 8-9, 2015. The total conference participants are 133 including the invited speakers. The conference emphasized the multidisciplinary chemical issue and impact of today's sustainable chemistry which covering the following topics: • Material innovation for sustainable goals • Development of renewable and sustainable energy based on chemistry • New drug design, experimental and theoretical methods • Green synthesis and characterization of material (from molecule to functionalized materials) • Catalysis as core technology in industry • Natural product isolation and optimization

Granular chaos and mixing: Whirled in a grain of sand

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

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

2015-09-15

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

Universality in quantum chaos and the one-parameter scaling theory.

PubMed

García-García, Antonio M; Wang, Jiao

2008-02-22

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.

Aram Chaos: A Long Lived Subsurface Aqueous Environment with Strong Water Resource Potential for Human Missions on Mars

NASA Astrophysics Data System (ADS)

Sibille, L.; Mueller, R. P.; Niles, P. B.; Glotch, T.; Archer, P. D.; Bell, M. S.

2015-10-01

Aram Chaos is a 280-km-wide near-circular structure near the outflow channel Ares Vallis and Aureum Chaos. It is a compelling landing site for human explorers featuring multiple science ROIs with a compelling resource ROI with polyhydrated sulfates.

Building CHAOS: An Operating System for Livermore Linux Clusters

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

Garlick, J E; Dunlap, C M

2003-02-21

The Livermore Computing (LC) Linux Integration and Development Project (the Linux Project) produces and supports the Clustered High Availability Operating System (CHAOS), a cluster operating environment based on Red Hat Linux. Each CHAOS release begins with a set of requirements and ends with a formally tested, packaged, and documented release suitable for use on LC's production Linux clusters. One characteristic of CHAOS is that component software packages come from different sources under varying degrees of project control. Some are developed by the Linux Project, some are developed by other LC projects, some are external open source projects, and some aremore » commercial software packages. A challenge to the Linux Project is to adhere to release schedules and testing disciplines in a diverse, highly decentralized development environment. Communication channels are maintained for externally developed packages in order to obtain support, influence development decisions, and coordinate/understand release schedules. The Linux Project embraces open source by releasing locally developed packages under open source license, by collaborating with open source projects where mutually beneficial, and by preferring open source over proprietary software. Project members generally use open source development tools. The Linux Project requires system administrators and developers to work together to resolve problems that arise in production. This tight coupling of production and development is a key strategy for making a product that directly addresses LC's production requirements. It is another challenge to balance support and development activities in such a way that one does not overwhelm the other.« less

A novel image encryption algorithm using chaos and reversible cellular automata

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Luan, Dapeng

2013-11-01

In this paper, a novel image encryption scheme is proposed based on reversible cellular automata (RCA) combining chaos. In this algorithm, an intertwining logistic map with complex behavior and periodic boundary reversible cellular automata are used. We split each pixel of image into units of 4 bits, then adopt pseudorandom key stream generated by the intertwining logistic map to permute these units in confusion stage. And in diffusion stage, two-dimensional reversible cellular automata which are discrete dynamical systems are applied to iterate many rounds to achieve diffusion on bit-level, in which we only consider the higher 4 bits in a pixel because the higher 4 bits carry almost the information of an image. Theoretical analysis and experimental results demonstrate the proposed algorithm achieves a high security level and processes good performance against common attacks like differential attack and statistical attack. This algorithm belongs to the class of symmetric systems.

The role of household chaos in understanding relations between early poverty and children's academic achievement

PubMed Central

Mokrova, Irina; Vernon-Feagans, Lynne; Willoughby, Michael; Pan, Yi

2016-01-01

The following prospective longitudinal study used an epidemiological sample (N = 1,236) to consider the potential mediating role of early cumulative household chaos (6–58 months) on associations between early family income poverty (6 months) and children's academic achievement in kindergarten. Two dimensions of household chaos, disorganization and instability, were examined as mediators. Results revealed that, in the presence of household disorganization (but not instability) and relevant covariates, income poverty was no longer directly related to academic achievement. Income poverty was, however, positively related to household disorganization, which was, in turn, associated with lower academic achievement. Study results are consistent with previous research indicating that household chaos conveys some of the adverse longitudinal effects of income poverty on children's outcomes and extend previous findings specifically to academic achievement in early childhood. PMID:27330247

PREFACE: XXI Fluid Mechanics Conference

NASA Astrophysics Data System (ADS)

Szmyd, Janusz S.; Fornalik-Wajs, Elzbieta; Jaszczur, Marek

2014-08-01

This Conference Volume contains the papers presented at the 21st Fluid Mechanics Conference (XXI FMC) held at AGH - University of Science and Technology in Krakow, Poland, 15-18 June 2014, and accepted for Proceedings published in the Journal of Physics: Conference Series. The Fluid Mechanics Conferences have been taking place every two years since 1974, a total of forty years. The 21st Fluid Mechanics Conference (XXI FMC) is being organized under the auspices of the Polish Academy of Sciences, Committee of Mechanics. The goal of this conference is to provide a forum for the exposure and exchange of ideas, methods and results in fluid mechanics. Conference topics include, but are not limited to Aerodynamics, Atmospheric Science, Bio-Fluids, Combustion and Reacting Flows, Computational Fluid Dynamics, Experimental Fluid Mechanics, Flow Machinery, General Fluid Dynamics, Hydromechanics, Heat and Fluid Flow, Measurement Techniques, Micro- and Nano- Flow, Multi-Phase Flow, Non-Newtonian Fluids, Rotating and Stratified Flows, Turbulence. Within the general subjects of this conference, the Professor Janusz W. Elsner Competition for the best fluid mechanics paper presented during the Conference is organized. Authors holding a M.Sc. or a Ph.D. degree and who are not older than 35 years of age may enter the Competition. Authors with a Ph.D. degree must present individual papers; authors with a M.Sc. degree may present papers with their supervisor as coauthor, including original results of experimental, numerical or analytic research. Six state-of-the-art keynote papers were delivered by world leading experts. All contributed papers were peer reviewed. Recommendations were received from the International Scientific Committee, reviewers and the advisory board. Accordingly, of the 163 eligible extended abstracts submitted, after a review process by the International Scientific Committee, 137 papers were selected for presentation at the 21st Fluid Mechanics Conference, 68

Chaos and the evolution of cooperation.

PubMed

Nowak, M; Sigmund, K

1993-06-01

The "iterated prisoner's dilemma" is the most widely used model for the evolution of cooperation in biological societies. Here we show that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular (chaotic) oscillations in the frequencies of the strategies and the overall level of cooperation. The levels of cooperation jump up and down in an apparently unpredictable fashion. Small recurrent and simultaneous invasion attempts (caused by mutation) can change the evolutionary dynamics from converging to an evolutionarily stable strategy to periodic oscillations and chaos. Evolution can be twisted away from defection, toward cooperation. Adding "generous tit-for-tat" greatly increases the overall level of cooperation and can lead to long periods of steady cooperation. Since May's paper [May, R. M. (1976) Nature (London) 261, 459-467], "simple mathematical models with very complicated dynamics" have been found in many biological applications, but here we provide an example of a biologically relevant evolutionary game whose dynamics display deterministic chaos. The simulations bear some resemblance to the irregular cycles displayed by the frequencies of host genotypes and specialized parasites in evolutionary "arms races" [Hamilton, W. D., Axelrod, R. & Tanese, R. (1990) Proc. Natl. Acad. Sci. USA 87, 3566-3573; Seger, J. (1988) Philos. Trans. R. Soc. London B 319, 541-555].

Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.

ERIC Educational Resources Information Center

Raw, Cecil J. G.; Stacey, Larry M.

1989-01-01

Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity.

PubMed

Choi, Daeyoung; Wishon, Michael J; Chang, C Y; Citrin, D S; Locquet, A

2018-01-01

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium

NASA Astrophysics Data System (ADS)

Lundqvist, Stig

1985-01-01

The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and

The Complex and Dynamic Nature of Quality in Early Care and Educational Programs: A Case for Chaos.

ERIC Educational Resources Information Center

Buell, Martha J.; Cassidy, Deborah J.

2001-01-01

Describes how chaos theory can be used to understand the nature of quality in early care and education settings. Reviews research on quality and quality initiatives, noting challenges to such quality enhancement initiatives. Details an application of the tenets of chaos theory to early care and educational settings, and includes recommendations…

Conduction at the onset of chaos

NASA Astrophysics Data System (ADS)

Baldovin, Fulvio

2017-02-01

After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.

Change in Chaos: Seven Lessons Learned from Katrina

ERIC Educational Resources Information Center

Carr-Chellman, Alison A.; Beabout, Brian; Alkandari, Khaled A.; Almeida, Luis C.; Gursoy, Husra T.; Ma, Ziyan; Modak, Rucha S.; Pastore, Raymond S.

2008-01-01

This article discusses seven lessons learned from Katrina, suggesting that after chaos: (1) there is hope; (2) there is a strong atmosphere of indeterminacy; (3) things tend to break apart and reform in somewhat similar ways but with different values; (4) there is a desire for organization, leadership, and familiarity; (5) there is a sense of…

Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

ERIC Educational Resources Information Center

Salazar, R.; Tellez, G.

2012-01-01

We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

Liquid computing on and off the edge of chaos with a striatal microcircuit

PubMed Central

Toledo-Suárez, Carlos; Duarte, Renato; Morrison, Abigail

2014-01-01

In reinforcement learning theories of the basal ganglia, there is a need for the expected rewards corresponding to relevant environmental states to be maintained and modified during the learning process. However, the representation of these states that allows them to be associated with reward expectations remains unclear. Previous studies have tended to rely on pre-defined partitioning of states encoded by disjunct neuronal groups or sparse topological drives. A more likely scenario is that striatal neurons are involved in the encoding of multiple different states through their spike patterns, and that an appropriate partitioning of an environment is learned on the basis of task constraints, thus minimizing the number of states involved in solving a particular task. Here we show that striatal activity is sufficient to implement a liquid state, an important prerequisite for such a computation, whereby transient patterns of striatal activity are mapped onto the relevant states. We develop a simple small scale model of the striatum which can reproduce key features of the experimentally observed activity of the major cell types of the striatum. We then use the activity of this network as input for the supervised training of four simple linear readouts to learn three different functions on a plane, where the network is stimulated with the spike coded position of the agent. We discover that the network configuration that best reproduces striatal activity statistics lies on the edge of chaos and has good performance on all three tasks, but that in general, the edge of chaos is a poor predictor of network performance. PMID:25484864

Positive Maladjustment as a Transition from Chaos to Order

ERIC Educational Resources Information Center

Laycraft, Krystyna

2009-01-01

Dabrowski's theory of positive disintegration describes patterns and explains mechanisms of human development and has been successfully applied to understanding of gifted individuals. This article shows how the concepts of chaos theory and self-organization such as the sensitivity to initial conditions, positive and negative feedback, bifurcation…

'Chaos is come again': Nothingness in Shakespeare's metadramatic time and space

NASA Astrophysics Data System (ADS)

Oswald, John David

The extraordinary advances of twentieth-century science, which overlay, and in some cases overturn, the Newtonian precepts upon which physics was founded, have captured a share of the popular imagination. Quantum mechanics, relativity theory, and chaos theory are the stuff of science fact and science fiction, of technological innovation and artistic invention. Intricate ``fractal'' images adorn poster art, and science fiction fantasy (long a niche market for popular fiction) is the genre of the blockbuster film and the television franchise. Astronomers and physicists are writing pop-science bestsellers for the layman, making theory accessible to those who cannot do the math. This work focuses on Shakespearean notions of time and space in selected metadramatic passages from three plays that feature embattled monarchs: Richard II, King Lear, and The Winter's Tale. Shakespeare's employment of metaphors that are also ``cardinal metaphors'' of science is examined to determine how his dramatic works fare under a post-deterministic paradigm. A chaos-theory model is advanced for theatrical performance, and analogies are drawn from scientific theory to discuss dramatic language and action (e.g., ``nothingness'' in different contexts is compared variously with black holes, dark matter, vacuum genesis in a spatial void roiling with virtual particles, the empty space within matter, etc.). Of primary importance are the notions of quantum observership (the impossibility of separating observation from participation in scientific experimentation) and complementarity (Bohr's theory to account for the dual behavior of radiation as both waves and particles). Shakespeare's persistent metadramatic emphasis is seen as an effort to draw his audience (observers) into conscious participation in the imaginative act of bringing his plays into being. Complementarity relates to the promotion of multiple perspectives in all three plays and to the dramaturgical structure of The Winter's Tale.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Perspectives on Advertising Education: Curricula, Research--Descriptive, Research--Experimental, Industry/Educators' Cooperation, Special Interest Areas, and Instruction; Proceedings of the 1974 National Conference for University Professors of Advertising at the Univ. of Rhode Island.

ERIC Educational Resources Information Center

Zeigler, Sherilyn K., Ed.

This document contains all of the presentations given at the 1974 National American Academy of Advertising Conference in Newport, Rhode Island. The theme of the conference was "Perspectives on Advertising" and the areas of focus were curricula and instruction, descriptive and experimental research, cooperation between educators and the advertising…

Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology.

PubMed

Mittal, Khushboo; Gupta, Shalabh

2017-05-01

Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes. This paper addresses this research gap by using topological data analysis as a tool to study system evolution and develop a mathematical framework for detecting the topological changes in the underlying system using persistent homology. Using the proposed technique, topological features (e.g., number of relevant k-dimensional holes, etc.) are extracted from nonlinear time series data which are useful for deeper analysis of the system behavior and early detection of bifurcations and chaos. When applied to a Logistic map, a Duffing oscillator, and a real life Op-amp based Jerk circuit, these features are shown to accurately characterize the system dynamics and detect the onset of chaos.

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

Household chaos moderates the link between maternal attribution bias and parenting: Parenting: Science and Practice.

PubMed

Wang, Z; Deater-Deckard, K; Bell, M A

2013-10-01

Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers' ratings. The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability.