Scaling of chaos in strongly nonlinear lattices
Mulansky, Mario; Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden; Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden
2014-06-15
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.
Detecting nonlinearity and chaos in epidemic data
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 of 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.
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:
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science
NASA Astrophysics Data System (ADS)
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.
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.
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. PMID:26428558
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
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…
Chaos synchronizations of chaotic systems via active nonlinear control
NASA Astrophysics Data System (ADS)
Huang, J.; Xiao, T. J.
2008-02-01
This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective.
Specifying the Links Between Household Chaos and Preschool Children's Development.
Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne
2012-10-01
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
Linear vs nonlinear and infinite vs finite: An interpretation of chaos
Protopopescu, V.
1990-10-01
An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.
Bifurcations and Chaos in Two Coupled Weakly Nonlinear Oscillators.
NASA Astrophysics Data System (ADS)
Poliashenko, Maxim
1992-01-01
Two coupled oscillators are one of the classical models for studies of coupled dynamical systems encountered in a variety of fields including physics, biology and chemistry. This work considers various new phenomena that arise in such coupled systems under the presence of weak nonlinearities. Both autonomous and nonautonomous systems are studied. It is shown for the first time that weak nonlinearity can cause the system, isolated from any external influence, to exhibit dynamical chaos, homoclinic and heteroclinic orbits and three-frequency motion, as well as multistability and competition between different oscillatory regimes. Theoretical description is developed for the competition between one and two-frequency oscillations using a nonlinear pendulum approximation. It is also established that the mechanisms of transitions to chaos in such system include period doubling, intermittency and a Shilnikov-like scenario. One of the crucial factors leading to the complexity of the system behavior and to chaos was nonisochronism of the system. The impact of slow parametric perturbations on the dynamics of this system was analyzed and applied to the problem of stability of a van der Pol oscillator coupled with a stabilizing resonator. The analysis showed that, if parametric perturbations cause multiple crossing of regions of hysteresis, chaotic behavior may arise and the system will be extremely unstable. The studies indicate that chaos can be excited both in isochronous and nonisochronous systems, in contrast with an autonomous system where nonisochronism appeared to be essential for chaotic phenomena. From the results of the analytical and numerical investigations, approximate conditions for chaotic dynamics to occur in two coupled weakly nonlinear oscillators are formulated and illustrated in full bifurcation diagrams for both the autonomous and parametrically driven cases.
Utilizing nonlinearity of transistors for reconfigurable chaos computation
NASA Astrophysics Data System (ADS)
Ditto, William; Kia, Behnam
2014-03-01
A VLSI circuit design for chaos computing is presented that exploits the intrinsic nonlinearity of transistors to implement a novel approach for conventional and chaotic computing circuit design. In conventional digital circuit design and implementation, transistors are simply switched on or off. We argue that by using the full range of nonlinear dynamics of transistors, we can design and build more efficient computational elements and logic blocks. Furthermore, the nonlinearity of these transistor circuits can be used to program the logic block to implement different types of computational elements that can be reconfigured. Because the intrinsic nonlinear dynamics of the transistors are utilized the resulting circuits typically require fewer transistors compared to conventional digital circuits as we exploit the intrinsic nonlinearity of the transistors to realize computations. This work was done with support from ONR grant N00014-12-1-0026 and from an ONR STTR and First Pass Engineering.
Classical chaos and fluctuation-dissipation relations for nonlinear response
NASA Astrophysics Data System (ADS)
Mukamel, Shaul; Khidekel, Vadim; Chernyak, Vladimir
1996-01-01
The classical nonlinear optical response is expressed in a form that closely resembles the fluctuation-dissipation theorem. The nth-order response is shown to depend on interferences among n closely lying trajectories. The relevant dynamical information on the vicinity of a given trajectory can be recast using the stability matrix related to the Lyapunov exponents. No such interference exists in the linear response, and the nonlinear response is consequently a much more sensitive probe for classical chaos. Sequences of multiple femtosecond pulses can be designed to directly probe the stability matrix.
Chaos in the fractional order nonlinear Bloch equation with delay
NASA Astrophysics Data System (ADS)
Baleanu, Dumitru; Magin, Richard L.; Bhalekar, Sachin; Daftardar-Gejji, Varsha
2015-08-01
The Bloch equation describes the dynamics of nuclear magnetization in the presence of static and time-varying magnetic fields. In this paper we extend a nonlinear model of the Bloch equation to include both fractional derivatives and time delays. The Caputo fractional time derivative (α) in the range from 0.85 to 1.00 is introduced on the left side of the Bloch equation in a commensurate manner in increments of 0.01 to provide an adjustable degree of system memory. Time delays for the z component of magnetization are inserted on the right side of the Bloch equation with values of 0, 10 and 100 ms to balance the fractional derivative with delay terms that also express the history of an earlier state. In the absence of delay, τ = 0 , we obtained results consistent with the previously published bifurcation diagram, with two cycles appearing at α = 0.8548 with subsequent period doubling that leads to chaos at α = 0.9436 . A periodic window is observed for the range 0.962 < α < 0.9858 , with chaos arising again as α nears 1.00. The bifurcation diagram for the case with a 10 ms delay is similar: two cycles appear at the value α = 0.8532 , and the transition from two to four cycles at α = 0.9259 . With further increases in the fractional order, period doubling continues until at α = 0.9449 chaos ensues. In the case of a 100 millisecond delay the transitions from one cycle to two cycles and two cycles to four cycles are observed at α = 0.8441 , and α = 0.8635 , respectively. However, the system exhibits chaos at much lower values of α (α = 0.8635). A periodic window is observed in the interval 0.897 < α < 0.9341 , with chaos again appearing for larger values of α . In general, as the value of α decreased the system showed transitions from chaos to transient chaos, and then to stability. Delays naturally appear in many NMR systems, and pulse programming allows the user control over the process. By including both the fractional derivative and time delays in the Bloch equation, we have developed a delay-dependent model that predicts instability in this non-linear fractional order system consistent with the experimental observations of spin turbulence.
Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.
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. PMID:21382261
Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.
TOXLINE Toxicology Bibliographic Information
Zausner T
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.
Nonlinear dynamics, chaos and complex cardiac arrhythmias
NASA Technical Reports Server (NTRS)
Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.
1987-01-01
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Chaos in a 4D dissipative nonlinear fermionic model
NASA Astrophysics Data System (ADS)
Aydogmus, Fatma
2015-12-01
Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.
Nonlinearly-enhanced energy transport in many dimensional quantum chaos.
Brambila, D S; Fratalocchi, A
2013-01-01
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.; Fratalocchi, A.
2013-01-01
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934
Integrability and chaos in nonlinearly coupled optical beams
David, D.
1989-01-01
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity
NASA Astrophysics Data System (ADS)
Sun, Yeong-Jeu
2009-08-01
In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.
Chaos Theory, Nonlinear Dynamical Models, and Psychological Assessment.
ERIC Educational Resources Information Center
Heiby, Elaine M.
1995-01-01
This introduction to a special section provides the basic definitions and presents the measurement approaches and data analytic techniques that are collectively referred to as chaos theory. The conceptualization and assessment of unstable behavioral disorders can be strengthened by incorporating elements of chaos theory. (SLD)
Riede, Tobias; Owren, Michael J; Arcadi, Adam Clark
2004-11-01
The pant hoot calls produced by common chimpanzees (Pan troglodytes) are multi-call vocalizations that have figured prominently in investigations of acoustic communication in this species. Although pant hoots are predominantly harmonically structured, they can exhibit an acoustic complexity that has recently been linked to nonlinearity in the vocal-fold dynamics underlying typical mammalian sound production. We examined the occurrence of these sorts of nonlinear phenomena in pant hoot vocalizations, contrasting quieter and lower-pitched "introduction" components with loud and high-pitched "climax" calls in the same bouts. Spectrographic evidence revealed four kinds of nonlinear phenomena, including discrete frequency jumps, subharmonics, biphonation, and deterministic chaos. While these events were virtually never observed during the introduction, they occurred in more than half of the climax calls. Biphonation was by far the most common phenomenon, followed by subharmonics, chaos, and frequency jumps. Individual callers varied in the degree to which their climax calls exhibited nonlinear phenomena, but were consistent in showing more biphonation than other forms. These outcomes show that nonlinear phenomena are routinely present in chimpanzee pant hoots, and help lay the foundation for investigating the function of such events. PMID:15538766
Specifying the Links Between Household Chaos and Preschool Children’s Development
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
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
1988-01-01
Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been impossible without the aid and moral support provided by Tormod Riste. Gerd Jarrett helped and befriended me and my family in more ways than I should wish to count, and the entire physics staff at IFE, E Andersen, A F Andresen, G Jarrett, K Otnes, T Riste, A Skjeltorp and O. Steinsvoll helped to slake my heavy thirst for Norwegian history and culture, and agreed from the start to speak Norwegian to me daily in order to help me in my effort to learn to speak that language. Gerd Jarrett performed above and beyond the call of duty by tirelessly typing the original lecture notes, which appear as the internal report IFE/I-86/003 + KGF. I also owe thanks to Lynn Smith for typing the revisions that yielded this final version at the University of Houston. I willingly thank J Fröyland, J Palmore and F Ravndal for several helpful discussions and comments, and M Golubitsky, J Palmore, D Schiller and O Steinsvoll for proof-reading several of the chapters (blame for remaining errors is entirely my own, however). I also wish to thank P Alström, E Aurell, T Bohr, P Cvitanovic, E H Hauge, P C Hemmer, J Hertz, J Ketoja, T Kohonen, J Kurkijärvi, K Lindgren, J Myrheim, R Ritala and S Stenholm for interesting discussions during my journeys to other Scandinavian institutions. I am especially grateful to J Fröyland for guestfriendship at the University of Oslo, and to A K M F Hussain for encouraging in 1984 that I should put my lecture notes into print. Finally, my academic free-year was supported financially by the American Scandinavian Foundation, NORDITA and the University of Houston. All my travel costs within Scandinavia were paid by NORDITA
Socioeconomic risk moderates the link between household chaos and maternal executive function.
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. PMID:22563703
ERIC Educational Resources Information Center
Crutchfield, James P.; And Others
1986-01-01
Discusses how the discovery of chaos has created a new paradigm in scientific modeling and how findings are contributing to changes in thought about many different branches of science. Includes explanations and examples of how chaotic behavior can be understood. (ML)
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
ERIC Educational Resources Information Center
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
ERIC Educational Resources Information Center
Bussolari, Cori J.; Goodell, Judith A.
2009-01-01
Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
ERIC Educational Resources Information Center
Bussolari, Cori J.; Goodell, Judith A.
2009-01-01
Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…
NASA Technical Reports Server (NTRS)
Hooker, John C.
1991-01-01
Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
ERIC Educational Resources Information Center
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
Household chaos moderates the link between maternal attribution bias and parenting
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 characteristics (chaos) of high-power microwave (HPM) sources
NASA Astrophysics Data System (ADS)
Gaudet, John A.; Luginsland, John W.; Wallace, Christopher B.
2000-07-01
Recent advances in the understanding of dynamical systems and chaotic behavior have resulted in the investigation of HPM source design issues. Modern dynamical systems theory can improve our understanding of the dynamics of space charge dominated beams and the RF waveforms generated by them. This paper will review the work done to date using time series analysis techniques to study the state space dynamics of high power microwave sources using simulation (particle-in-cell) code results. Low-dimensional chaos has been observed in simulation results from a variety of HPM sources, including the MILO (Magnetically Insulated Line Oscillator). Additionally, the particle behavior within the diode portion of HPM tubes can have chaotic characteristics. Knowing when these features occur and how they develop are important first steps in our ability to control and/or eliminate them. Central to understanding source behavior is the initial use of joint time frequency analysis to assess whether the dynamics are stationary or not. Subsequently we use delay coordinate embedding techniques to reconstruct an effective state space global dynamics. From this, Poincare sections are examined. Lyapunov exponents are then calculated to determine whether the behavior of the source is noise or deterministic chaos.
Berman, G.P.; Bulgakov, E.N.; Campbell, D.K.; Krive, I.V.
1997-10-01
We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of {open_quotes}quantum nonlinear resonance{close_quotes} applies, and thus that this system represents a possible solid-state realization of {open_quotes}quantum nonlinear resonance{close_quotes} and {open_quotes}quantum chaos.{close_quotes} In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged energy exhibits sharp resonant behavior as a function of the applied constant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequency. We compare and contrast the quantum chaos expected in these mesoscopic {open_quotes}solid-state atoms{close_quotes} with that observed in Rydberg atoms in microwave fields, and discuss the prospects for experimental observation of the effects we predict. {copyright} {ital 1997} {ital The American Physical Society}
Nonlinear effects on Turing patterns: Time oscillations and chaos
NASA Astrophysics Data System (ADS)
Aragn, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
2012-08-01
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.
Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering
Gao, Jianbo; Hu, Jing; Tung, Wen-wen
2011-01-01
Background Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. Methodology/Principal Findings To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component. Conclusions The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals. PMID:21915312
Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John
2009-08-01
We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup. PMID:19792231
Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad
2014-11-01
This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. PMID:25440951
Nonlinear resonance and dynamical chaos in a diatomic molecule driven by a resonant ir field
Berman, G.P.; Bulgakov, E.N.; Holm, D.D.
1995-10-01
We consider the transition from regular motion to dynamical chaos in a classical model of a diatomic molecule which is driven by a circularly polarized resonant ir field. Under the conditions of a nearly two-dimensional case, the Hamiltonian reduces to that for the nonintegrable motion of a charged particle in an electromagnetic wave [A. J. Lichtenberg and M. A. Lieberman, {ital Regular} {ital and} {ital Stochastic} {ital Motion} (Springer-Verlag, City, 1983)]. In the general case, the transition to chaos is connected with the overlapping of vibrational-rotational nonlinear resonances and appears even at rather low radiation field intensity, {ital S}{approx_gt}1 GW/cm{sup 2}. We also discuss the possibility of experimentally observing this transition.
Basko, D.M.
2011-07-15
Research Highlights: > In a one-dimensional disordered chain of oscillators all normal modes are localized. > Nonlinearity leads to chaotic dynamics. > Chaos is concentrated on rare chaotic spots. > Chaotic spots drive energy exchange between oscillators. > Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.
Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes
NASA Astrophysics Data System (ADS)
McHarris, Wm C.
2011-07-01
In recent years we have suggested that many of the so-called paradoxes resulting from the Copenhagen interpretation of quantum mechanics could well have more logical parallels based in nonlinear dynamics and chaos theory. Perhaps quantum mechanics might not be strictly linear as has been commonly postulated, and indeed, during the past year experimentalists have discovered signatures of chaos in a definitely quantum system. As an illustration of what can go wrong when quantum effects are forced into a linear interpretation, I examine Bell-type inequalities. In conventional derivations of such inequalities, classical systems are found to impose upper limits on the statistical correlations between, say, the properties of a pair of separated but entangled particles, whereas quantum systems allow greater correlations. Numerous experiments have upheld the quantum predictions (greater statistical correlations than allowed classically), which has led to inferences such as the instantaneous transmission of information between effectively infinitely separated particles Einstein's "spooky action-at-a-distance," incompatible with relativity. I argue that there is nothing wrong with the quantum mechanical side of such derivations (the usual point of attack by those attempting to debunk Bell-type arguments), but implicit in the derivations on the classical side is the assumption of independent, uncorrelated particles. As a result, one is comparing uncorrelated probabilities versus conditional probabilities rather than comparing classical versus quantum mechanics, making moot the experimental inferences. Further, nonlinear classical systems are known to exhibit correlations that can easily be as great as and overlap with quantum correlations so-called nonextensive thermodynamics with its nonadditive entropy has verified this with numerous examples. Perhaps quantum mechanics does contain fundamental nonlinear elements. Nonlinear dynamics and chaos theory could well provide a bridge between the determinism so dear to Einstein and the statisical interpretation of the Copenhagen school. Einstein and Bohr both could have been right in their debates.
Nonlinear instability and chaos in plasma wave-wave interactions
Kueny, C.S.
1993-12-31
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods.
A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
NASA Astrophysics Data System (ADS)
Cherubini, S.; De Palma, P.; Robinet, J.-Ch; Bottaro, A.
2012-06-01
The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Λ and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.
Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems
NASA Astrophysics Data System (ADS)
Luo, Albert C. J.
This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps are discussed first, and the periodic flows predicted by the multistep implicit maps are also presented. Periodic flows in time-delay nonlinear dynamical systems are discussed by the single-step and multistep implicit maps. The time-delay nodes in discretization of time-delay nonlinear systems were treated by both an interpolation and a direct integration. Based on the discrete nodes of periodic flows in nonlinear dynamical systems with/without time-delay, the discrete Fourier series responses of periodic flows are presented. To demonstrate the methodology, the bifurcation tree of period-1 motion to chaos in a Duffing oscillator is presented as a sampled problem. The method presented in this paper can be applied to nonlinear dynamical systems, which cannot be solved directly by analytical methods.
Study of nonlinear dynamics and chaos in MEMS/NEMS resonators
NASA Astrophysics Data System (ADS)
Miandoab, Ehsan Maani; Yousefi-Koma, Aghil; Pishkenari, Hossein Nejat; Tajaddodianfar, Farid
2015-05-01
With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and phase portrait of the unperturbed system, the resonator dynamics is categorized to four physical situations and it is shown that the system undergoes homoclinic and heteroclinic orbits which are responsible for the appearance of chaos in the resonator response. Bifurcation diagram of nano resonator is plotted by variation of applied AC actuation voltage and it is shown that the system possess rich dynamic behavior such as periodic doubling, quasi-periodic, bifurcation and chaotic motion which are classified and studied in more details by plotting time response and phase plane of the each category. The main result of this paper indicates that the necessary condition for the creation of chaos in the resonator is intersection of the system steady state response with the homoclinic orbit. This occurs when the system steady state velocity or amplitude reaches to the homoclinic orbit maximum speed or amplitude. The critical oscillating amplitudes corresponding to these situations are derived based on the system parameters which can be used to propose the new analytical criteria for chaos detection in resonators.
Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1996-01-01
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
Chaos and related nonlinear noise phenomena in Josephson tunnel junctions
Miracky, R.F.
1984-07-01
The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial self-inductance have been thoroughly investigated. The current-voltage characteristics of these devices exhibit stable regions of negative differential resistance. Very large increases in the low-frequency voltage noise with equivalent noise temperatures of 10/sup 6/ K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes. Moderate increases in the noise, with temperatures of about 10/sup 3/ K, arise from chaotic behavior. Analog and digital simulations indicate that under somewhat rarer circumstances the same junction system can sustain a purely deterministic hopping between two unstable subharmonic modes, accompanied by excess low-frequency noise. Unlike the noise-induced case, this chaotic process occurs over a much narrower range in bias current and is destroyed by the addition of thermal noise. The differential equation describing the junction system can be reduced to a one-dimensional mapping in the vicinity of one of the unstable modes. A general analytical calculation of switching processes for a class of mappings yields the frequency dependence of the noise spectrum in terms of the parameters of the mapping. Finally, the concepts of noise-induced hopping near bifurcation thresholds are applied to the problem of the three-photon Josephson parametric amplifier. Analog simulations indicate that the noise rise observed in experimental devices arises from occasional hopping between a mode at the pump frequency ..omega../sub p/ and a mode at the half harmonic ..omega../sub p//2. The hopping is induced by thermal noise associated with the shunt resistance. 71 references.
Coupled nonlinear oscillators: A paradigm for spatiotemporal chaos and nonequilibrium phenomena
NASA Astrophysics Data System (ADS)
Locher, Markus
1997-12-01
The control of high-dimensional chaos and the thermal nucleation of kink-antikink pairs are investigated in a chain of locally coupled, nonlinear, electronic resonators. Experimental evidence for the universality of spatiotemporal stochastic resonance is given. We also show that recently developed feedback control techniques will not succeed in the presence of certain symmetries. First, we demonstrated the stabilization of complex waveforms embedded within convective spatiotemporal chaos. The employed coupling was unidirectional, giving rise to instabilities and patterns as observed in so- called open flow systems. The stability of the nonlinear waves was associated with the presence of kink-antikink pairs. We measured dynamic properties of the kinks such as speed, shape and width. For the case of (symmetric) diffusive coupling we then examined the interplay between a periodic modulation and spatially distributed thermal noise. The phenomenon of array enhanced stochastic resonance was confirmed and its relation to the nucleation of kink-antikink pairs established. The third part of this work applies mainly to low- dimensional dynamical systems. A new method of local stability analysis was developed and verified for a system of two coupled diode resonators. We found that symmetries generic of homogeneous orbits in systems of coupled oscillators, preclude one-parameter control schemes.
Universal theory of dynamical chaos in nonlinear dissipative systems of differential equations
NASA Astrophysics Data System (ADS)
Magnitskii, Nikolai A.
2008-03-01
A new universal theory of dynamical chaos in nonlinear dissipative systems of differential equations including ordinary and partial, autonomous and non-autonomous differential equations and differential equations with delay arguments is presented in this paper. Four corner-stones lie in the foundation of this theory: the Feigenbaum's theory of period doubling bifurcations in one-dimensional mappings, the Sharkovskii's theory of bifurcations of cycles of an arbitrary period up to the cycle of period three in one-dimensional mappings, the Magnitskii's theory of rotor type singular points of two-dimensional non-autonomous systems of differential equations as a bridge between one-dimensional mappings and differential equations and the theory of homoclinic cascade of bifurcations of stable cycles in nonlinear differential equations. All propositions of the theory are strictly proved and illustrated by numerous analytical and computing examples.
Nonlinear elasticity of cross-linked networks
NASA Astrophysics Data System (ADS)
John, Karin; Caillerie, Denis; Peyla, Philippe; Raoult, Annie; Misbah, Chaouqi
2013-04-01
Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects.
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu
2009-01-01
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincar maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu
2009-01-01
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincar maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340
The nonlinear bifurcation and chaos of coupled heave and pitch motions of a truss spar platform
NASA Astrophysics Data System (ADS)
Huang, Lei; Liu, Liqin; Liu, Chunyuan; Tang, Yougang
2015-10-01
This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincaré maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave frequency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional ternately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.
Watts, C.A.
1993-09-01
In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
NASA Astrophysics Data System (ADS)
Zhang, Yongfang; Hei, Di; L, Yanjun; Wang, Quandai; Mller, Norbert
2014-03-01
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson- ?-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
A Self-Check System for Mental Health Care based on Nonlinear and Chaos Analysis
NASA Astrophysics Data System (ADS)
Oyama-Higa, Mayumi; Miao, Tiejun; Cheng, Huaichang; Tang, Yuan Guang
2007-11-01
We applied nonlinear and chaos analysis to fingertip pulse wave data. The largest Lyapunov exponent, a measure of the "divergence" of the trajectory of the attractor in phase space, was found to be a useful index of mental health in humans, particularly for the early detection of dementia and depressive psychosis, and for monitoring mental changes in healthy persons. Most of the methods used for assessing mental health are subjective. A few of existing objective methods, such as those using EEG and ECG, for example, are not simple to use and expansive. Therefore, we developed an easy-to-use economical device, a PC mouse with an integrated sensor for measuring the pulse waves, and its required software, to make the measurements. After about 1 min of measurement, the Lyapunov exponent is calculated and displayed as a graph on the PC. An advantage of this system is that the measurements can be made very easily, and hence mental health can be assessed during operating a PC using the pulse wave mouse. Moreover, the measured data can be saved according to the time and date, so diurnal changes and changes over longer time periods can be monitored as a time series and history. At the time the pulse waves are measured, we ask the subject about his or her physical health and mood, and use their responses, along with the Lyapunov exponents, as factors causing variation in the divergence. The changes in the Lyapunov exponent are displayed on the PC as constellation graphs, which we developed to facilitate simpler self-diagnosis and problem resolution.
Bifurcation Trees of Period-1 Motions to Chaos in a Two-Degree-of-Freedom, Nonlinear Oscillator
NASA Astrophysics Data System (ADS)
Luo, Albert C. J.; Yu, Bo
2015-12-01
In this paper, analytical solutions for period-m motions in a two-degree-of-freedom (2-DOF) nonlinear oscillator are developed through the finite Fourier series. From the finite Fourier series transformation, the dynamical system of coefficients of the finite Fourier series is developed. From such a dynamical system, the solutions of period-m motions are obtained and the corresponding stability and bifurcation analyses of period-m motions are carried out. Analytical bifurcation trees of period-1 motions to chaos are presented. Displacements, velocities and trajectories of periodic motions in the 2-DOF nonlinear oscillator are used to illustrate motion complexity, and harmonic amplitude spectrums give harmonic effects on periodic motions of the 2-DOF nonlinear oscillator.
Makarov, Vladimir A; Petnikova, V M; Potravkin, N N; Shuvalov, Vladimir V
2012-12-31
It is found that chirped elliptically polarised cnoidal waves can propagate and aperiodic regimes, resembling polarisation chaos, can emerge in an isotropic medium with local and nonlocal components of cubic nonlinearity and second-order frequency dispersion. In the particular case of the formation of the waveguides of the same profile for two circularly polarised components of the light field relevant analytical solutions are derived and the frequencies of chirped components are shown to vary in concord with periodic changes of their intensities. In this case, the nature of the changes in the polarisation state during the light wave propagation depends on the values of nonlinear phase shifts of circularly polarised components of the field during the period and is sensitive to changes in the initial conditions. (nonlinear optical phenomena)
Position Control for Non-linear, Multiple-Link Robots
NASA Technical Reports Server (NTRS)
Seraji, H.; Moya, M. M.
1987-01-01
Several approaches to complicated control problem examined. Report surveys methods for controlling motion of robot manipulators. Applies to coupled, highly nonlinear multiple-link robots. Presents adaptive control technique based on discrete linear model of robot arm, obtained by linearizing nonlinear dynamical equations about nominal trajectory. Parameters of model calculated with adaptive parameter-identification algorithm. Based on system model, optimal control input computed using position and velocity feedback.
Milonni, P.W.
1989-01-01
The theoretical and experimental status of chaos in nonlinear optics and laser physics will be reviewed. Attention will then be focused on the possibility of chaotic behavior in individual atoms and molecules driven by intense radiation fields. 46 refs., 7 figs.
NASA Astrophysics Data System (ADS)
Makarov, Vladimir A.; Petnikova, V. M.; Potravkin, N. N.; Shuvalov, Vladimir V.
2012-12-01
It is found that chirped elliptically polarised cnoidal waves can propagate and aperiodic regimes, resembling polarisation chaos, can emerge in an isotropic medium with local and nonlocal components of cubic nonlinearity and second-order frequency dispersion. In the particular case of the formation of the waveguides of the same profile for two circularly polarised components of the light field relevant analytical solutions are derived and the frequencies of chirped components are shown to vary in concord with periodic changes of their intensities. In this case, the nature of the changes in the polarisation state during the light wave propagation depends on the values of nonlinear phase shifts of circularly polarised components of the field during the period and is sensitive to changes in the initial conditions.
Sharma, R.P.; Batra, K.; Verga, A.D.
2005-02-01
Nonlinear evolution of modulational instability by using the nonlinear Schroedinger equation in one dimension reveals a periodic reoccurrence of initial conditions. The nonlinear Schroedinger equation is the adiabatic limit of Zakharov equations, which couples the electrostatic electron plasma wave and ion-acoustic wave propagation. In the present paper nonlinear evolution of modulational instability is investigated by using one-dimensional Zakharov equations numerically. A simplified model is predicted that establishes the fact that the effect of relaxing the condition of adiabaticity is drastic on the nonlinear evolution patterns of modulational instability. These evolutions are quite sensitive to initial conditions, Fermi-Pasta-Ulam recurrence is broken up and a chaotic state develops. Next, quantitative methods like calculation of Lyapunov exponents and their variation with wave number is used to study spatial and temporally chaotic behavior. It is shown that regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wave numbers.
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
NASA Astrophysics Data System (ADS)
Sugihara, George; May, Robert M.
1990-04-01
An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.
NASA Astrophysics Data System (ADS)
Peil, Michael; Jacquot, Maxime; Chembo, Yanne Kouomou; Larger, Laurent; Erneux, Thomas
2009-02-01
The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time ?10ps and by a low cutoff frequency with a response time ?1?s . Moreover, the optoelectronic feedback also consists of a significant delay ?D of the order of 100ns . Depending on two key physical parameters, the loop gain ? and the nonlinearity operating point ? , a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants ? , ? , and ?D . We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of ? . One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations).
Peil, Michael; Jacquot, Maxime; Chembo, Yanne Kouomou; Larger, Laurent; Erneux, Thomas
2009-02-01
The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time tau approximately 10 ps and by a low cutoff frequency with a response time theta approximately 1 micros. Moreover, the optoelectronic feedback also consists of a significant delay tauD of the order of 100 ns. Depending on two key physical parameters, the loop gain beta and the nonlinearity operating point Phi, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants tau, theta, and tauD. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of Phi. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations). PMID:19391821
Spatiotemporal chaos in mixed linear-nonlinear coupled logistic map lattice
NASA Astrophysics Data System (ADS)
Zhang, Ying-Qian; Wang, Xing-Yuan
2014-05-01
We investigate the spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps in coupling connections. Here, the coupling methods between lattices are both linear neighborhood coupling and the nonlinear chaotic map coupling of lattices. While strictly nearest neighborhood coupling is only a special case in the proposed system. We employed the criteria such as Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and space-time diagrams to investigate the chaotic behaviors of the proposed system in this paper. In fact, the proposed system contains new features for applications of cryptography such as the larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic windows in bifurcation diagrams. Furthermore, we also show the parameter ranges of the proposed system which hold those features in cryptography compared with those of the CML system. Finally, we design the encryption scheme based on the proposed system for an explicit illustration.
Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves
NASA Technical Reports Server (NTRS)
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.
Nonlinear instability and chaos in plasma wave--wave interactions. I. Introduction
Kueny, C.S.; Morrison, P.J.
1995-06-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave--wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Nonlinear vibration and radiation from a panel with transition to chaos
NASA Technical Reports Server (NTRS)
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.
Experimental observation of space-time chaos in a nonlinear optical system with 2D feedback
NASA Astrophysics Data System (ADS)
Arecchi, F. T.; Larichev, A. V.; Ramazza, P. L.; Residori, S.; Ricklin, J. C.; Vorontsov, M. A.
1995-02-01
We report the emergence of a space-time disordered dynamical regime from a regular, patterned state in a system formed by a Liquid Crystal Light Valve (LCLV) with nonlocal feedback. This is obtained for increasing the amplitude of the supply voltage applied to the LCLV, thus inducing a strengthening in the nonlinear coupling between light and matter in this device. Evidence of loss of correlation of the signal is given both in the temporal and in the spatial domain. A comparison is drawn with turbulence in hydrodynamics.
NASA Astrophysics Data System (ADS)
Tl, Tams
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.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
A Structure behind Primitive Chaos
NASA Astrophysics Data System (ADS)
Ogasawara, Yoshihito
2015-06-01
Recently, a new concept, primitive chaos, has been proposed as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [
Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)
2002-01-01
The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.
Controlling Beam Halo-Chaos for ADS
NASA Astrophysics Data System (ADS)
Fang, Jin-Qing; Zhao, Geng; Zhou, Liu-Lai; Chen, Guanrong
Accelerator driven clean nuclear power system (ADS) as an innovative technique in the 21st century is among the most challenge of high-tech fields since it makes nuclear power system safer, cleaner, cheaper, and more reliable. ADS is very necessary option for sustainable development of nuclear energy in the 21st century. However, beam halo-chaos occurred in high-current accelerators of ADS has become a key concerned issue for many important applications of intensity ion beam.To understand the complex of beam halo-chaos, this paper analyzes one of the main physical mechanism for halo-chaos formation, i.e. nonlinear resonance overlapping routes to halo-chaos. Then some efficient nonlinear control methods of beam halo-chaos are presented. The simulation results demonstrate that the control methods we proposed are very effective for beam halo-chaos suppression.
"Chaos" Theory: Implications for Educational Research.
ERIC Educational Resources Information Center
Lindsay, Jean S.
"Chaos" theory is a revolutionary new paradigm developed by scientists to study the behavior of natural systems. "Chaos" refers to the tendency of dynamic non-linear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Major tenets of the theory are presented. The precedent for use of models developed in the natural…
NASA Astrophysics Data System (ADS)
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.
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. PMID:26428571
Dynamic non-linear response of cross-linked actin networks: an energy dissipation approach
NASA Astrophysics Data System (ADS)
Majumdar, Sayantan; Gardel, Margaret L.
2014-03-01
Cross-linked bio-polymer networks that primarily maintain the shape and rigidity in eukaryotic cells show striking non-linear mechanical properties. Here, we study the steady-state energy dissipation (Ediss) over a complete sinusoidal shear strain cycle for a macroscopic assembly of reconstituted network of actin filaments cross-linked with Filamin A, over wide range of strain amplitude and frequency values. For small values of the applied strain amplitudes (linear regime) Ediss increases monotonously with the increasing frequency over the entire frequency range studied but in the non-linear regime (larger applied strain amplitudes), a clear saturation in Ediss is observed at higher frequencies. Also, the normalized dissipated energy distribution binned over the fixed strain intervals along the shear cycle show frequency dependence in the nonlinear regime but remains frequency independent in the linear regime. Remarkably, the monotonously increasing behavior of Ediss with frequency is also observed in the non-linear regime when a more rigid cross-linker A-Actinin is used, suggesting the importance of flexibility of cross-linkers in controlling the non-linear mechanical response in this class of materials. MRSEC Kadanoff-Rice Post Doctoral Fellowship.
Nonlinear Optimization-Based Device-Free Localization with Outlier Link Rejection
Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan
2015-01-01
Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406
Nonlinear optimization-based device-free localization with outlier link rejection.
Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan
2015-01-01
Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406
Chen, Zhiyu; Yan, Lianshan; Pan, Wei; Luo, Bin; Zou, Xihua; Guo, Yinghui; Jiang, Hengyun; Zhou, Tao
2013-09-01
A method to improve the spurious-free dynamic range (SFDR) of analog photonic links has been proposed and experimentally demonstrated, which only consists of a phase modulator (PM), a polarizer and an optical filter. Such structure could compensate for the chromatic dispersion and the nonlinearity of the modulator simultaneously. In addition, by adjusting the states of polarization (SOPs) launching into the PM and the polarizer, the proposed scheme could also be reconfigured to mitigate the second harmonic nonlinearity induced by the photodetector. Experimental results show that the suppressions of the second-order and third-order intermodulation distortions (IMD2 & IMD3) are larger than 14-dB and 25.4-dB, respectively. Furthermore, the SFDR can achieve ~110-dB · Hz(4/5) for 40-km fiber transmission, which is 26-dB higher than that of the link without compensation. PMID:24103972
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)
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 development in children.
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.
Apthorp, Deborah; Nagle, Fintan; Palmisano, Stephen
2014-01-01
Visually-induced illusions of self-motion (vection) can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP) over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP) in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods) was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway) significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA) of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open); this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures. PMID:25462216
Kot, M.
1991-01-01
Much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forded double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation of inflowing substrate, suggested that simple microbial systems might provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. Progress in two areas of research, mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, (and also judge the usefulness of various new techniques of nonlinear dynamics to the study of populations) is reported.
On nonlinear Koopman's construction
NASA Astrophysics Data System (ADS)
Majewski, W?adys?aw A.; Marciniak, Marcin
1997-12-01
We show that there exists a possibility for a nonlinear variant of Koopman's construction. This gives a natural way for introducing nonlinear quantum maps. Applications to quantum chaos are indicated.
Physicalism, Chaos and Reductionism
NASA Astrophysics Data System (ADS)
Scott, Alwyn
In addition to ignoring the severe practical problems posed by decoherence phenomena, quantum mind hypotheses are motivated by a misunderstanding of the nature of classical (i. e. nonquantum) dynamics. As presently understood, nonlinear dynamical systems of which the brain is clearly one exhibit the twin phenomena of chaos and emergence. The first of these impedes reductionist formulations as does quantum theory, and the second leads to hierarchical structures in biological organisms and cognitive systems, which are difficult to analyze reductively. Thus a quantum mind theory must rest on empirical evidence rather than philosophical speculation.
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)
Controllable chaos in hybrid electro-optomechanical systems
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.
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
Ma, Fang; Bai, Dong-Sheng; Xu, Hong-Liang
2014-09-01
It is well known that settling transparency-efficiency tradeoff is important to design nonlinear optical (NLO) materials. In this work, we constructed one-dimensional polymeric cyanoacetylene (NCCCH)n by hydrogen-bond-directed-linking to understand this tradeoff from molecular level. Results show that the first hyperpolarizability of (NCCCH)n (n=2-8) gradually increased with the increase of n, and what is more important is that the red-shifts, associated with the increase of n, were very little. It is proposed that these polymeric structures possess double-degenerated charge transitions, which contribute to the hyperpolarizability in an additive fashion, and that the coupled oscillators are gradually improved, which lead to the increase of the first hyperpolarizability. Therefore, we propose the hydrogen-bond-directed-linking idea is helpful to develop the potential high-performance NLO materials. PMID:25145287
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. Blmel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blmel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. Jos; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stckmann, J. Stein and M. Kollman; Index.
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. Blmel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blmel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. Jos; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stckmann, J. Stein and M. Kollman; Index.
Chaos in an imperfectly premixed model combustor.
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration. PMID:25725637
Chaos in an imperfectly premixed model combustor
Kabiraj, Lipika Saurabh, Aditya; Paschereit, Christian O.; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P.
2015-02-15
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Chaos in an imperfectly premixed model combustor
NASA Astrophysics Data System (ADS)
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P.; Paschereit, Christian O.
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Linearization of microwave photonic link based on nonlinearity of distributed feedback laser
NASA Astrophysics Data System (ADS)
Kang, Zi-jian; Gu, Yi-ying; Zhu, Wen-wu; Fan, Feng; Hu, Jing-jing; Zhao, Ming-shan
2016-02-01
A microwave photonic link (MPL) with spurious-free dynamic range (SFDR) improvement utilizing the nonlinearity of a distributed feedback (DFB) laser is proposed and demonstrated. First, the relationship between the bias current and nonlinearity of a semiconductor DFB laser is experimentally studied. On this basis, the proposed linear optimization of MPL is realized by the combination of the external intensity Mach-Zehnder modulator (MZM) modulation MPL and the direct modulation MPL with the nonlinear operation of the DFB laser. In the external modulation MPL, the MZM is biased at the linear point to achieve the radio frequency (RF) signal transmission. In the direct modulation MPL, the third-order intermodulation (IMD3) components are generated for enhancing the SFDR of the external modulation MPL. When the center frequency of the input RF signal is 5 GHz and the two-tone signal interval is 10 kHz, the experimental results show that IMD3 of the system is effectively suppressed by 29.3 dB and the SFDR is increased by 7.7 dB.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03046 Iani Chaos
This image shows a small portion of Iani Chaos. The brighter floor material is being covered by sand, probably eroded from the mesas of the Chaos.
Image information: VIS instrument. Latitude 1.7S, Longitude 341.6E. 17 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos
This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed.
Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Astrophysics Data System (ADS)
Maldonado, Armando; Bixler, David
2012-03-01
Chaos Theory is an interesting and important branch of physics. Many physical systems, such as weather or fluid flow, exhibit chaotic behavior. Experiments in simple mechanical or electrical systems, as well as simple simulations can be used as methods of studying chaos. Using a mechanical method, we connected a speaker and to a frequency modulator to bounce a table tennis ball. We recorded the ball's motion at different frequencies using a video camera. Using Tracker software we observed it's position versus it's velocity in order to analyze its chaotic behavior. For a simple simulation, we used the visual-based programming in LabView to examine chaotic behavior produced by some non-linear differential equations. Results from both the mechanical system and the simulations will be discussed. For future work, we plan to continue to explore some chaotic simulations and perform a sequence of experiments with an electrical system. Exploring these nonlinear chaotic systems can help us to better understand and model many phenomena found in nature.
Proceedings of the 2nd Experimental Chaos Conference
NASA Astrophysics Data System (ADS)
Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep
1995-02-01
The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud
Monitoring chaos of cardiac rhythms
Mayer-Kress, G.
1989-01-01
Chaos theory provides a new paradigm in monitoring complexity changes in heart rate variability. Even in cases where the spectral analysis only shows broad band characteristics estimations of dimensional complexity parameters can show quantitative changes in the degree of chaos present in the interbeat interval dynamics. We introduce the concept of dimensional complexity as dynamical monitoring parameter and discuss its properties in connection with control data and data taken during cardiac arrest. Whereas dimensional complexity provides a quantitative indicator of overall chaotic behavior, recurrence plots allow direct visualization of recurrences in arbitrary high dimensional pattern-space. In combination these two methods from non-linear dynamics exemplify a new approach in the problem of heart rate monitoring and identification of precursors of cardiac arrest. Finally we mention a new method of chaotic control, by which selective and highly effective perturbations of nonlinear dynamical systems could be used for improved pacing patterns. 11 refs., 6 figs.
Quantum Correlations, Chaos and Information
NASA Astrophysics Data System (ADS)
Madhok, Vaibhav
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The measurement record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find an increase in the rate of information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. Finally we discuss how this approach can be used in general as a benchmark for information gain in an experimental implementation based on nonlinear dynamics of atomic spins measured weakly by the Faraday rotation of a laser probe. The last part of this thesis is devoted to the study of the nature of quantum correlations themselves. Quantum correlations are at the heart of the weirdness of quantum mechanics and at the same time serve as a resource for the potential benefits quantum information processing might provide. For example, Einstein described quantum entanglement as "spooky action at a distance". However, even entanglement does not fully capture the complete quantum character of a system. Quantum discord aims to fill this gap and captures essentially all the quantum correlations in a quantum state. There is a considerable interest in the research community about quantum discord, since there is evidence showing this very quantity as responsible for the exponential speed up of a certain class of quantum algorithms over classical ones. Now, an important question arises: Is discord just a mathematical construct or does it have a definable physical role in information processing? This thesis provides a link between quantum discord and an actual physical task involving communication between two parties. We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. We further derive a quantitative relation between the yield of the fully quantum Slepian-Wolf protocol in the presence of noise and the quantum discord of the state involved. This protocol is the most general known in the family of protocols in quantum information theory, a unification of essentially all bipartite, unidirectional and memoryless quantum communication protocols. The significance of quantum discord in noisy versions of teleportation, super-dense coding, entanglement distillation and quantum state merging are discussed. We also demonstrate similar roles for quantum discord in quantum computation and correlation erasure. Our work shows that quantum discord captures and quantifies the advantage of quantum coherence in quantum communication.
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
Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links.
Eliasson, Henrik; Olsson, Samuel L I; Karlsson, Magnus; Andrekson, Peter A
2016-01-25
Hybrid systems combining distributed Raman amplification and phase-sensitive amplifiers (PSAs) are investigated in numerical simulations. We focus on the mitigation of fiber nonlinearities and the impact of the span power map which is also important in systems employing optical phase conjugation or phase-conjugated twin waves. We simulate multi-span PSA links with and without distributed Raman amplification and show that by including distributed Raman amplification, the transmission distance increases more at optimum launch power than in the linear regime. For a 5-channel WDM QPSK PSA-amplified system, we observe a transmission reach increase by a factor of 8.1 by including ideal distributed Raman amplification. PMID:26832472
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
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…
Experimental Chaos - Proceedings of the 3rd Conference
NASA Astrophysics Data System (ADS)
Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep
1996-10-01
The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina
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.
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.
Improvement and empirical research on chaos control by theory of "chaos?+?chaos?=?order".
Fulai, Wang
2012-12-01
This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos?=?order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ? 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos?=?order" also exist in the dynamics generated by non-Mandelbrot maps. PMID:23278080
Kot, M.
1990-07-01
A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.
Dissipative chaos in semiconductor superlattices
Alekseev, K.N.; Berman, G.P.; Campbell, D.K.; Cannon, E.H.; Cargo, M.C.
1996-10-01
We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use a semiclassical, balance-equation approach, which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free-electron lasers, chaos may be observable in SSL{close_quote}s. We clarify the nature of this interesting nonlinear dynamics in the superlattice{endash}external-field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field, and to Josephson junctions. {copyright} {ital 1996 The American Physical Society.}
ERIC Educational Resources Information Center
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Experimental Evidence of Chaos from Memristors
NASA Astrophysics Data System (ADS)
Gambuzza, Lucia Valentina; Fortuna, Luigi; Frasca, Mattia; Gale, Ella
Until now, most memristor-based chaotic circuits proposed in the literature are based on mathematical models which assume ideal characteristics such as piecewise-linear or cubic nonlinearities. The idea, illustrated here and originating from the experimental approach for device characterization, is to realize a chaotic system exploiting the nonlinearity of only one memristor with a very simple experimental set-up using feedback. In this way, a simple circuit is obtained and chaos is experimentally observed and is confirmed by the calculation of the largest Lyapunov exponent. Numerical results using the Strukov model support the existence of robust chaos in our circuit. To our knowledge, this is the first experimental demonstration of chaos in a real memristor circuit and suggests that memristors are well placed for hardware encryption.
Magnetic field induced dynamical chaos
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-15
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the xy 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.
Magnetic field induced dynamical chaos
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-15
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x–y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.
ERIC Educational Resources Information Center
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with some degree…
ERIC Educational Resources Information Center
Bedford, Crayton W.
1998-01-01
Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)
ERIC Educational Resources Information Center
Huwe, Terence K.
2009-01-01
"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with some degree
NASA Technical Reports Server (NTRS)
2002-01-01
[figure removed for brevity, see original site]
Collapsed terrain in Hydapsis Chaos.
This is the source terrain for several outflow channels. 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.
VIS Instrument. Latitude 3.2, Longitude 333.2 East. 19 meter/pixel resolution.
Coherence and chaos in extended dynamical systems
Bishop, A.R.
1994-12-31
Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ``complexity.`` We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image was collected during Southern Fall and shows part of the Aureum Chaos.
Image information: VIS instrument. Latitude -3.6, Longitude 332.9 East (27.1 West). 35 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Technical Reports Server (NTRS)
2004-01-01
[figure removed for brevity, see original site]
Released 7 May 2004 This daytime visible color image was collected on May 30, 2002 during the Southern Fall season in Atlantis Chaos.
The THEMIS VIS camera is capable of capturing color images of the martian surface using its five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from the use of multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
Image information: VIS instrument. Latitude -34.5, Longitude 183.6 East (176.4 West). 38 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
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 in the Belousov-Zhabotinsky reaction
NASA Astrophysics Data System (ADS)
Field, Richard J.
2015-12-01
The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle.
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
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
Fully integrated CMOS VCSEL driver with nonlinearity suppression for RF optical fiber links
NASA Astrophysics Data System (ADS)
Lin, Fu-Chuan; Lalithambika, Vinod A.; Holburn, David M.; Mears, Robert J.; Hum, Chak H.; Walker, Stuart D.
2004-06-01
A CMOS optical fibre transmitter front-end with an analogue predistortion technique is proposed for reducing laser nonlinearity distortion to achieve broadband linearisation of radio frequency (RF) optical fibre communication systems. The technique uses a nonlinearity having the inverse transfer characteristic of the directly modulated vertical cavity surface emitting laser (VCSEL). The analogue predistortion lineariser comprises a linear and a non-linear transconductance differential amplifier. The combined linear and non-linear transconductance differential amplifiers provide the transfer characteristic to counteract the characteristic of the VCSEL laser diode. The post-layout simulation of the linearity of RF optical fibre systems using the predistortion linearisation technique shows 12dBm improvement. The integrated CMOS optical fibre transmitter circuit with the predistortion lineariser is being implemented using the austriamicrosystems (AMS) 0.35?m CMOS technology.
High-dimensional chaos from self-sustained collisions of solitons
Yildirim, O. Ozgur E-mail: oozgury@gmail.com; Ham, Donhee E-mail: oozgury@gmail.com
2014-06-16
We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.
[Medicine at the "edge of chaos". Life, entropy and complexity].
De Vito, Eduardo L
2016-01-01
The aim of this paper is to help physicians and health professionals, who constantly seek to improve their knowledge for the benefit of the ill, to incorporate new conceptual and methodological tools to understand the complexity inherent to the field of medicine. This article contains notions that are unfamiliar to these professionals and are intended to foster reflection and learning. It poses the need to define life from a thermodynamic point of view, linking it closely to complex systems, nonlinear dynamics and chaotic behavior, as well as to redefine conventional physiological control mechanisms based on the concept of homeostasis, and to travel the path that starts with the search for extraterrestrial life up to exposing medicine "near the edge of chaos". Complexity transcends the biological aspects; it includes a subjective and symbolic/social dimension. Viewing disease as a heterogeneous and multi-causal phenomenon can give rise to new approaches for the sick. PMID:26826995
Detecting chaos in heavy-noise environments.
Tung, Wen-wen; Gao, Jianbo; Hu, Jing; Yang, Lei
2011-04-01
Detecting chaos and estimating the limit of prediction time in heavy-noise environments is an important and challenging task in many areas of science and engineering. An important first step toward this goal is to reduce noise in the signals. Two major types of methods for reducing noise in chaotic signals are chaos-based approaches and wavelet shrinkage. When noise is strong, chaos-based approaches are not very effective, due to failure to accurately approximate the local chaotic dynamics. Here, we propose a nonlinear adaptive algorithm to recover continuous-time chaotic signals in heavy-noise environments. We show that it is more effective than both chaos-based approaches and wavelet shrinkage. Furthermore, we apply our algorithm to study two important issues in geophysics. One is whether chaos exists in river flow dynamics. The other is the limit of prediction time for the Madden-Julian oscillation (MJO), which is one of the most dominant modes of low-frequency variability in the tropical troposphere and affects a wide range of weather and climate systems. Using the adaptive filter, we show that river flow dynamics can indeed be chaotic. We also show that the MJO is weakly chaotic with the prediction time around 50 days, which is considerably longer than the prediction times determined by other approaches. PMID:21599273
Decoherence, determinism and chaos
Noyes, H.P.
1994-01-01
The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is `deterministic`. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of `test-particle` is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as `particles` or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a `scale invariance bounded from below` by measurement accuracy, then Tanimura`s generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of `particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated.
Invoking the muse: Dada's chaos.
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. PMID:24894264
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.
THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT
Lithwick, Yoram; Wu Yanqin
2011-09-20
We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within {approx}25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software
Missing link: A nonlinear post-Friedmann framework for small and large scales
NASA Astrophysics Data System (ADS)
Milillo, Irene; Bertacca, Daniele; Bruni, Marco; Maselli, Andrea
2015-07-01
We present a nonlinear post-Friedmann framework for structure formation, generalizing to cosmology the weak-field (post-Minkowskian) approximation, unifying the treatment of small and large scales. We consider a universe filled with a pressureless fluid and a cosmological constant ? , the theory of gravity is Einstein's general relativity and the background is the standard flat ? CDM cosmological model. We expand the metric and the energy-momentum tensor in powers of 1 /c , keeping the matter density and peculiar velocity as exact fundamental variables. We assume the Poisson gauge, including scalar and tensor modes up to 1 /c4 order and vector modes up to 1 /c5 terms. Through a redefinition of the scalar potentials as a resummation of the metric contributions at different orders, we obtain a complete set of nonlinear equations, providing a unified framework to study structure formation from small to superhorizon scales, from the nonlinear Newtonian to the linear relativistic regime. We explicitly show the validity of our scheme in the two limits: at leading order we recover the fully nonlinear equations of Newtonian cosmology; when linearized, our equations become those for scalar and vector modes of first-order relativistic perturbation theory in the Poisson gauge. Tensor modes are nondynamical at the 1 /c4 order we consider (gravitational waves only appear at higher order): they are purely nonlinear and describe a distortion of the spatial slices determined at this order by a constraint, quadratic in the scalar and vector variables. The main results of our analysis are as follows: (a) at leading order a purely Newtonian nonlinear energy current sources a frame-dragging gravitomagnetic vector potential, and (b) in the leading-order Newtonian regime and in the linear relativistic regime, the two scalar metric potentials are the same, while the nonlinearity of general relativity makes them different. Possible applications of our formalism include the calculations of the vector potential and the difference between the two scalar potentials from Newtonian N-body simulations, and the extension of Newtonian approximations used in structure formation studies, to include relativistic effects.
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
Understanding chaos via nuclei
Cejnar, Pavel; Stránský, Pavel
2014-01-08
We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.
ERIC Educational Resources Information Center
Murphy, David
2011-01-01
About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…
ERIC Educational Resources Information Center
Moseley, Bryan; Dustin, Daniel
2008-01-01
In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…
Abraham, N.B.; Arecchi, F.T.; Lugiato, L.A.
1988-01-01
The following topics are considered: laser and maser instabilities, classical and quantum noise, transverse effects, dynamics in optical bistability and nonlinear optical media, and methods of analysis in nonlinear dynamics. Particular papers are presented on multistability and chaos in a two-photon microscopic maser, quantum chaos in quantum optics, spatial chaos in bistable optical arrays, four-wave mixing and dynamics, and bifurcation problems in nonlinear optics.
Chaotic operation and chaos control of travelling wave ultrasonic motor.
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. PMID:23490014
Solitons in the midst of chaos
Seghete, Vlad; Menyuk, Curtis R.; Marks, Brian S.
2007-10-15
A system of coupled nonlinear Schroedinger equations describes pulse propagation in weakly birefringent optical fibers. Soliton solutions of this system are found numerically through the shooting method. We employ Poincare surface of section plots - a standard dynamical systems approach - to analyze the phase space behavior of these solutions and neighboring trajectories. Chaotic behavior around the solitons is apparent and suggests dynamical instability. A Lyapunov stability analysis confirms this result. Thus, solitons exist in the midst of chaos.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Harnessing quantum transport by transient chaos.
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. PMID:23556962
Harnessing quantum transport by transient chaos
NASA Astrophysics Data System (ADS)
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.
Chaos Induction in a Laser Diode
NASA Astrophysics Data System (ADS)
Reyes, Mauricio; Solarte, Efran
2008-04-01
Chaos is a class of complex behavior that can emerge from nonlinear dynamical systems, and it exists in both the natural and the technological world. Many biological systems such as the human heart and invertebrate neurons naturally exhibit chaotic behavior. Furthermore, digital computing has made feasible the creation of fractal patterns based on chaos. The beauty of chaos, however, lies not in the aesthetic of fractals, but in the simplicity of the system from which such complex, unpredictable behavior can emerge. The chaotic behavior of a non-linear R-L-Diode circuit has been studied. The non-linear behavior of the diode was modeled to compare the measured curves with the predicted ones. Period unfolding was observed by feeding the R-L-Diode circuit with a sinusoidal signal, varying the frequency and holding constant the amplitude of the input signal. The output voltage was measured on the resistor and bifurcation phenomenon was observed for 2, 4 and 8 periods and for a wide range of frequencies, before reaching the chaotic behavior. The voltage drop on the resistor was used as a source, and coupled to a diode laser excitation circuit. This signal has been coupled to the laser circuit using operational amplifiers to secure the extinction of noises, to provide the adequate signal level and to couple the circuit impedances. The laser response was studied as a function of output signal of the R-L-Diode circuit, especially where it becomes chaotic.
NASA Astrophysics Data System (ADS)
Tauxe, L.
2002-12-01
When I finished graduate school I suppose I imagined myself as my dad. He worked hard, loved his job and family, made a good living. But I also saw myself as my mom - making a home, raising kids, cooking dinner, saving the world. I thought: I can handle being my mom and my dad. I can handle being a scientist and a mother. I can DO this. What I never imagined was the chaotic dynamic of the two career couple. The motions of bodies moving in response to the force of gravity cannot be predicted exactly if there are too many bodies. They dance in a jerky jumble, now faster, then slowly, bouncing, jostling, bumping and flying apart. Just so are the career trajectories of the two career couple. One rises up, the other, slower, pulls it down; overtaking, blocking preventing, now supporting, pulling along, now holding back - not moving, leap frogging, racing in opposite directions and snapping back together with a crack. The problem is non-linear. The outcome depends on feedback, whether positive or negative. The outcome cannot be predicted. Cannot be determined. Perhaps it cannot be done. Perhaps both husband and wife cannot be both mother and father. Too many mothers, too many fathers. Chaos. But I believe it can be done. Not like our mothers and fathers but a different way. And maybe our jerky paths will keep us sharp, make us work harder, and lead us through lives that at least cannot be described as dull.
Chaos and order in models of black hole pairs
NASA Astrophysics Data System (ADS)
Levin, Janna
2006-12-01
Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.
Quantum chaos in Aharonov-Bohm oscillations
Berman, G.P.; Campbell, D.K.; Bulgakov, E.N.; Krive, I.V.
1995-10-01
Aharonov-Bohm oscillations in a mesoscopic ballistic ring are considered under the influence of a resonant magnetic field with one and two frequencies. The authors investigate the oscillations of the time-averaged electron energy at zero temperature in the regime of an isolated quantum nonlinear resonance and at the transition to quantum chaos, when two quantum nonlinear resonances overlap. It is shown that the time-averaged energy exhibits resonant behavior as a function of the magnetic flux, and has a ``staircase`` dependence on the amplitude of the external field. The delocalization of the quasi-energy eigenfunctions is analyzed.
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)
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.
Estimation of missing streamflow data using principles of chaos theory
NASA Astrophysics Data System (ADS)
Elshorbagy, Amin; Simonovic, S. P.; Panu, U. S.
2002-01-01
In this paper, missing consecutive streamflows are estimated, using the principles of chaos theory, in two steps. First, the existence of chaotic behavior in the daily flows of the river is investigated. The time delay embedding method of reconstructing the phase space of a time series is utilized to identify the characteristics of the nonlinear deterministic dynamics. Second, the analysis of chaos is used to configure two models employed to estimate the missing data, artificial neural networks (ANNs) and K-nearest neighbor ( K-nn). The results indicate the utility of using the analysis of chaos for configuring the models. ANN model is configured using the identified correlation dimension (measure of chaos), and ( K-nn) technique is applied within a subspace of the reconstructed attractor. ANNs show some superiority over K-nn in estimating the missing data of the English River, which is used as a case study.
NASA Astrophysics Data System (ADS)
Gaponov-Grekhov, Andrei V.; Rabinovich, Mikhail I.; Engelbrecht, Jri
Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet Scientists working in this field. Since 1989 the proceedings appear in English. They present a good cross section of nonlinear physics in the USSR. This third volume emerged from material presented at the 1989 School. It contains sections dealing with nonlinear problems in physics and astrophysics, quantum and solid state physics, dynamical chaos and self-organization.
NASA Astrophysics Data System (ADS)
Price-Whelan, Adrian M.; Johnston, Kathryn V.; Valluri, Monica; Pearson, Sarah; Kupper, Andreas Hans Wilhelm; Hogg, David W.
2016-01-01
Cosmological simulations predict that dark matter halos around galaxies should be triaxial in shape with universal density profiles. A significant number of orbits in such systems are chaotic, though it is commonly assumed that chaos is not dynamically relevant for galaxy halos because the timescales over which chaos is computed to be important are generally long relative to the dynamical time. In recent work, we showed that even when chaos is not important for restructuring the global structure of a galaxy, chaos can greatly enhance the density evolution and alter the morphologies of stellar streams over just a few orbital times by causing streams to 'fan out.' This occurs because the orbits of the stars in stellar streams have small distributions of fundamental frequencies and are therefore sensitive to mild chaos that modulates the frequencies on small-scales over much faster timescales. This suggests that the morphology of tidal streams alone can be used to estimate the significance of chaos along the orbits of the progenitor systems, thereby placing constraints on the global properties of the gravitational potential. I will explain our theoretical understanding of this phenomenon and discuss implications for a recently discovered stellar stream (the Ophiuchus stream) that may be on a chaotic orbit in the inner Milky Way due to the influence of the time-dependent, triaxial potential of the Galactic bar.
Low dimensional chaos in cardiac tissue
NASA Astrophysics Data System (ADS)
Chialvo, Dante R.; Gilmour, Robert F., Jr.; Jalife, Jose
1990-02-01
CHAOS is a term uvd to characterize aperiodic activity arising in a dynamical system, or in a set of equations describing the system's temporal evolution as a result of a deterministic mechanism that has sensitive dependence on initial conditions1. Chaos, in that sense, has been proposed to make an important contribution to normal and abnormal cardiac rhythms2-6. To date, however, descriptions of chaos in heart tissue have been limited primarily to periodically forced cardiac pacemakers2,6. Because many cardiac rhythm disturbances, particularly those initiated or perpetuated by re-entrant excitation, originate from within non-pacemaker cardiac tissues7-9, demonstrations of chaos in non-pacemaker tissue might provide a deterministic explanation for a wide variety of complex dysrhythmias. Here we report experimental evidence for chaotic patterns of activation and action potential characteristics in externally driven, non-spontaneously active Purkinje fibres and ventricular muscle. The results indicate that there is an apparent link between the mechanism of low dimensional chaos and the occurrence of reflected responses which could lead to more spatially disorganized phenomena. A detailed mechanism for the low dimensional chaos observed experimentally is pursued using a difference equation model. Critical features of the model include a non-monotonic relationship between recovery time during rhythmic stimulation and the state of membrane properties, and a steeply sloped recovery of membrane properties over certain ranges of recovery times. Besides explaining our results, the analytical model may pertain to irregular dynamics in other excitable systems, particularly the intact dysrhythmic heart.
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. PMID:25705790
Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling.
Peil, Michael; Larger, Laurent; Fischer, Ingo
2007-10-01
In a joint experimental and modeling approach we demonstrate chaos synchronization imposed by a delayed shared feedback coupling between two nonlinear electro-optic oscillators. Robust identical synchronization is obtained for both symmetric and strongly asymmetric timing of the mutual coupling, offering great potential for applications such as chaos-based communications. We further demonstrate antisynchronization as well as generalized synchronization with vanishing linear correlation, by detuning the nonlinearity in one of the oscillators. PMID:17995049
Parrondos paradox for chaos control and anticontrol of fractional-order systems
NASA Astrophysics Data System (ADS)
Marius-F, Danca; Wallace, K. S. Tang
2016-01-01
We present the generalized forms of Parrondos paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N ? 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words winning and loosing in the classical Parrondos paradox with order and chaos", respectively, the PS algorithm leads to the generalized Parrondos paradox: chaos1 + chaos2 + + chaosN = order and order1 + order2 + + orderN = chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system.
NASA Astrophysics Data System (ADS)
Chai, Dongyul; Juhasz, Tibor; Brown, Donald J.; Jester, James V.
2013-03-01
In this study we test the hypothesis that nonlinear optical (NLO) multiphoton photoactivation of riboflavin using a focused femtosecond (FS) laser light can be used to induce cross-linking (CXL) and mechanically stiffen collagen as a potential clinical therapy for the treatment of keratoconus and corneal ectasia. Riboflavin-soaked, compressed collagen hydrogels are cross-linked using a FS laser tuned to 760 nm and set to either 100 mW (NLO CXL I) or 150 mW (NLO CXL II) of laser power. FS pulses are focused into the hydrogel using a 0.75 NA objective lens, and the hydrogel is three-dimensionally scanned. Measurement of hydrogel stiffness by indentation testing show that the calculated elastic modulus (E) values are significantly increased over twofold following NLO CXL I and II compared with baseline values (P<0.05). Additionally, no significant differences are detected between NLO CXL and single photon, UVA CXL (P>0.05). This data suggests that NLO CXL has a comparable effect to conventional UVA CXL in mechanically stiffening collagen and may provide a safe and effective approach to localize CXL at different regions and depths within the cornea.
Chaos in the Classroom: An Application of Chaos Theory.
ERIC Educational Resources Information Center
Trygestad, JoAnn
A review of studies on chaos theory suggests that some elements of the theory (systems, fractals, initial effects, and bifurcations) may be applied to classroom learning. Chaos theory considers learning holistic, constructive, and dynamic. Some researchers suggest that applying chaos theory to the classroom enhances learning by reinforcing
ERIC Educational Resources Information Center
Glasser, L.
1989-01-01
The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)
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.
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.
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
Ecosystem Simulations and Chaos on the Graphing Calculator
ERIC Educational Resources Information Center
Sinn, Robb
2007-01-01
An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful
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…
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.
Transient Spatiotemporal Chaos in a Synaptically Coupled Neural Network
NASA Astrophysics Data System (ADS)
Lafranceschina, Jacopo; Wackerbauer, Renate
2014-03-01
Spatiotemporal chaos is transient in a diffusively coupled Morris-Lecar neural network. This study shows that the addition of synaptic coupling in the ring network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strength and almost all numbers of synapses. For large coupling strength, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyaponov exponent and degree of phase coherence as the number of synaptic links increases. The presence of transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provides a possibility for switching between metastable states observed in information processing and brain function. This research is supported by the University of Alaska Fairbanks.
NASA Astrophysics Data System (ADS)
Schertzer, D. J.; Schertzer, D. J.; Lovejoy, S.
2001-12-01
Chaos revolution has been a popular theme. Indeed, low dimensional deterministic chaos had been very helpful in order to better understand the limitations of classical methods in analyzing and modeling complex systems in Geophysics. This was achieved with the help of apparently simple caricatures of complex systems) leading nevertheless to nontrivial behaviors. The prototype example is the celebrated Lorenz model (Lorenz, 1963), which was introduced as a mathematical caricature of atmospheric convection and has the lowest possible dimensionality, i.e. three, for chaotic differential systems. However, in the name of a very interesting extension of the classical Whitney's embedding theorem (for integer dimensional manifolds), there had been an awkward tendency to attempt to reduce complex systems to their low dimensional caricatures. We show that it corresponds to a fundamental misinterpretation of this theorem. However, this tendency was reinforced by the apparent success of a rather straightforward algorithm to estimate the dimensionality for various complex systems by its correlation dimension (Grassberger and Proccaccia, 1983). Indeed, this algorithm yielded rather low dimensionality estimates for various geophysical systems. However, these estimates turn out to be spurious for two rather well known reasons: sample size limitation, stochasticity. In the latter case, we discuss the non-classical case of (stochastic) multiplicative chaos. We review some geophysical examples that point out the irrelevance of low dimensional chaos to Geophysics. We point out that it is rather clear that the chaos of these spatially extended systems, requires approaches dealing with very large number of degrees of freedom and that some asymptotic behavior s rather corresponds to infinite numbers. We point out that progress in that direction should result from an original blending of stochastics and dynamics, as well as a confrontation between the ergodic theory of chaos and the singularities of multifractal fields.
Application of Chaos Theory to Psychological Models
NASA Astrophysics Data System (ADS)
Blackerby, Rae Fortunato
This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in still other cases, they oscillate periodically among two or more precise values. At certain values, the equations iterate random results, with no convergence, divergence or periodicity: "chaos." At still other values, the equations behave chaotically for many iterations; then a periodic oscillation emerges from the chaos. These emergent patterns provide a significantly better model fit to the dynamic reality of psychological behavior because qualitatively reorganized behavior is logically possible and incorporated in the model's metaphysical assumptions.
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.
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,
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)
ERIC Educational Resources Information Center
Paul, Danette
2000-01-01
Examines the role of citations both as reward and as rhetoric. Examines the reward system by tracing over time the citation patterns of 13 research articles by two groups of scientists in chaos theory. Reveals that scientists consistently used five rhetorical practices. Describes these five practices. (SG)
Intramolecular and nonlinear dynamics
Davis, M.J.
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
NASA Astrophysics Data System (ADS)
Greenberg, Richard; Hoppa, Gregory V.; Tufts, B. R.; Geissler, Paul; Riley, Jeannemarie; Kadel, Steven
1999-10-01
The characteristics of chaos regions on Europa suggest they may be sites of melt-through from below. They are wide ranging in size, location, and age. The largest are hundreds of kilometers across. Most are similar to Conamara with a matrix reminiscent of frozen slush and often rafts of preexisting crust. Edges are of two types: ramps, perhaps the tapering of crustal thickness to zero, or cliffs, where rafts appear to have broken clear from the shore. The small features called lenticulae generally appear to be small chaoses with textured matrix and occasional rafts, and many domes may be small chaoses raised by isostatic compensation following refreezing of the crust. The extent of chaoses often appears to be limited by ridge systems with the coastline parallel and set back by a distance comparable to the width of the ridge system. Preexisting ridges often survive as causeways or chains of rafts. Boundaries of chaoses are apparently not controlled by preexisting cracks, consistent with formation by a thermal, rather than mechanical, process. Ridges may thicken the crust such that melt-through is more likely (but not always) between ridge systems. Subsequent cracks and ridges form across preexisting chaoses, ranging from fresh cases with few cracks or ridges across them (with paths somewhat jagged as they meander among rafts) to heavily dissected examples. Isolated tilted raft-like blocks surrounded by densely ridged terrain may be relics of former chaotic terrain. Thus two fundamental resurfacing processes have alternated over Europa's geological history: melt-through (at various places and times) forming chaos terrain, and tectonic cracking and dilation building densely ridged and banded terrain. Mapping of chaos features based on morphology at 200 m shows that they correlate, albeit imperfectly, with dark regions in global (2-km resolution) mosaics (except dark regions due to ridge margins or craters). Extrapolating from our mapping of the 5% of Europa covered by appropriate images, at least 18% of the surface of Europa is fresh appearing chaos, an additional 4% is slightly modified chaos, and much more older chaotic terrain has been overprinted by tectonic structures. Considerable area has been available globally to accommodate the expansion of crust that occurs along extensional ridges and bands. Chaos ubiquity suggests that europan geology has been dominated by the effects of having liquid water under a very thin ice shell, with chaos regions being widespread indicators of occasional zero shell thickness.
Chaos and The Changing Nature of Science and Medicine. Proceedings
Herbert, D.E.; Croft, P.; Silver, D.S.; Williams, S.G.; Woodall, M.
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)
Quasiperiodic graphs at the onset of chaos.
Luque, B; Cordero-Gracia, M; Gmez, M; Robledo, A
2013-12-01
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers. PMID:24483542
Chaos in a Fractional Order Chua System
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory
1996-01-01
This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.
Quasiperiodic graphs at the onset of chaos
NASA Astrophysics Data System (ADS)
Luque, B.; Cordero-Gracia, M.; Gómez, M.; Robledo, A.
2013-12-01
We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.
Chaos in neurons and its application: Perspective of chaos engineering
NASA Astrophysics Data System (ADS)
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.
Chaos in neurons and its application: perspective of chaos engineering.
Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki
2012-12-01
We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain. PMID:23278097
Noise tolerant spatiotemporal chaos computing
Kia, Behnam; Kia, Sarvenaz; Ditto, William L.; Lindner, John F.; Sinha, Sudeshna
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.
NASA Astrophysics Data System (ADS)
Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni
2016-02-01
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 up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.
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.
Warshawsky, Nora E; Joseph, M Lindell; Fowler, Debra L; Edmonson, Cole; Nelson-Brantley, Heather V; Kowalski, Karren
2015-03-01
The 2014 International Nursing Administration Research Conference, "Pioneering Through Chaos: Leadership for a Changing World," was held at the Texas Woman's University in Dallas, Texas, in the fall of 2014. The program drew more than 100 attendees from 4 countries. The conference informed attendees from both academe and practice about the role of nursing administration in navigating the dynamic healthcare climate. This article will report on the insights from the conference presenters. PMID:25689497
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.
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.
Frequency comb formation and transition to chaos in microresonators with near-zero dispersion.
Rogov, Andrei S; Narimanov, Evgenii E
2014-08-01
We investigate the frequency comb formation in microresonators with near-zero dispersion, study the route from integrability to chaos in the corresponding nonlinear system, and demonstrate the key role of nonlinear dynamics of such a system for frequency comb generation and stability. PMID:25078163
Chaos and unpredictability in evolution.
Doebeli, Michael; Ispolatov, Iaroslav
2014-05-01
The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are selective interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. PMID:24433364
Local bifurcations in delayed chaos anticontrol systems
NASA Astrophysics Data System (ADS)
Lu, Hongtao; Yu, Xinzhen
2005-09-01
In this paper, we analyze the local bifurcation phenomena in a simple system described by equation , which is an one-dimensional linear system with nonlinear delayed feedback. Such systems have been proven to exhibit chaotic behavior, and thus can be viewed as the so-called chaos anticontrol systems. In this paper, the nonlinearity is chosen as the trigonometric function sin([middle dot]), different from the existing ones. By local analysis we prove that with increasing parameters, the number of equilibria increases and Hopf bifurcation occurs near some equilibria. This complex bifurcation phenomenon can help to understand the complex behavior of such models. To illustrate the theoretical results, bifurcation diagrams are numerically calculated and Hopf bifurcation and chaotic behavior are identified.
Self-generation and management of spin-electromagnetic wave solitons and chaos
Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A.
2014-06-09
Self-generation of microwave spin-electromagnetic wave envelope solitons and chaos has been observed and studied. For the investigation, we used a feedback active ring oscillator based on artificial multiferroic, which served as a nonlinear waveguide. We show that by increasing the wave amplification in the feedback ring circuit, a transition from monochromatic auto-generation to soliton train waveform and then to dynamical chaos occurs in accordance with the Ruelle-Takens scenario. Management of spin-electromagnetic-wave solitons and chaos parameters by both dielectric permittivity and magnetic permeability of the multiferroic waveguiding structure is demonstrated.
Evolution of periodic states and chaos in two types of neuronal models
NASA Astrophysics Data System (ADS)
Chay, Teresa R.; Fan, Yinshui
1993-11-01
Studies on how chaos theory may be applied to neural disorders is a very challenging theoretical problem. But, to determine the applications of chaos theory cellular functions, it is best to study the genesis of chaos and its characteristics using a minimal model of cellular excitability. In this paper we present two neuronal models which gives rise to interesting types of bursting and chaos. The first model is based on the model of Chay, in which the bursting of neuronal cells is caused by voltage- and time-dependent inactivation of calcium channels. The second model is based on Chay's work in which the bursting is caused by the conformational transformation of the calcium channels that is induced by binding of Ca2+ ion to the receptor site. With these two models, we elucidate how the periodic states and chaos can be evolved when the properties of two types of inward current change. Our bifurcation diagram reveals new types of bifurcations and chaos which were not seen in the other non-linear dynamic models. The predicted chaos from the models closely resembles that observed experimentally in neuronal cells. An implication of our finding is that chaos theory may be used to understand and improve the treatment of certain irregular activities in the brain.
Regularization of chaos by noise in electrically driven nanowire systems
NASA Astrophysics Data System (ADS)
Hessari, Peyman; Do, Younghae; Lai, Ying-Cheng; Chae, Junseok; Park, Cheol Woo; Lee, GyuWon
2014-04-01
The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.
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 and its critical properties depend on the shape of the single-neuron nonlinear input-output transfer function, near firing threshold. In particular, for nonlinear transfer functions with a sharp rise near threshold, the transition to chaos disappears in the limit of a large network; instead, the system exhibits chaotic fluctuations even for small synaptic gain. Finally, we investigate transition to chaos in network models with spiking dynamics. We show that when synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a transition from fast spiking fluctuations with constant rates to a state where the firing rates exhibit chaotic fluctuations, similar to the transition predicted by rate-based dynamics. Systems with finite synaptic time constants and firing rates exhibit a smooth transition from a regime dominated by stationary firing rates to a regime of slow rate fluctuations. This smooth crossover obeys scaling properties, similar to crossover phenomena in statistical mechanics. The theoretical results are supported by computer simulations of several neuronal architectures and dynamics. Consequences for cortical circuit dynamics are discussed. These results advance our understanding of the properties of intrinsic dynamics in realistic neuronal networks and their functional consequences.
Counseling Chaos: Techniques for Practitioners
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim E. H.
2006-01-01
The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three
Chaos Theory and Post Modernism
ERIC Educational Resources Information Center
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a
Counseling Chaos: Techniques for Practitioners
ERIC Educational Resources Information Center
Pryor, Robert G. L.; Bright, Jim E. H.
2006-01-01
The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…
Chaos Theory and Post Modernism
ERIC Educational Resources Information Center
Snell, Joel
2009-01-01
Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…
Chaos Theory, Philosophically Old, Scientifically New.
ERIC Educational Resources Information Center
Butz, Michael R.
1995-01-01
Chaos theory has recently become a central area of scientific interest in psychology. This article explores the psychological meaning and deeper philosophical issues and cultural roots surrounding various views of chaos and provides a multicultural perspective of origins and development of the idea of chaos and its relationship to chaos theory.
Chaos Theory, Philosophically Old, Scientifically New.
ERIC Educational Resources Information Center
Butz, Michael R.
1995-01-01
Chaos theory has recently become a central area of scientific interest in psychology. This article explores the psychological meaning and deeper philosophical issues and cultural roots surrounding various views of chaos and provides a multicultural perspective of origins and development of the idea of chaos and its relationship to chaos theory.…
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
NASA Astrophysics Data System (ADS)
Bai, Xiaojian; Lee, Bum-Hoon; Chen, Junde; Moon, Taeyoon
2016-03-01
We investigate the chaotic behavior of a circular test string in the Lifshitz spacetimes by considering the critical exponent z as an external control parameter. We demonstrate that two primary tools to observe chaos in this system are the Poincaré section and the Lyapunov exponent. Finally, the numerical result shows that if z = 1, the string dynamics is regular while in a case slightly larger than z = 1, the dynamics can be irregular and chaotic, which implies that the space time anisotropy, which breaks Lorentz symmetry, may cause the system to be chaotic.
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.
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.
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.
Classical chaos and its correspondence in superconducting qubits
NASA Astrophysics Data System (ADS)
Neill, C.; Campbell, B.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fang, M.; Hoi, I.; Kelly, J.; Megrant, A.; O'Malley, P.; Quintana, C.; Vainsencher, A.; Wenner, J.; White, T.; Barends, R.; Chen, Yu; Fowler, A.; Jeffrey, E.; Mutus, J.; Roushan, P.; Sank, D.; Martinis, J. M.
2015-03-01
Advances in superconducting qubits have made it possible to experimentally investigate quantum-classical correspondence by constructing quantum systems with chaotic classical limits. We study the quantum equivalent of a classical spinning top using three fully coupled qubits that behave as a single spin-3/2 and subject the spin to a sequence of non-linear rotations. The resulting entanglement bears a striking resemblance to the classical phase space, including bifurcation, and suggests that classical chaos manifests itself as quantum entanglement. Studying the orientation of the spin-3/2 reveals that the rotations which generate chaos and entanglement are at the same time the source of disagreement between the quantum and classical trajectories. Our experiment highlights the correspondence between classical non-linear dynamics and interacting quantum systems.
Transient chaos in room acoustics.
Mortessagne, Fabrice; Legrand, Olivier; Sornette, Didier
1993-10-01
The decay of sound in an auditorium due to absorption is central to the theory and practice of room acoustics. Within geometrical acoustics, this problem involves the partial trapping of chaotic ray trajectories in billiards, hence transient chaos. We first present a theoretical and numerical analysis of the decay of rays in 2-D chaotic billiards (2-D room acoustic models) and show that the existence of fluctuations (in the mean-free path and in the rate of phase space exploration) leads to modifications from the standard statistical theory. An ergodic wave theory of room acoustics based on a wave formulation is then discussed and tested by direct numerical calculations of the eigenmodes in 2-D billiards. Finally, we present a semiclassical calculation of the acoustic Green's functions in the time domain, based on a summation over rays, viewed as generalized wave impulses, and successfully compare its predictions with a direct numerical integration of the wave equation. This formalism provides a framework to link the geometrical ray description to the ergodic wave theory. PMID:12780059
ONSET OF CHAOS IN A MODEL OF QUANTUM COMPUTATION
G. BERMAN; ET AL
2001-02-01
Recently, the question of a relevance of the so-called quantum chaos has been raised in applications to quantum computation [2,3]. Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. [4,5]), with an increase of an interaction between qubits a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very strong and described by the Random Matrix Theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence of quantum computations due to internal decoherence inside many-body states. It is important to stress that quantum chaos occurs not only in the systems with random interaction, but also for purely dynamical interaction. In the latter case, the mechanism of chaos is due to a complex (non-linear) form of a two-body interaction represented in the basis of non-interacting particles. Numerical analysis [2] of a simplest model of quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that with an increase of the number L of qubits, the chaos threshold J{sub cr} decreases as J{sub cr} {infinity} 1/L. On this ground, it was claimed that the onset of quantum chaos could be dangerous for quantum computers, since their effectiveness requires L >> 1. On the other hand, in [3] it was argued that in order to treat this problem properly, one needs to distinguish between chaotic properties of stationary states, and the dynamical process of quantum computation.
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.
Route to chaos for combustion instability in ducted laminar premixed flames.
Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R I
2012-06-01
Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario. PMID:22757536
Route to chaos for combustion instability in ducted laminar premixed flames
NASA Astrophysics Data System (ADS)
Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R. I.
2012-06-01
Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.
NASA Astrophysics Data System (ADS)
Schmidt, Britney E.
2013-10-01
A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europas chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europas ice and ocean in light of active processes that may form a chaos conveyor belt that drives material exchange on Europa.
Nonlinear dynamics established in the ENSO
Elsner, J.B. ); Tsonis, A.A. )
1993-02-05
A time series describing the El-Nino-Southern Oscillation (ENSO) is analyzed using the latest techniques of chaos theory. The methods which rely on resampling statistics were developed to more finely distinguish between nonlinearity and linear correlated noise. From the results significant nonlinear structure arising from ENSO dynamics on the monthly time scale is established. 14 refs., 4 figs.
NASA Astrophysics Data System (ADS)
Sander, Evelyn; Yorke, James A.
There are many ways that a person can encounter chaos, such as through a time series from a lab experiment, a basin of attraction with fractal boundaries, a map with a crossing of stable and unstable manifolds, a fractal attractor, or in a system for which uncertainty doubles after some time period. These encounters appear so diverse, but the chaos is the same in all of the underlying systems; it is just observed in different ways. We describe these different types of chaos. We then give two conjectures about the types of dynamical behavior that is observable if one randomly picks out a dynamical system without searching for a specific property. In particular, we conjecture that from picking a system at random, one observes (1) only three types of basic invariant sets: periodic orbits, quasiperiodic orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement.
NASA 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
Optical digital chaos cryptography
NASA Astrophysics Data System (ADS)
Arenas-Pingarrn, lvaro; Gonzlez-Marcos, Ana P.; Rivas-Moscoso, Jos M.; Martn-Pereda, Jos A.
2007-10-01
In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.
Ercsey-Ravasz, Mria; Toroczkai, Zoltn
2012-01-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = -log??? can be used to define a "Richter"-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4. PMID:23061008
Ercsey-Ravasz, Mria; Toroczkai, Zoltn
2012-01-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = ?log10 ? can be used to define a Richter-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4. PMID:23061008
NASA Astrophysics Data System (ADS)
Ercsey-Ravasz, Mria; Toroczkai, Zoltn
2012-10-01
The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = -log10 ? can be used to define a ``Richter''-type scale for puzzle hardness, with easy puzzles having 0 < ? <= 1, medium ones 1 < ? <= 2, hard with 2 < ? <= 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4.
NASA Technical Reports Server (NTRS)
2003-01-01
MGS MOC Release No. MOC2-504, 5 October 2003
This August 2003 Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a valley near Nilus Chaos, around 25.2oN, 80.3oW. The scene has a uniform albedo, indicating that all of the landforms are probably mantled by fine, bright dust. Dark streaks on the valley walls indicate places where recent dust avalanches have occurred. The ripple-like dune features on the valley floor were formed by wind, but today they are inactive and covered with dust. A few craters, created by impacting debris, have formed on the dunes, again attesting to their inactivity in the modern martian environment. The image covers an area 3 km (1.9 mi) wide; it is illuminated by sunlight from the lower left.
NASA Technical Reports Server (NTRS)
2004-01-01
2 August 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a circular mesa and layered materials that are partially-exposed from beneath a thick, dark mantle in the Aureum Chaos region of Mars. The features are part of a much larger circular form (bigger than the image shown here) that marks the location of a crater that was filled with light-toned sedimentary rock, buried, and then later re-exposed when the upper crust of Mars broke apart in this region to form buttes and mesas of 'chaotic terrain.' The circular mesa in this image might also be the location of a formerly filled and buried crater. This image is located near 4.0oS, 26.9oW. It covers an area about 3 km (1.9 mi) across; sunlight illuminates the scene from the left/upper left.
Chao Family Comprehensive Cancer Center
The University of California, Irvine (UCI) Cancer Center was established in 1989 as a university-based cancer center. In 1994, it became an NCI-designated cancer center, and it achieved comprehensive cancer center status in 1997. Soon after, it was renamed in honor of the Chao family as the Chao Family Comprehensive Cancer Center (CFCCC), operating fully integrated research, prevention, diagnostic, treatment, and rehabilitation programs.
NASA Astrophysics Data System (ADS)
Geddada, Nagesh; Karanki, Srinivas B.; Mishra, Mahesh K.
2014-06-01
This paper proposes a modified four-leg distribution static compensator (DSTATCOM) topology for compensation of unbalanced and nonlinear loads in three-phase four-wire distribution system. DSTATCOM, connected in parallel to the load, supplies reactive and harmonic powers demanded by unbalanced nonlinear loads. In this proposed topology, the voltage source inverter (VSI) of DSTATCOM is connected to point of common coupling (point of interconnection of source, load, DSTATCOM) through interface inductor and series capacitance, unlike the conventional topology which consists of interface inductor alone. Load compensation with a lower value of input DC link voltage of VSI is possible in this modified topology compared to conventional topology. A comparative study on modified and conventional topologies in terms of voltage rating of inverter power switches, switching losses in VSI and power rating of input DC capacitor of VSI is presented. The detailed design aspects of DC link capacitor and interface series capacitor are also presented. The reference filter currents are generated using instantaneous symmetrical component theory and are tracked using hysteresis current control technique. A detailed simulation study is carried out, to compare the compensation performances of conventional, modified topologies using PSCAD simulator and experimental studies are done to validate the simulation results.
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
Adaptive functional systems: Learning with chaos
NASA Astrophysics Data System (ADS)
Komarov, M. A.; Osipov, G. V.; Burtsev, M. S.
2010-12-01
We propose a new model of adaptive behavior that combines a winnerless competition principle and chaos to learn new functional systems. The model consists of a complex network of nonlinear dynamical elements producing sequences of goal-directed actions. Each element describes dynamics and activity of the functional system which is supposed to be a distributed set of interacting physiological elements such as nerve or muscle that cooperates to obtain certain goal at the level of the whole organism. During "normal" behavior, the dynamics of the system follows heteroclinic channels, but in the novel situation chaotic search is activated and a new channel leading to the target state is gradually created simulating the process of learning. The model was tested in single and multigoal environments and had demonstrated a good potential for generation of new adaptations.
Quantifying chaos of curvilinear beams via exponents
NASA Astrophysics Data System (ADS)
Awrejcewicz, J.; Krysko, V. A.; Kutepov, I. E.; Vygodchikova, I. Yu.; Krysko, A. V.
2015-10-01
We propose a procedure for predicting the stability loss and transition into chaos of a network of oscillators lying on a curve, where each of the oscillators can move in two perpendicular directions. Dynamics of the coupled oscillators are governed by the sixth-order PDE, which is directly derived using the classical hypotheses of a curvilinear flexible beam movement theory. We apply FDM (Finite Difference Method) to reduce PDEs into ODEs, and the used number of spatial coordinate positions defines the number of involved oscillators approximating the dynamics of our continuous structural member (beam). Our procedure has a few advantages over the classical approaches, which has been illustrated and discussed. The proposed method has been validated for non-linear dynamical regimes by using the classical vibrational analysis (time histories, frequency power spectra and Poincaré maps).
Multi-scale continuum mechanics: from global bifurcations to noise induced high-dimensional chaos.
Schwartz, Ira B; Morgan, David S; Billings, Lora; Lai, Ying-Cheng
2004-06-01
Many mechanical systems consist of continuum mechanical structures, having either linear or nonlinear elasticity or geometry, coupled to nonlinear oscillators. In this paper, we consider the class of linear continua coupled to mechanical pendula. In such mechanical systems, there often exist several natural time scales determined by the physics of the problem. Using a time scale splitting, we analyze a prototypical structural-mechanical system consisting of a planar nonlinear pendulum coupled to a flexible rod made of linear viscoelastic material. In this system both low-dimensional and high-dimensional chaos is observed. The low-dimensional chaos appears in the limit of small coupling between the continua and oscillator, where the natural frequency of the primary mode of the rod is much greater than the natural frequency of the pendulum. In this case, the motion resides on a slow manifold. As the coupling is increased, global motion moves off of the slow manifold and high-dimensional chaos is observed. We present a numerical bifurcation analysis of the resulting system illustrating the mechanism for the onset of high-dimensional chaos. Constrained invariant sets are computed to reveal a process from low-dimensional to high-dimensional transitions. Applications will be to both deterministic and stochastic bifurcations. Practical implications of the bifurcation from low-dimensional to high-dimensional chaos for detection of damage as well as global effects of noise will also be discussed. PMID:15189066
NASA Astrophysics Data System (ADS)
Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S.
2013-08-01
Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.
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.
Theory and applications of ray chaos to underwater acoustics.
Smirnov, I P; Virovlyansky, A L; Zaslavsky, G M
2001-09-01
Chaotic ray dynamics in deep sea propagation models is considered using the approaches developed in the theory of dynamical chaos. It has been demonstrated that the mechanism of emergence of ray chaos due to overlapping of nonlinear ray-medium resonances should play an important role in long range sound propagation. Analytical estimations, supported by numerical simulations, show that for realistic values of spatial periods and sound speed fluctuation amplitudes associated with internal-wave-induced perturbations, the resonance overlapping causes stochastic instability of ray paths. The influence of the form of the smooth unperturbed sound speed profile on ray sensitivity to the perturbation is studied. Stability analysis has been conducted by constructing the Poincar maps and examining depth differences of ray trajectories with close take-off angles. The properties of ray travel times, including fractal properties of the time front fine structures, under condition of ray chaos have been investigated. It has been shown that the coexistence of chaotic and regular rays, typical for dynamical chaos, leads to the appearance of gaps in ray travel time distributions, which are absent in unperturbed waveguides. This phenomenon has a prototype in theory of dynamical chaos called the stochastic particle acceleration. It has been shown that mesoscale inhomogeneities with greater spatial scales than that of internal waves, create irregular local waveguide channels in the vicinity of the axis (i.e., sound speed minimum) of the unperturbed waveguide. Near-axial rays propagating at small grazing angles, "jump" irregularly between these microchannels. This mechanism determines chaotic behavior of the near-axial rays. PMID:11580436
Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations
Misra, A. P.; Shukla, P. K.
2009-05-15
The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.
Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations.
Misra, A P; Shukla, P K
2009-05-01
The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas. PMID:19518570
Low-Dimensional Chaos of High-Latitude Solar Activity
NASA Astrophysics Data System (ADS)
Li, Qi-Xiu; Li, Ke-Jun
2007-10-01
The chaos of high-latitude solar activity has been investigated by determining the behavior of the monthly averaged polar facula counts obtained from the National Astronomical Observatory of Japan (NAOJ) on the basis of nonlinear dynamics theories and methods. It is found that the high-latitude solar activity is also governed by a low-dimensional chaotic attractor in both the northern and southern solar hemispheres, which is the same as that of the low-latitude solar activity. However, their maximal Lyapunov exponents are different, showing different strength of chaos. The maximal Lyapunov exponent (MLE) of polar faculae in the southern solar hemisphere is about 0.0211 0.0003 (month-1), which is nearly consistent with the low-latitude Wolf sunspot numbers, while the MLE in the northern one is approximately 0.0944 0.0066 (month-1), which is obviously greater than the above two.
Spiral defect chaos in an advection-reaction-diffusion system
NASA Astrophysics Data System (ADS)
Affan, H.; Friedrich, R.
2014-06-01
This paper comprises numerical and theoretical studies of spatiotemporal patterns in advection-reaction-diffusion systems in which the chemical species interact with the hydrodynamic fluid. Due to the interplay between the two, we obtained the spiral defect chaos in the activator-inhibitor-type model. We formulated the generalized Swift-Hohenberg-type model for this system. Then the evolution of fractal boundaries due to the effect of the strong nonlinearity at the interface of the two chemical species is studied numerically. The purpose of the present paper is to point out that spiral defect chaos, observed in model equations of the extended Swift-Hohenberg equation for low Prandtl number convection, may actually be obtained also in certain advection-reaction-diffusion systems.
Spiral defect chaos in an advection-reaction-diffusion system.
Affan, H; Friedrich, R
2014-06-01
This paper comprises numerical and theoretical studies of spatiotemporal patterns in advection-reaction-diffusion systems in which the chemical species interact with the hydrodynamic fluid. Due to the interplay between the two, we obtained the spiral defect chaos in the activator-inhibitor-type model. We formulated the generalized Swift-Hohenberg-type model for this system. Then the evolution of fractal boundaries due to the effect of the strong nonlinearity at the interface of the two chemical species is studied numerically. The purpose of the present paper is to point out that spiral defect chaos, observed in model equations of the extended Swift-Hohenberg equation for low Prandtl number convection, may actually be obtained also in certain advection-reaction-diffusion systems. PMID:25019864
Intermittency and chaos in intracavity doubled lasers. II
James, G.E.; Harrell, E.M. II ); Roy, R. )
1990-03-01
We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer (J. Opt. Soc. Am. B 3, 1175 (1986)) observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota (Opt. Lett. 13, 805 (1988)) demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.
Photonic Josephson effect, phase transitions, and chaos in optomechanical systems
NASA Astrophysics Data System (ADS)
Larson, Jonas; Horsdal, Mats
2011-08-01
A photonic analog of the Josephson effect is analyzed for a system formed by a partly transparent mechanical membrane dividing an optical cavity into two halves. Photons tunneling between the two subcavities constitute the coherent Jospehson current. The force acting upon the membrane due to the light pressure induces a nonlinearity, which results in a rich dynamical structure. For example, contrary to standard bosonic Josephson systems, we encounter chaos. By means of a mean-field approach, we identify the various regimes and corresponding phase diagram. At the short time scale, chaos is demonstrated to prevent regular self-trapping, while for longer times a dissipation-induced self-trapping effect is possible.
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).
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1976-01-01
Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.
NASA Astrophysics Data System (ADS)
Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo
2014-10-01
The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (?y/?x) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.
Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?
ERIC Educational Resources Information Center
Wong, Marina
2013-01-01
This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of
Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?
ERIC Educational Resources Information Center
Wong, Marina
2013-01-01
This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…
Ma, Teng-Ying; Ma, Na-Na; Yan, Li-Kai; Guan, Wei; Su, Zhong-Min
2013-03-01
The switchable second-order nonlinear optical (NLO) responses of the photoisomerized chromophore dithienylperfluorocyclopentene (DTE) derivatives, organic-inorganic systems of Lindqvist-type [Mo?O??]?, have been investigated by tuning open-ring and the closed-ring form. In the present paper, we performed density functional theory (DFT) combined with finite field (FF) methods to calculate the second-order NLO coefficients for these organic-inorganic compounds. The calculations with three functionals (B3LYP/CAM-B3LYP/LC-BLYP) confirm the switching behavior on NLO properties by the photoisomerization reaction. The ?(tot) value of system 2c (closed-ring form) is 10 times larger than that of its open-ring form (system 2o). And the other two pairs of systems also show good tuning properties. The ampliative ratio on second-order NLO coefficients between systems 2o and 2c (?(2c)/?(2o)) is 13 times as large as that of DTE (?(DTEc)/?(DTEo)). It suggests that introduction of [Mo?O??]? and organic groups to the DTE monomer effectively improve the conversion ratio of second-order NLO coefficients between the open-ring and closed-ring forms. PMID:23419765
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 provides an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.
Channeling chaos by building barriers.
Chandre, C; Ciraolo, G; Doveil, F; Lima, R; Macor, A; Vittot, M
2005-02-25
Chaotic diffusion often represents a severe obstacle for the setup of experiments, e.g., in fusion plasmas or particle accelerators. We present a complete test of a method of control of Hamiltonian chaos, with both its numerical test and its first experimental realization on a paradigm for wave-particle interaction, i.e., a travelling wave tube. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. Its experimental realization opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy. PMID:15783819
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. PMID:26428567
ergodicity and chaos in geomorphology
NASA Astrophysics Data System (ADS)
Aadel, S.; Gaiumi, M.
2009-04-01
The past three dicades can be considered as a period in which the fundamentals of scientific epistemology have been subjected to drastic revision.The dissemination of the general theory of systems in 1972 , one year after the death of ludwing von Berthalanfi , the proposition of fuzzy logic by Zade, and the foemulation of chaos theory in 1986 by Harison and Biswas allserved to explode the myth that scientific thought was invulnerable. This paper , which has resulted from the theoretical investigation of project based on the paraglicial sediment and glacial evidence on the Zagros-pishkoh to explain the elements of chaos theory and their compatibility with ergodic geomorphology
Chaos in coherence modulation: bifurcations of an oscillator generating optical delay fluctuations
Larger, Laurent; Lee, Min Won; Goedgebuer, Jean-Pierre; Elflein, Wilhelm; Erneux, Thomas
2001-08-01
A new chaos generator is described that produces chaotic fluctuations of the optical-path difference in a coherence modulator driven electrically by a nonlinear delayed-feedback loop. Numerical simulations and experimental results are reported. A closed branch of periodic solutions bounded by a forward and a reverse Hopf bifurcation is observed for the first time, to our knowledge, for this type of nonlinear dynamical system. {copyright} 2001 Optical Society of America
Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential
Ishkhanyan, H. A.; Krainov, V. P.
2011-09-15
We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.
Process and meaning: nonlinear dynamics and psychology in visual art.
Zausner, Tobi
2007-01-01
Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life. PMID:17173732
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
Valentini, F.; Vecchio, A.; Donato, S.; Carbone, V.; Veltri, P.; Briand, C.; Bougeret, J.
2014-06-10
The local heating of the solar-wind gas during its expansion represents one of the most intriguing problems in space plasma physics and is at present the subject of a relevant scientific effort. The possible mechanisms that could account for local heat production in the interplanetary medium are most likely related to the turbulent character of the solar-wind plasma. Nowadays, many observational and numerical analyses are devoted to the identification of fluctuation channels along which energy is carried from large to short wavelengths during the development of the turbulent cascade; these fluctuation channels establish the link between macroscopic and microscopic scales. In this Letter, by means of a quantitative comparison between in situ measurements in the solar wind from the STEREO spacecraft and numerical results from kinetic simulations, we identify an electrostatic channel of fluctuations that develops along the turbulent cascade in a direction parallel to the ambient magnetic field. This channel appears to be efficient in transferring the energy from large Alfvénic to short electrostatic acoustic-like scales up to a range of wavelengths where it can finally be turned into heat, even when the electron to proton temperature ratio is of the order of unity.
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
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…
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!
NASA Astrophysics Data System (ADS)
Wang, Ling; Wu, Zheng-Mao; Wu, Jia-Gui; Xia, Guang-Qiong
2015-01-01
Based on the polarization-resolved chaos synchronization between twin 1550 nm vertical-cavity surface-emitting lasers (VCSELs), a novel long-haul dual-channel bidirectional chaos communication system is proposed. In this system, a time delay signature (TDS)-suppressed chaotic signal, generated by a driving VCSEL (D-VCSEL) under double external cavity feedbacks (DECFs), simultaneously injects into twin VCSELs by variable-polarization optical injection (VPOI) to synchronize them and enhance the chaos output bandwidth of the two VCSELs. The simulated results show that, under proper injection parameters, high-quality polarization-resolved chaos synchronization between the twin VCSELs can be achieved; meanwhile the bandwidths of chaotic signals output from the twin VCSELs have been enhanced in comparison with that of the driven chaotic signal. Based on the high-quality polarization-resolved chaos synchronization, after adopting polarization-division-multiplexing (PDM) and chaos masking (CM) techniques, four 10 Gb/s messages hidden respectively in four chaotic carriers can be decrypted effectively after propagating 15 km in single-mode fiber (SMF) links. After adopting dispersion-shifted fibers (DSFs) as fiber links, the dual-channel bidirectional chaos communication distance can be extended to 140 km.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image continues the northward trend through the Iani Chaos region. Compare this image to Monday's and Tuesday's. This image was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -0.1 Longitude 342.6 East (17.4 West). 19 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image is located in a different part of Aureum Chaos. Compare the surface textures with yesterday's image. This image was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -4.1, Longitude 333.9 East (26.1 West). 35 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
NASA Astrophysics Data System (ADS)
Wang, Shihong; Li, Da; Zhou, Hu
2012-02-01
The collision problem of a chaos-based hash function with both modification detection and localization capability is investigated [Xiao D, Shih FY, Liao XF. A chaos-based hash function with both modification detection and localization capabilities. Commun Nonlinear Sci Numer Simulat 2010;15(9):2254-61]. The simulation gives the same detection and localization hash values for distinct messages. The expense of the birthday attack on the hash function is far less than expected. The certain symmetries of message distribution may result in the same detection hash value for distinct messages.
Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement
NASA Astrophysics Data System (ADS)
Ataei, Mohammad; Kiyoumarsi, Arash; Ghorbani, Behzad
2010-09-01
Permanent Magnet Synchronous Motor (PMSM) experiences chaotic behavior for a certain range of its parameters. In this case, since the performance of the PMSM degrades, the chaos should be eliminated. In this Letter, the control of the undesirable chaos in PMSM using Lyapunov exponents (LEs) placement is proposed that is also improved by choosing optimal locations of the LEs in the sense of predefined cost function. Moreover, in order to provide the physical realization of the method, nonlinear parameter estimator for the system is suggested. Finally, to show the effectiveness of the proposed methodology, the simulation results for applying this control strategy are provided.
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.
Chaos in a three-species food chain
Hastings, A.; Powell, T. )
1991-06-01
A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food webs must contend with the question of how to couple the large number of interacting species.
Hamiltonian chaos in a coupled BEC-optomechanical-cavity system
Zhang, K.; Chen, W.; Bhattacharya, M.; Meystre, P.
2010-01-15
We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.
Chaos of radiative heat-loss-induced flame front instability
NASA Astrophysics Data System (ADS)
Kinugawa, Hikaru; Ueda, Kazuhiro; Gotoda, Hiroshi
2016-03-01
We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.
ERIC Educational Resources Information Center
Snyder, Herbert; Kurtze, Douglas
1992-01-01
Discusses the use of chaos, or nonlinear dynamics, for investigating computer-mediated communication. A comparison between real, human-generated data from a computer network and similarly constructed random-generated data is made, and mathematical procedures for determining chaos are described. (seven references) (LRW)
NASA Astrophysics Data System (ADS)
Lafranceschina, Jacopo
Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors.
Subharmonics, Chaos, and Beyond
NASA Technical Reports Server (NTRS)
Adler, Laszlo; Yost, William T.; Cantrell, John H.
2011-01-01
While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity, which is formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed in addition to the expected harmonic structure. Subsequently it was realized that the system was one of the many examples where parametric resonance takes place and in which the observed subharmonics are parametrically generated. Parametric resonance occurs in any physical system which has a periodically modulated natural frequency. 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 objective of this presentation. An ultrasonic interferometer with optical precision was built. The transducers were compressional undamped quartz and Lithium Niobate crystals ranging from 1-10 Mhz, and driven by a high power amplifier. Both an optical diffraction system and a receive transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to observe the generated frequency components in the cavity.
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.
Does chaos assist localization or delocalization?
Tan, Jintao; Luo, Yunrong; Hai, Wenhua; Lu, Gengbiao
2014-12-01
We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.
BOOK REVIEW: Chaos: A Very Short Introduction
NASA Astrophysics Data System (ADS)
Klages, R.
2007-07-01
This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a popular science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book is also getting a bit too intricate for the complete layman, and experts may not agree on all details of the more conceptual discussions. Altogether I thoroughly enjoyed reading this book. It was a happy companion while travelling and a nice bedtime literature. It is furthermore an excellent reminder of the `big picture' underlying nonlinear science as it applies to the real world. I will gladly recommend this book as background literature for students in my introductory course on dynamical systems. However, the book will be of interest to anyone who is looking for a very short account on fundamental problems and principles in modern nonlinear science.
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
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…
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.
Ecological chaos in the wake of invasion.
Sherratt, J A; Lewis, M A; Fowler, A C
1995-01-01
Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos. Images Fig. 7 PMID:7708678
Quantum chaos: An entropy approach
NASA Astrophysics Data System (ADS)
Sl/omczy?ski, Wojciech; ?yczkowski, 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 ??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
Spatiotemporal chaos from bursting dynamics
NASA Astrophysics Data System (ADS)
Berenstein, Igal; De Decker, Yannick
2015-08-01
In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators.
Spatiotemporal chaos from bursting dynamics.
Berenstein, Igal; De Decker, Yannick
2015-08-14
In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators. PMID:26277125
Fighting Chaos: Applications of Breeding
NASA Astrophysics Data System (ADS)
Kalnay, E.
2012-12-01
I will discuss basic concepts of chaos, and describe techniques that have allowed taking advantage of chaos and improve forecasts and their information. One example is "breeding of instabilities" a very simple technique to estimate the fastest growing instabilities. Breeding allows predicting when a regime change will take place and how long will the new regime last in the famous Lorenz (1963) "unpredictable chaotic model", something that surprised Lorenz himself. These techniques can be applied to any dynamic chaotic system. Some examples include detection of ocean instabilities and their physical origin, breeding in coupled ocean-atmosphere systems, detecting instabilities in the atmosphere of Mars, and breeding on the phase-space reconstructed from single time series using the time-delay embedding method. Finally I'll discuss the implications of these results for data assimilation.
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.
Nonlinear dynamics in cardiac conduction
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.
1988-01-01
Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.
Nonlinear dynamics, fractals, cardiac physiology and sudden death
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.
1987-01-01
The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.
Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars
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 plateau subsidence and chaos formation may have continued well into the Amazonian Period. The geologic and paleohydrologic histories presented here have important implications, as new mechanisms for outflow channel formation and other fluvial activity are described, and new reactivation mechanisms are proposed for the origin of chaotic terrain as contributors to flooding. Detailed geomorphic analysis indicates that subterranean caverns may have been exposed during chaos formation, and thus chaotic terrains mark prime locations for future geologic, hydrologic, and possible astrobiologic exploration. ?? 2004 Elsevier Inc. All rights reserved.
Polynomial Chaos Using Transformed Sparse Grids
NASA Astrophysics Data System (ADS)
Tompkins, M. J.; Prange, M.
2011-12-01
The topic of general polynomial chaos has received significant attention in the last few years as a means to efficiently estimate model outcomes based on known stochastic processes. The method requires numerical integrations in order to evaluate the expectation integrals that are the coefficients of the stochastic polynomial. The key concern is that these numerical integrations are very time consuming when applied to demanding computational problems such as flow simulation. Therefore, methods which can perform this integration with a minimum number of integration points are highly desirable. An obvious choice is a sparse-grid method based on a 1D Gauss-quadrature rule, because this allows highly accurate integration rules to be designed for arbitrary PDFs in the expectation integral. Unfortunately, Gauss quadrature is a very poor choice for sparse-grid integration, because the corresponding integration rules are weakly nested, and thus do not allow reuse of integration points from one sparse-grid level to the next. Alternatively, Clenshaw-Curtis integration produces very strongly nested quadrature rules, but these are designed for uniform distributions and are inefficient for many PDFs, e.g., Gaussians. In this work, we present a nonlinear transformation of Fejer type 2 quadrature rules that realizes the benefits of having both a high degree of sparsity and being tailored to specific PDFs. We demonstrate that this method has the potential to integrate arbitrary functions in high stochastic dimensions (>8) with orders of magnitude fewer integration points than are required for similar Gauss-quadrature rules.
Fast and Secure Chaos-Based Cryptosystem for Images
NASA Astrophysics Data System (ADS)
Farajallah, Mousa; El Assad, Safwan; Deforges, Olivier
Nonlinear dynamic cryptosystems or chaos-based cryptosystems have been attracting a large amount of research since 1990. The critical aspect of cryptography is to face the growth of communication and to achieve the design of fast and secure cryptosystems. In this paper, we introduce three versions of a chaos-based cryptosystem based on a similar structure of the Zhang and Fridrich cryptosystems. Each version is composed of two layers: a confusion layer and a diffusion layer. The confusion layer is achieved by using a modified 2-D cat map to overcome the fixed-point problem and some other weaknesses, and also to increase the dynamic key space. The 32-bit logistic map is used as a diffusion layer for the first version, which is more robust than using it in 8-bit. In the other versions, the logistic map is replaced by a modified Finite Skew Tent Map (FSTM) for three reasons: to increase the nonlinearity properties of the diffusion layer, to overcome the fixed-point problem, and to increase the dynamic key space. Finally, all versions of the proposed cryptosystem are more resistant against known attacks and faster than Zhang cryptosystems. Moreover, the dynamic key space is much larger than the one used in Zhang cryptosystems. Performance and security analysis prove that the proposed cryptosystems are suitable for securing real-time applications.
Ray chaos and ray clustering in an ocean waveguide.
Makarov, D V; Uleysky, M Yu; Prants, S V
2004-03-01
We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a randomlike sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincare maps, plots of variations of the action per ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a randomlike multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves. PMID:15003047
Chaos in high-dimensional dissipative dynamical systems
Ispolatov, Iaroslav; Madhok, Vaibhav; Allende, Sebastian; Doebeli, Michael
2015-01-01
For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODEs with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10?5???10?4 for d?=?3 to essentially one for d?~?50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos. PMID:26224119
Chaos in Geophysical Fluids I. General Introduction
NASA Astrophysics Data System (ADS)
Hide, Raymond
1994-09-01
Irregular buoyancy-driven flows occur in the atmospheres and fluid interiors of the Earth and other planets, and of the Sun and other stars, where they influence and often control the transfer of heat. Their presence is manifest in or implied by a wide variety of observed phenomena, including external magnetic fields generated by self-exciting magnetohydrodynamic (MHD) dynamo action. Based on the laws of classical mechanics, thermodynamics and, in the case of electrically conducting fluids, electrodynamics, the governing mathematical equations are well known, but they are generally intractable owing to their essential nonlinearity. Computers play a key role in modern theoretical research in geophysical and astrophysical fluid dynamics, where ideas based on chaos theory are being applied in the analysis of models and the assessment of predictability. The aim of this paper is to provide a largely qualitative survey for non-specialists. The survey comprises two parts, namely a general introduction (Part I) followed by a discussion of two representative areas of research, both concerned with phenomena attributable to symmetry-breaking bifurcations caused by gyroscopic (Coriolis) forces (Part II), namely (a) large-scale waves and eddies in the atmospheres of the Earth, Jupiter and other planets (where, exceptionally, laboratory experiments have been influential), and (b) MHD dynamos. Various combinations of Faraday disc dynamos have been studied numerically as low-dimensional nonlinear electromechanical analogues of MHD dynamos, particularly in efforts to elucidate the complex time series of geomagnetic polarity reversals over geological time. The ability of the intensively studied Rikitake coupled disc dynamo system to behave chaotically appears to be a consequence of the neglect of mechanical friction, the inclusion of which renders the system structurally unstable.
Haotic, Fractal, and Nonlinear Signal Processing. Proceedings
Katz, R.A.
1996-10-01
These proceedings include papers presented at the Third Technical Conference on Nonlinear Dynamics and Full{minus}Spectrum Processing held in Mystic, Connecticut. The Conference focus was on the latest advances in chaotic, fractal and nonlinear signal processing methods. Topics of discussion covered in the Conference include: mathematical frontiers; predictability and control of chaos, detection and classification with applications in acoustics; advanced applied signal processing methods(linear and nonlinear); stochastic resonance; machinery diagnostics; turbulence; geophysics; medicine; and recent novel approaches to modeling nonlinear systems. There were 58 papers in the conference and all have been abstracted for the Energy Science and Technology database. (AIP)
Game as a Career Metaphor: A Chaos Theory Career Counselling Application
ERIC Educational Resources Information Center
Pryor, Robert George Leslie; Bright, Jim E. H.
2009-01-01
The potential of game as a career metaphor for use in counselling is explored and it is argued that it has been largely overlooked in the literature to date. This metaphor is then explicitly linked with the Chaos Theory of Careers (CTC), by showing how the notion of attractors within the CTC can be illustrated effectively using games metaphors.
Game as a Career Metaphor: A Chaos Theory Career Counselling Application
ERIC Educational Resources Information Center
Pryor, Robert George Leslie; Bright, Jim E. H.
2009-01-01
The potential of game as a career metaphor for use in counselling is explored and it is argued that it has been largely overlooked in the literature to date. This metaphor is then explicitly linked with the Chaos Theory of Careers (CTC), by showing how the notion of attractors within the CTC can be illustrated effectively using games metaphors.…
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos.
Chaotic behavior in coupled superconducting weak links
Nerenberg, M.A.H.; Blackburn, J.A.; Vik, S.
1984-11-01
Computer simulations have been carried out for a system consisting of a pair of coupled superconducting weak links described by a noncapacitive, resistively shunted equivalent circuit. Both dc and ac bias currents are assumed for each link. It is found that for certain ranges of ac amplitude, chaotic behavior occurs. Coupling is crucial to this result: without it no chaos will appear.
Advising Undecided Students: Lessons from Chaos Theory.
ERIC Educational Resources Information Center
Beck, Amy
1999-01-01
Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's
Chaos in Derrida and Student Texts.
ERIC Educational Resources Information Center
Corbett, Janice M.
Students must learn to maintain authority over their texts as they attempt to deal with the chaos they encounter when they approach a writing task. The authority with which Jacques Derrida deals with chaos in his essay, "...That Dangerous Supplement," suggests some strategies. In his essay, Derrida seems to be able to move the reader back and
Advising Undecided Students: Lessons from Chaos Theory.
ERIC Educational Resources Information Center
Beck, Amy
1999-01-01
Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's…
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.
Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^
NASA Astrophysics Data System (ADS)
Mackey, Peter Francis
1995-01-01
These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately, despite ungovernable fate and chance, Bloom asserts his will with Stephen and Molly, proving that he will live on, attempting to create his own destiny, wresting hope from the "chaos" of his experience.
Three-frequency quasiperiodicity, phase locking, and the onset of chaos
NASA Astrophysics Data System (ADS)
Linsay, Paul S.; Cumming, Andrew W.
1989-12-01
We have performed a series of experiments with coupled relaxation oscillators to study three-frequency quasiperiodicity. There is strong evidence for the Ruelle-Takens scenario for the transition to chaos although only a very small portion of parameter space is occupied by chaos. The chaotic transition is via an exchange of stability between states which have phase locked to two-frequency quasiperiodicity. The overall structure of parameter space is a very complicated fractal devil's cobweb of periodic resonances linked by bands of two-frequency phase lockings.
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.
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.
Maintaining Chaos in High Dimensions
NASA Astrophysics Data System (ADS)
in, Visarath; Spano, Mark L.; Ding, Mingzhou
1998-01-01
In dynamical systems, as a parameter is varied past a critical value, a chaotic attractor may be destroyed by a crisis. This attractor is replaced by a chaotic transient, which eventually leads to a different attractor. We present a method for maintaining chaotic dynamics after the crisis. The model, formulated for arbitrary dimensions, directs the phase space trajectory toward a target region near the periodic saddle orbit that mediates the crisis. It is used to maintain chaos numerically in the Ikeda map and experimentally in a magnetoelastic ribbon.
Decoherence, determinism and chaos revisited
NASA Astrophysics Data System (ADS)
Noyes, H. P.
1994-11-01
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L. H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
Bunimovich, Leonid A.; Vela-Arevalo, Luz V.
2015-09-15
A 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.
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 plateau.
CRISM is one of six science instruments on NASA's Mars Reconnaissance Orbiter. Led by The Johns Hopkins University Applied Physics Laboratory, Laurel, Md., the CRISM team includes expertise from universities, government agencies and small businesses in the United States and abroad. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Mars Reconnaissance Orbiter and the Mars Science Laboratory for NASA's Science Mission Directorate, Washington. Lockheed Martin Space Systems, Denver, built the orbiter.
Decoherence, determinism and chaos revisited
Noyes, H.P.
1994-11-15
We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.
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.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
NASA Astrophysics Data System (ADS)
Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia
2014-12-01
In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.
Control design and robustness analysis of a ball and plate system by using polynomial chaos
Colón, Diego; Balthazar, José M.; Reis, Célia A. dos; Bueno, Átila M.; Diniz, Ivando S.; Rosa, Suelia de S. R. F.
2014-12-10
In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.
NASA Astrophysics Data System (ADS)
Gouesbet, G.
1990-11-01
A very simple model is designed to understand dynamical states and bifurcations ranging up to chaos in thermal lens oscillations and associated hot-wire experiments. The present system is governed by partial derivative equations in the case of bulk liquid and also at a free surface which is a boundary of the liquid. It is reduced to a set of three nonlinear ordinary differential equations with two control parameters to be studied within the framework of the theory of nonlinear dynamical systems. The model may evolve to chaos in three domains of the parameter plane. Metric and dynamical properties (generalized dimensions and entropies, and associated singularity spectra) of a (presumably) strange chaotic attractor produced by the model are determined.
NASA Astrophysics Data System (ADS)
Kondrashov, A. V.; Ustinov, A. B.; Lhderanta, E.; Pakhomov, O. V.; Nikitin, A. A.; Kalinikos, B. A.
2015-12-01
Properties of spin-electromagnetic wave chaos developed in active ring oscillators have been investigated. A multiferroic structure composed of yttrium iron garnet film and barium strontium titanate (BST) slab served as a nonlinear dispersive medium of the oscillator. Dual control of the fractal dimension of the chaotic signal attractor was realized by variation of the ring gain and dielectric permittivity of the BST slab.
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.
Transitions to chaos in squeeze-film dampers
NASA Astrophysics Data System (ADS)
Inayat-Hussain, Jawaid I.; Mureithi, Njuki W.
2006-09-01
This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.
The route to chaos for the Kuramoto-Sivashinsky equation
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.; Smyrlis, Yiorgos
1990-01-01
The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609... . Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
NASA Astrophysics Data System (ADS)
Xu, Deyi; Yu, Chongwen; Cheng, Qiuming; Bao, Zhengyu
2011-12-01
To gain insight into complex processes in hydrothermal deposit-forming systems, we mapped the Zhabotinskii model onto a two-dimensional reaction-diffusion CNN (cellular neural/nonlinear network) of two state variables and two diffusion coefficients. The edge of chaos domain of the Zhabotinskii CNN was numerically determined according to a theory of complexity. The simulation of dynamic systems, with parameters taken from the edge of chaos domain as described in this study, can generate some interesting distribution patterns of component concentrations that plausibly characterize certain complex phenomena involved in hydrothermal mineralization.
Chaos detection in the space debris population.
NASA Astrophysics Data System (ADS)
Deleflie, Florent; Hautesserres, Denis; Daquin, Jrme; Morand, Vincent; Pretot, Nastassia; Fouchard, Marc
Semi-analytical propagations, on the basis of long term analysis of artificial satellite trajectories, are a very efficient tool to define storage orbits, and to characterize the main properties within a given region. In particular the altitude of the perigee or the lifetime can be estimated. Dedicated s/w such as STELA (Semi-analytical Tool for End of Life Analysis), developed in the frame of the French Space Operations Act, offer these kinds of capabilities. With a very large integration step size, it is then possible to get time series of the equinoctial elements over long period of time (typically, from 20 to 200yr), after only a few seconds of CPU. In case of resonant trajectories, due to the third body potential or to the Earth gravity field, getting an accurate lifetime estimation is not that obvious: it is likely to be much more time consuming since a Monte Carlo analysis may be required. The last version of the STELA s/w offers as well the capability to derive some quantities linked to the chaoticity of a trajectory, or a family of trajectories, linked to the resonances. In particular the FLI (Fast Lyapunov Indicator) and the maximum exponent of Lyapunov are now implemented into the s/w. We show in this presentation some examples that are obtained from the propagation of the transition matrix, simultaneously with the equations of motion. We derive some general properties about the detection of chaos in the space debris population by propagating the whole TLE catalogue.
Accessing Creativity: Jungian Night Sea Journeys, Wandering Minds, and Chaos.
Rosen, Diane
2016-01-01
NDS theory has been meaningfully applied to the dynamics of creativity and psychology. These complex systems have much in common, including a broad definition of "product" as new order emerging from disorder, a new whole (etymologically, 'health') out of disintegration or destabilization. From a nonlinear dynamical systems perspective, this paper explores the far-from-equilibrium zone of creative incubation: first in the Jungian night sea journey, a primordial myth of psychological and creative transformation; then in the neuroscience of mind wandering, the well-spring of creative ideation within the larger neural matrix. Finally, chaos theory grounds the elusive subject of creativity, modeling chaotic generation of idea elements that tend toward strange attractors, combine unpredictably, and produce change by means of tension between opposites, particularly notes consciousness (light) and the poetic unconscious (darkness). Examples from my own artwork illustrate this dialectical process. Considered together, the unconscious mythic sea journey, the unknowing wandering mind, and the generative paradigm of deterministic chaos suggest conditions that facilitate creativity across disciplines, providing fresh indications that the darkness of the unknown or irrational is, paradoxically, the illuminative source and strength of creativity. PMID:26639923
Predictability of normal heart rhythms and deterministic chaos
NASA Astrophysics Data System (ADS)
Lefebvre, J. H.; Goodings, D. A.; Kamath, M. V.; Fallen, E. L.
1993-04-01
The evidence for deterministic chaos in normal heart rhythms is examined. Electrocardiograms were recorded of 29 subjects falling into four groupsa young healthy group, an older healthy group, and two groups of patients who had recently suffered an acute myocardial infarction. From the measured R-R intervals, a time series of 1000 first differences was constructed for each subject. The correlation integral of Grassberger and Procaccia was calculated for several subjects using these relatively short time series. No evidence was found for the existence of an attractor having a dimension less than about 4. However, a prediction method recently proposed by Sugihara and May and an autoregressive linear predictor both show that there is a measure of short-term predictability in the differenced R-R intervals. Further analysis revealed that the short-term predictability calculated by the Sugihara-May method is not consistent with the null hypothesis of a Gaussian random process. The evidence for a small amount of nonlinear dynamical behavior together with the short-term predictability suggest that there is an element of deterministic chaos in normal heart rhythms, although it is not strong or persistent. Finally, two useful parameters of the predictability curves are identified, namely, the `first step predictability' and the `predictability decay rate,' neither of which appears to be significantly correlated with the standard deviation of the R-R intervals.
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) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)
Nonlinear lattice waves in heterogeneous media
NASA Astrophysics Data System (ADS)
Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S.
2014-12-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andr localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
Chaos automata: iterated function systems with memory
NASA Astrophysics Data System (ADS)
Ashlock, Dan; Golden, Jim
2003-07-01
Transforming biological sequences into fractals in order to visualize them is a long standing technique, in the form of the traditional four-cornered chaos game. In this paper we give a generalization of the standard chaos game visualization for DNA sequences. It incorporates iterated function systems that are called under the control of a finite state automaton, yielding a DNA to fractal transformation system with memory. We term these fractal visualizers chaos automata. The use of memory enables association of widely separated sequence events in the drawing of the fractal, finessing the forgetfulness of other fractal visualization methods. We use a genetic algorithm to train chaos automata to distinguish introns and exons in Zea mays (corn). A substantial issue treated here is the creation of a fitness function that leads to good visual separation of distinct data types.
Chaos and Fractals in Human Physiology.
ERIC Educational Resources Information Center
Goldberger, Ary L.; And Others
1990-01-01
Discusses the irregularity and unpredictability of the human body. Presented are pictures showing the fractallike structures and research findings on the mechanism for chaos in the human body. Lists four further reading materials. (YP)
Chaos suppression in NEMs resonators by using nonlinear control design
NASA Astrophysics Data System (ADS)
Tusset, Angelo Marcelo; Bueno, Atila Madureira; Nascimento, Claudinor Bitencourt; Kaster, Mauricio Dos Santos; Balthazar, Jos Manoel
2012-11-01
In this work the chaotic behavior of a micro-mechanical resonator with electrostatic forces on both sides is suppressed. The aim is to control the system in an orbit of the analytical solution obtained by the Method of Multiple Scales. Two control strategies are used for controlling the trajectory of the system, namely: State Dependent Riccati Equation (SDRE) Control and Optimal Linear Feedback Control (OLFC). The controls proved effectiveness in controlling the trajectory of the system. Additionally, the robustness of each strategy is tested considering the presence of parametric errors and measurement noise in control.
NASA Astrophysics Data System (ADS)
Macor, Alessandro; Doveil, Fabrice; Elskens, Yves
2006-10-01
A specially designed Traveling Wave Tube allows to carefully study wave-particle interaction; in the case when the beam electrons can be considered as test particles a devil's staircase has been observed by recording the beam velocity distribution function vs the amplitude of two induced waves. Its existence was related to the transition to large scale chaos in such a system, paradigm of two degrees of freedom systems in Hamiltonian dynamics^1. Chaos often represents an obstacle for the control of experiments; we showed the robustness of a control method for Hamiltonian chaos by varying methodically the pertinent parameters of system^2. Increasing the beam intensity self-consistent phenomena gradually enter; commonly leading to wave growth and further nonlinear saturation. A generator able to produce subnanosecond electron pulses at high repetition rate was installed allowing to explore the influence of the relative phase of electron packets with respect to waves^3. 1 A. Macor, F.Doveil and Y.Elskens, Phys. Rev. Lett. 95, 264102 (2005) and Chaos 16, 1 (2006) 2 C.Chandre et al., Phys. Rev. Lett. 94, 074101 (2005) 3 A.Macor, F.Doveil and E.Garabedian, J-NPCS (in press)
Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram
NASA Astrophysics Data System (ADS)
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.
Ergodic theory, randomness, and "chaos".
Ornstein, D S
1989-01-13
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability. PMID:17747421
Sndor, Bulcs; Jrai-Szab, Ferenc; Tl, Tams; Nda, Zoltn
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). PMID:23679502
Transient chaos in optical metamaterials.
Ni, Xuan; Lai, Ying-Cheng
2011-09-01
We investigate the dynamics of light rays in two classes of optical metamaterial systems: (1) time-dependent system with a volcano-shaped, inhomogeneous and isotropic refractive-index distribution, subject to external electromagnetic perturbations and (2) time-independent system consisting of three overlapping or non-overlapping refractive-index distributions. Utilizing a mechanical-optical analogy and coordinate transformation, the wave-propagation problem governed by the Maxwell's equations can be modeled by a set of ordinary differential equations for light rays. We find that transient chaotic dynamics, hyperbolic or nonhyperbolic, are common in optical metamaterial systems. Due to the analogy between light-ray dynamics in metamaterials and the motion of light in matter as described by general relativity, our results reinforce the recent idea that chaos in gravitational systems can be observed and studied in laboratory experiments. PMID:21974651
NASA Technical Reports Server (NTRS)
2008-01-01
[figure removed for brevity, see original site] Click on image for animation of 3-dimensional model with 5x vertical exaggeration
This image of chaotic terrain in the Aureum Chaos region of Mars was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0858UTC (3:58 a.m. EST) on January 24, 2008, near 3.66 degrees south latitude, 26.5 degrees west longitude. The image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 18 meters (60 feet) across. The image is about 10 kilometers (6.2 miles) wide at its narrowest point.
Aureum Chaos is a 368 kilometer (229 mile) wide area of chaotic terrain in the eastern part of Valles Marineris. The chaotic terrain is thought to have formed by collapse of the surrounding Margaritifer Terra highland region. Aureum Chaos contains heavily eroded, randomly oriented mesas, plateaus, and knobs many revealing distinct layered deposits along their slopes. These deposits may be formed from remnants of the collapsed highlands, sand carried by Martian winds, dust or volcanic ash that settled out of the atmosphere, or sediments laid down on the floor of an ancient lake.
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 cover a narrow plateau near the edge of the chaotic terrain, that stretches across from the southwest to the northeast.
The lower left image, an infrared false color image, reveals the plateau and several eroded knobs of varying sizes. The plateau's layer-cake structure is similar to that of other layered outcrops in Valles Marineris.
The lower right image reveals the strengths of mineral spectral features overlain on a black-and-white version of the infrared image. Areas shaded in red hold more of the mineral pyroxene, a primary component of basaltic rocks that are prevalent in the highlands. Spots of green indicate monohydrated sulfate minerals (sulfates with one water molecule incorporated into each molecule of the mineral), while blue indicates polyhydrated sulfate minerals (sulfates with multiple waters per mineral molecule).
Although the plateau's dark cap rock is somewhat mineralogically non-descript, the bright, white swath of underlying material cascading down the plateau's flanks appears to hold polyhydrated sulfates. Dark eolian or wind deposited sediments in the south-central part of the plateau are also rich in polyhydrated sulfates.
Surrounding the plateau are small greenish spots of monoyhydrated sulfates. These are erosional remnants of an even lower part of the layered deposits that is compositionally distinct from the main part of the plateau.
The deepest layer visible is preexisting 'basement' rock that forms the floor of Aureum Chaos around the plateau. It is comprised of basaltic rock exposed by collapse of the crust and the debris derived from that collapse.
The animation (see above) of a 3-dimensional topographic model illustrates the relationship of these materials. It was made using the lower right CRISM image, draped over MOLA topography with 5X vertical exaggeration.
CRISM is one of six science instruments on NASA's Mars Reconnaissance Orbiter. Led by The Johns Hopkins University Applied Physics Laboratory, Laurel, Md., the CRISM team includes expertise from universities, government agencies and small businesses in the United States and abroad. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Mars Reconnaissance Orbiter and the Mars Science Laboratory for NASA's Science Mission Directorate, Washington. Lockheed Martin Space Systems, Denver, built the orbiter.
Control of collective network chaos
Wagemakers, Alexandre Sanjuán, Miguel A. F.
2014-06-01
Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of “reduced” ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
Control of Chaos During Human Atrial Fibrillation
NASA Astrophysics Data System (ADS)
Ditto, William; Spano, Mark; in, Visarath; Langberg, Jonathan
1998-03-01
Previous studies( A. Garfinkel, M. L. Spano, W. L. Ditto and J. N. Weiss, Science) 257, 1230 (1992). have applied chaos control techniques to cardiac tissue, but such methods have yet to be applied to an in vivo human heart. In this talk we present evidence for determinism in human atrial fibrillation (AF) and report on efforts to control AF using established chaos control techniques.
Deterministic chaos in materials exhibiting phase transitions
NASA Astrophysics Data System (ADS)
Slemrod, M.
1983-06-01
The author spent one half of the Spring 1983 semester at the Institute for Mathematics and its Applications. During that time he interacted with colleagues, engaged in research, and gave two public lectures at the Institute: chaos in phase transitions, and dynamics of phase transitions. The main thrust of his research was in two areas, specifically: deterministic chaos in materials exhibiting phase transitions, and admissibility criteria for weak solutions of the non-hyperbolic conservation laws which describe dynamic phase transitions.
NASA Astrophysics Data System (ADS)
Kengne, J.
In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.
Drift waves and chaos in a LAPTAG plasma physics experiment
NASA Astrophysics Data System (ADS)
Gekelman, Walter; Pribyl, Patrick; Birge-Lee, Henry; Wise, Joe; Katz, Cami; Wolman, Ben; Baker, Bob; Marmie, Ken; Patankar, Vedang; Bridges, Gabriel; Buckley-Bonanno, Samuel; Buckley, Susan; Ge, Andrew; Thomas, Sam
2016-02-01
In a project involving an alliance between universities and high schools, a magnetized plasma column with a steep pressure gradient was established in an experimental device. A two-dimensional probe measured fluctuations in the plasma column in a plane transverse to the background magnetic field. Correlation techniques determined that the fluctuations were that of electrostatic drift waves. The time series data were used to generate the Bandt-Pompe entropy and Jensen-Shannon complexity for the data. These quantities, when plotted against one another, revealed that a combination of drift waves and other background fluctuations were a deterministically chaotic system. Our analysis can be used to tell the difference between deterministic chaos and random noise, making it a potentially useful technique in nonlinear dynamics.
Detection of "noisy" chaos in a time series
NASA Technical Reports Server (NTRS)
Chon, K. H.; Kanters, J. K.; Cohen, R. J.; Holstein-Rathlou, N. H.
1997-01-01
Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.
Relaxation Dynamics of Spatiotemporal Chaos in the Nematic Liquid Crystal
NASA Astrophysics Data System (ADS)
Nugroho, Fahrudin; Ueki, Tatsuhiro; Hidaka, Yoshiki; Kai, Shoichi
2011-11-01
We are working on the electroconvection of nematic liquid crystals, in which a kind of spatiotemporal chaos called as a soft-mode turbulence (SMT) is observed. The SMT is caused by the nonlinear interaction between the convective modes and the Nambu--Goldstone (NG) modes. By applying an external magnetic field H, the NG mode is suppressed and an ordered pattern can be observed. By removing the suppression effect the ordered state relax to its original SMT pattern. We revealed two types of instability govern the relaxation process: the zigzag instability and the free rotation of wavevector q(r). This work is partially supported by Grant-in-Aid for Scientific Research (Nos. 20111003, 21340110, and 21540391) from the Ministry of Education, Culture, Sport, Science, and Technology of Japan and the Japan Society for the Promotion of Science (JSPS).
Chaos and microbial systems. Progress report, July 1989--July 1990
Kot, M.
1990-07-01
A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.
Nonlinear analysis and prediction of pulsatile hormone secretion
Prank, K. |; Kloppstech, M.; Nowlan, S.J.; Harms, H.M.; Brabant, G.; Hesch, R.; Sejnowski, T.J.
1996-06-01
Pulsatile hormone secretion is observed in almost every hormonal system. The frequency of episodic hormone release ranges from approximately 10 to 100 pulses in 24 hours. This temporal mode of secretion is an important feature of intercellular information transfer in addition to a dose-response dependent regulation. It has been demonstrated in a number of experiments that changes in the temporal pattern of pulsatile hormone secretion specifically regulate cellular and organ function and structure. Recent evidence links osteoporosis, a disease characterized by loss of bone mass and structure, to changes in the dynamics of pulsatile parathyroid hormone (PTH) secretion. In our study we applied nonlinear and linear time series prediction to characterize the secretory dynamics of PTH in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack periods of high predictability found in normal humans. In contrast to patients with osteoporosis patients with hyperparathyroidism, a condition which despite sometimes reduced bone mass has a preserved bone architecture, show periods of high predictability of PTH secretion. Using stochastic surrogate data sets which match certain statistical properties of the original time series significant nonlinear determinism could be found for the PTH time series of a group of healthy subjects. Using classical nonlinear analytical techniques we could demonstrate that the irregular pattern of pulsatile PTH secretion in healthy men exhibits characteristics of deterministic chaos. Pulsatile secretion of PTH in healthy subjects seems to be a first example of nonlinear determinism in an apparently irregular hormonal rhythm in human physiology. {copyright} {ital 1996 American Institute of Physics.}
Observation and Control of Hamiltonian Chaos in Wave-particle Interaction
Doveil, F.; Ruzzon, A.; Elskens, Y.
2010-11-23
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 field of electron devices and plasma physics.
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 field of electron devices and plasma physics.
Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure
NASA Technical Reports Server (NTRS)
Maestrello, L.
2000-01-01
Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.
Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence
NASA Technical Reports Server (NTRS)
Lipsitz, L. A.; Goldberger, A. L.
1992-01-01
The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.
Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul
2012-09-01
In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate. PMID:23020447
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper
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
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…
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…
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…
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
The capabilities of chaos and complexity.
Abel, David L
2009-01-01
To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. "System" will be rigorously defined. Can a low-informational rapid succession of Prigogine's dissipative structures self-order into bona fide organization? PMID:19333445
The Capabilities of Chaos and Complexity
Abel, David L.
2009-01-01
To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? PMID:19333445
Controlling chaos in a defined trajectory using adaptive fuzzy logic algorithm
NASA Astrophysics Data System (ADS)
Sadeghi, Maryam; Menhaj, Bagher
2012-09-01
Chaos is a nonlinear behavior of chaotic system with the extreme sensitivity to the initial conditions. Chaos control is so complicated that solutions never converge to a specific numbers and vary chaotically from one amount to the other next. A tiny perturbation in a chaotic system may result in chaotic, periodic, or stationary behavior. Modern controllers are introduced for controlling the chaotic behavior. In this research an adaptive Fuzzy Logic Controller (AFLC) is proposed to control the chaotic system with two equilibrium points. This method is introduced as an adaptive progressed fashion with the full ability to control the nonlinear systems even in the undertrained conditions. Using AFLC designers are released to determine the precise mathematical model of system and satisfy the vast adaption that is needed for a rapid variation which may be caused in the dynamic of nonlinear system. Rules and system parameters are generated through the AFLC and expert knowledge is downright only in the initialization stage. So if the knowledge was not assuring the dynamic of system it could be changed through the adaption procedure of parameters values. AFLC methodology is an advanced control fashion in control yielding to both robustness and smooth motion in nonlinear system control.
Regularly timed events amid chaos
NASA Astrophysics Data System (ADS)
Blakely, Jonathan N.; Cooper, Roy M.; Corron, Ned J.
2015-11-01
We show rigorously that the solutions of a class of chaotic oscillators are characterized by regularly timed events in which the derivative of the solution is instantaneously zero. The perfect regularity of these events is in stark contrast with the well-known unpredictability of chaos. We explore some consequences of these regularly timed events through experiments using chaotic electronic circuits. First, we show that a feedback loop can be implemented to phase lock the regularly timed events to a periodic external signal. In this arrangement the external signal regulates the timing of the chaotic signal but does not strictly lock its phase. That is, phase slips of the chaotic oscillation persist without disturbing timing of the regular events. Second, we couple the regularly timed events of one chaotic oscillator to those of another. A state of synchronization is observed where the oscillators exhibit synchronized regular events while their chaotic amplitudes and phases evolve independently. Finally, we add additional coupling to synchronize the amplitudes, as well, however in the opposite direction illustrating the independence of the amplitudes from the regularly timed events.
NASA Astrophysics Data System (ADS)
Gekelman, Walter; Dehaas, Tim; van Compernolle, Bart
2013-10-01
Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data. The permutation entropy can be calculated from the time series of the magnetic field data or flows is used to calculate the positions of the data on a Jensen Shannon complexity map. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. Other types of chaotic dynamical models (Gissinger , Lorentz and Henon) also fall on the map and can give a clue to the nature of the turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time, which reflects the change and possibly type of chaos associated with the ropes. Work sponsoerd by a LANL-UC grant and done at the Basic Plasma Science Facility (supported by DOE and NSF).
Control mechanisms for a nonlinear model of international relations
Pentek, A.; Kadtke, J.; Lenhart, S.; Protopopescu, V.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Analyzing Thought-related Electroencephalographic Data Using Nonlinear Techniques
NASA Technical Reports Server (NTRS)
Skidmore, Trent
1990-01-01
A unique method is presented for collecting, studying and interpreting thought-related electroencephalogram (EEG) data. The use of a chaos based nonlinear analysis technique is shown to be promising in providing insight into relating conscious thought to specific EEG data. A discussion of the practical limitations of this technique is also included.
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model
NASA Astrophysics Data System (ADS)
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.
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model
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
Vernon-Feagans, Lynne; Willoughby, Michael; Garrett-Peters, Patricia
2016-03-01
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 1,292 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 3 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 3 years of life, as well as EF skills, which were measured when children were 3 to 5 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. (PsycINFO Database Record PMID:26751500
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
Harmonic modulation instability and spatiotemporal chaos.
He, X T; Zheng, C Y; Zhu, S P
2002-09-01
It is shown from the conserved Zakharov equations that many solitary patterns are formed from the modulational instability of unstable harmonic modes that are excited by a perturbative wave number. Pattern selection in our case is discussed. It is found that the evolution of solitary patterns may appear in three states: spatiotemporal coherence, chaos in time but the partial coherence in space, and spatiotemporal chaos. The spatially partial coherent state is essentially due to ion-acoustic wave emission, while spatiotemporal chaos characterized by its incoherent patterns in both space and time is caused by collision and fusion among patterns in stochastic motion. So energy carried by patterns in the system is redistributed. PMID:12366301
Chaos-induced intensification of wave scattering.
Smirnov, I P; Virovlyansky, A L; Edelman, M; Zaslavsky, G M
2005-08-01
Sound-wave propagation in a strongly idealized model of the deep-water acoustic waveguide with a periodic range dependence is considered. It is investigated how the phenomenon of ray and wave chaos affects the sound scattering at a strong mesoscale inhomogeneity of the refractive index caused by the synoptic eddy. Methods derived in the theory of dynamical and quantum chaos are applied. When studying the properties of wave chaos we decompose the wave field into a sum of Floquet modes analogous to quantum states with fixed quasi-energies. It is demonstrated numerically that the "stable islands" from the phase portrait of the ray system reveal themselves in the coarse-grained Wigner functions of individual Floquet modes. A perturbation theory has been derived which gives an insight into the role of the mode-medium resonance in the formation of Floquet modes. It is shown that the presence of a weak internal-wave-induced perturbation giving rise to ray and wave chaos strongly increases the sensitivity of the monochromatic wave field to an appearance of the eddy. To investigate the sensitivity of the transient wave field we have considered variations of the ray travel times--arrival times of sound pulses coming to the receiver through individual ray paths--caused by the eddy. It turns out that even under conditions of ray chaos these variations are relatively predictable. This result suggests that the influence of chaotic-ray motion may be partially suppressed by using pulse signals. However, the relative predictability of travel time variations caused by a large-scale inhomogeneity is not a general property of the ray chaos. This statement is illustrated numerically by considering an inhomogeneity in the form of a perfectly reflecting bar. PMID:16196683
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.
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.
Wave chaos in rapidly rotating stars.
Lignires, Franois; Georgeot, Bertrand
2008-07-01
The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system. PMID:18764043
Chaos Based Secure IP Communications over Satellite DVB
NASA Astrophysics Data System (ADS)
Caragata, Daniel; El Assad, Safwan; Tutanescu, Ion; Sofron, Emil
2010-06-01
The Digital Video Broadcasting—Satellite (DVB-S) standard was originally conceived for TV and radio broadcasting. Later, it became possible to send IP packets using encapsulation methods such as Multi Protocol Encapsulation, MPE, or Unidirectional Lightweight Encapsulation, ULE. This paper proposes a chaos based security system for IP communications over DVB-S with ULE encapsulation. The proposed security system satisfies all the security requirements while respecting the characteristics of satellite links, such as the importance of efficient bandwidth utilization and high latency time. It uses chaotic functions to generate the keys and to encrypt the data. The key management is realized using a multi-layer architecture. A theoretical analysis of the system and a simulation of FTP and HTTP traffic are presented and discussed to show the cost of the security enhancement and to provide the necessary tools for security parameters setup.
Socioeconomic Adversity and Women's Sleep: Stress and Chaos as Mediators.
El-Sheikh, Mona; Keiley, Margaret; Bagley, Erika J; Chen, Edith
2015-11-01
We examined income-to-needs ratio, perceived economic well-being, and education and their relations with European and African American women's sleep (n = 219). Sleep was examined through actigraphy and self-reports. Income-to-needs ratio was related to sleep minutes. Perceived economic well-being and education were associated with subjective sleep problems. Perceived stress mediated relations between both income-to-needs ratio and economic well-being and subjective sleep problems. Chaos emerged as a mediator linking income-to-needs ratio and subjective sleep problems. African American women had fewer sleep minutes and lower sleep efficiency than European Americans, and more robust relations between economic well-being and stress was observed for European Americans. Findings highlight the importance of economic adversity for women's sleep and explicate some pathways of risk. PMID:25115947
AIDS in India: constructive chaos?
Chatterjee, A
1991-08-01
Until recently, the only sustained AIDS activity in India has been alarmist media attention complemented by occasional messages calling for comfort and dignity. Public perception of the AIDS epidemic in India has been effectively shaped by mass media. Press reports have, however, bolstered awareness of the problem among literate elements of urban populations. In the absence of sustained guidance in the campaign against AIDS, responsibility has fallen to voluntary health activists who have become catalysts for community awareness and participation. This voluntary initiative, in effect, seems to be the only immediate avenue for constructive public action, and signals the gradual development of an AIDS network in India. Proceedings from a seminar in Ahmedabad are discussed, and include plans for an information and education program targeting sex workers, health and communication programs for 150 commercial blood donors and their agents, surveillance and awareness programs for safer blood and blood products, and dialogue with the business community and trade unions. Despite the lack of coordination among volunteers and activists, every major city in India now has an AIDS group. A controversial bill on AIDS has ben circulating through government ministries and committees since mid-1989, a national AIDS committee exists with the Secretary of Health as its director, and a 3-year medium-term national plan exists for the reduction of AIDS and HIV infection and morbidity. UNICEF programs target mothers and children for AIDS awareness, and blood testing facilities are expected to be expanded. The article considers the present chaos effectively productive in forcing the Indian population to face up to previously taboo issued of sexuality, sex education, and sexually transmitted disease. PMID:12284225
Feigenbaum Graphs: A Complex Network Perspective of Chaos
Luque, Bartolo; Lacasa, Lucas; Ballesteros, Fernando J.; Robledo, Alberto
2011-01-01
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos. PMID:21915254
Feigenbaum graphs: a complex network perspective of chaos.
Luque, Bartolo; Lacasa, Lucas; Ballesteros, Fernando J; Robledo, Alberto
2011-01-01
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos. PMID:21915254
Prospects for chaos control of machine tool chatter
Hively, L.M.; Protopopescu, V.A.; Clapp, N.E.; Daw, C.S.
1998-06-01
The authors analyze the nonlinear tool-part dynamics during turning of stainless steel in the nonchatter and chatter regimes, toward the ultimate objective of chatter control. Their previous work analyzed tool acceleration in three dimensions at four spindle speeds. In the present work, the authors analyze the machining power and obtain nonlinear measures of this power. They also calculate the cycle-to-cycle energy for the turning process. Return maps for power cycle times do not reveal fixed points or (un)stable manifolds. Energy return maps do display stable and unstable directions (manifolds) to and from an unstable period-1 orbit, which is the dominant periodicity. Both nonchatter and chatter dynamics have the unusual feature of arriving at the unstable period-1 fixed point and departing from that fixed point of the energy return map in a single step. This unusual feature makes chaos maintenance, based on the well-known Ott-Grebogi-Yorke scheme, a very difficult option for chatter suppression. Alternative control schemes, such as synchronization of the tool-part motion to prerecorded nonchatter dynamics or dynamically damping the period-1 motion, are briefly discussed.
Deterministic Chaos in the X-ray Sources
NASA Astrophysics Data System (ADS)
Grzedzielski, M.; Sukova, P.; Janiuk, A.
2015-12-01
Hardly any of the observed black hole accretion disks in X-ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the quasi-periodic oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binary variabilities. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the surrogate series. We analyze here the data of two X-ray binaries - XTE J1550-564 and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leading to the possible instability of an accretion disk. The thermal-viscous instability and fluctuations around the fixed-point solution occurs at high accretion rate, when the radiation pressure gives dominant contribution to the stress tensor.
Nonlinear Dynamics of a Diffusing Interface
NASA Technical Reports Server (NTRS)
Duval, Walter M. B.
2001-01-01
Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.
Nonlinear Dynamics of Electronic Systems - Proceedings of the Workshop Ndes '93
NASA Astrophysics Data System (ADS)
Davies, A. C.; Schwarz, W.
1994-04-01
The Table of Contents for the book is as follows: * Editors' Preface * CHUA'S CIRCUIT -- ANALYSIS AND APPLICATIONS * Recent Generalisations of Chua's Circuit * Realisations of Chua's Circuit * From Chua's Circuit to Chua's Oscillator: A Picture Book of Attractors * A Simple Explanation of the Physical Behaviour of Chua's Circuit or A Route to the Hearts of Chua's Circuit * Chaos Control Techniques: A Study Using Chua's Circuit * Stochastic Properties of Signals Generated by Chua's Circuit * ANALYSIS AND METHODS * Contemporary Problems in Dynamical Chaos * Methods of Global Bifurcation Analysis and Applications to Nonlinear Circuits * Geometrical Analysis of the Behaviour of Third-Order Digital Filters * Identification of the Irregular Behaviour in Nonlinear Electrical Circuits by the Time Series Method * Investigations to the Influence of Noise on the Irregular Behaviour of Nonlinear Dynamical Circuits and Systems * On Integration of Nonlinear Dynamics of Large Electrical Power Systems * NEURAL NETWORKS * Complex Dynamics in Cellular Neural Networks * Polynomial Cellular Neural Network: A New Dynamical Circuit for Pattern Recognition * Wave Propagation in Arrays of Active Nonlinear Circuits * A Noise Generator Based on Chaos for a Neural Network Application * PHENOMENA AND APPLICATIONS * Synchronization of Chaotic Signals * Experimental Demonstration of Binary Chaos-Shift-Keying Using Self-Synchronising Chua's Circuits * Two Simulation Experiments in Chaotic Synchronization * Chaotic Bridges -- A New Concept for High Sensitive Devices * Hyperchaos and Related Phenomena from Odd-Dimensional Hysteresis System * The Role of Chaos in a Gyrotron-Type of Interaction * Chaos and Regularity in a Ferroelectric Duffing-Like Oscillator * Acquisition Properties and Chaotic Behaviour of the Sampling Phase-Locked Loop * Generating Low Frequency Noise Using a Chaotic Circuit * DESIGN OF CHAOTIC SYSTEMS * Chaos and Pseudorandomness * Digital Counters and Pseudorandom Number Generators from a Perspective of Dynamics * VLSI-Design of a Reconfigurable Pseudorandom Number Generator * VLSI Design of Chaotic Circuits * Integrated Realization of Analogue Systems with Chaotic Behaviour * Author Index * Subject Index
Universal learning network and its application to chaos control.
Hirasawa, K; Wang, X; Murata, J; Hu, J; Jin, C
2000-03-01
Universal Learning Networks (ULNs) are proposed and their application to chaos control is discussed. ULNs provide a generalized framework to model and control complex systems. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. Therefore, physical systems, which can be described by differential or difference equations and also their controllers, can be modeled in a unified way, and so ULNs may form a super set of neural networks and fuzzy neural networks. In order to optimize the ULNs, a generalized learning algorithm is derived, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. These algorithms for calculating the derivatives are extended versions of Back Propagation Through Time (BPTT) and Real Time Recurrent Learning (RTRL) of Williams in the sense that generalized node functions, generalized network connections with multi-branch of arbitrary time delays, generalized criterion functions and higher order derivatives can be deal with. As an application of ULNs, a chaos control method using maximum Lyapunov exponent of ULNs is proposed. Maximum Lyapunov exponent of ULNs can be formulated by using higher order derivatives of ULNs, and the parameters of ULNs can be adjusted so that the maximum Lyapunov exponent approaches the target value. From the simulation results, it has been shown that a fully connected ULN with three nodes is able to display chaotic behaviors. PMID:10935763
Chaos motion in robot manipulators
NASA Technical Reports Server (NTRS)
Lokshin, A.; Zak, M.
1987-01-01
It is shown that a simple two-link planar manipulator exhibits a phenomenon of global instability in a subspace of its configuration space. A numerical example, as well as results of a graphic simulation, is given.
Order, chaos and nuclear dynamics: An introduction
Swiatecki, W.J.
1990-08-01
This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs.
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.
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
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,
Applying Chaos Theory to School Reform.
ERIC Educational Resources Information Center
Wertheimer, Richard; Zinga, Mario
1998-01-01
Presents a case study of the ideology, strategies and process of the "Common Knowledge: Pittsburgh" project in its attempt at school reform in an urban school district. Reflects on the project's activities, and uses its experience to develop a conceptual framework based on chaos theory, as developed in mathematics and science, for discussing
Studies on Educational Reconstruction of Chaos Theory.
ERIC Educational Resources Information Center
Duit, Reinders; Komorek, Michael; Wilbers, Jens
1997-01-01
Critically analyzes the core ideas of chaos theory to determine whether they are worth teaching and explores the accessibility of these ideas for students. The studies are embedded in a Model of Educational Reconstruction which seeks to bring science content structure concerns and educational concerns into balance and interaction with one another.
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
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,…
Applying Chaos Theory to School Reform.
ERIC Educational Resources Information Center
Wertheimer, Richard; Zinga, Mario
1998-01-01
Presents a case study of the ideology, strategies and process of the "Common Knowledge: Pittsburgh" project in its attempt at school reform in an urban school district. Reflects on the project's activities, and uses its experience to develop a conceptual framework based on chaos theory, as developed in mathematics and science, for discussing…
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…
Neural control: Chaos control sets the pace
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2010-03-01
Even simple creatures, such as cockroaches, are capable of complex responses to changes in their environment. But robots usually require complicated dedicated control circuits to perform just a single action. Chaos control theory could allow simpler control strategies to realize more complex behaviour.
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…
Exponential sensitivity and chaos in quantum systems
NASA Astrophysics Data System (ADS)
Blmel, R.
1994-07-01
Exponential sensitivity and chaos can occur in quantum systems. An example is the propagation of spin-1/2 particles through a spin-precession apparatus consisting of a chain of magnetic field sections arranged spatially in a Fibonacci-like sequence. It is shown that the quantum propagation in this apparatus is as chaotic as Arnol'ds' cat map.
NASA Technical Reports Server (NTRS)
2005-01-01
[figure removed for brevity, see original site]
The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.
This false color image of a portion of the Iani Chaos region was collected during the Southern Fall season.
Image information: VIS instrument. Latitude -2.6 Longitude 342.4 East (17.6 West). 36 meter/pixel resolution.
Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.
NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Cantrell, John H. Yost, William T.; Adler, Laszlo
2015-02-15
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.
Cantrell, John H; Adler, Laszlo; Yost, William T
2015-02-01
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5?MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2?nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported. PMID:25725651
NASA Astrophysics Data System (ADS)
Cantrell, John H.; Adler, Laszlo; Yost, William T.
2015-02-01
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.
Simulation of stochastic systems via polynomial chaos expansions and convex optimization
NASA Astrophysics Data System (ADS)
Fagiano, Lorenzo; Khammash, Mustafa
2012-09-01
Polynomial chaos expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and nontrivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allows to take into account the specific features of polynomial chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated in the approach by means of convex constraints. We show the effectiveness of the proposed technique in three applications in diverse fields, including the analysis of a nonlinear electric circuit, a chaotic model of organizational behavior, and finally a chemical oscillator.
Fractal geometry and chaos theory: Their application in the Earth sciences
Barton, C.C. )
1990-11-01
Fractal geometry and chaos theory are major advances over previous methods for quantifying complex pattern encountered in nature. They provide methods for quantifying complex patterns encountered in nature. They provide methods for creating highly complex, detailed, and accurate synthetic analogs of natural systems. They redefine the way we think mathematically about the behavior of natural systems, much as the theory of relatively brought a deeper level of understanding to physics. Like other branches of mathematics, they do not necessarily provide a physical or mechanistic understanding. However, in natural systems, fractal behavior often breaks down or changes to a different fractal dimension at scales where the physical changes. Systems and processes that exhibit fractal scaling, such as earthquakes, have been shown to be self-organized critical phenomena, which means that they internally establish their own dynamically stable critical points and transfer energy on cascading fractal structures. A challenge for the future will be to develop methods to go from a fractal pattern in nature to its governing nonlinear iterated equation. The use of fractal geometry and chaos theory in the earth sciences has increased greatly in the past five years. Fractal geometry and chaos theory are redefining the way that they conceptualize, measure, and model natural systems in the earth sciences.
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
Nonlinear analysis of irregular animal vocalizations.
Tokuda, Isao; Riede, Tobias; Neubauer, Jrgen; Owren, Michael J; Herzel, Hanspeter
2002-06-01
Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos. PMID:12083224
NASA Astrophysics Data System (ADS)
Shevtsov, Maxim A.; Nikolaev, Boris P.; Ryzhov, Vyacheslav A.; Yakovleva, Ludmila Y.; Dobrodumov, Anatolii V.; Marchenko, Yaroslav Y.; Margulis, Boris A.; Pitkin, Emil; Guzhova, Irina V.
2015-08-01
Brain tumor targeting efficiency and biodistribution of the superparamagnetic nanoparticles conjugated with heat shock protein Hsp70 (SPION-Hsp70) were evaluated in experimental glioma model. Synthesized conjugates were characterized using the method of longitudinal nonlinear response of magnetic nanoparticles to a weak ac magnetic field with measurements of second harmonic of magnetization (NLR-M2). Cellular interaction of magnetic conjugates was analyzed in 9L glioma cell culture. The biodistribution of the nanoparticles and their accumulation in tumors was assessed by the latter approach as well. The efficacy of Hsp70-conjugates for contrast enhancement in the orthotopic model of 9L glioma was assessed by MR imaging (11 T). Magnetic nanoparticles conjugated with Hsp70 had the relaxivity properties of the MR-negative contrast agents. Morphological observation and cell viability test demonstrated good biocompatibility of Hsp70-conjugates. Analysis of the T2-weighted MR scans in tumor-bearing rats demonstrated the high efficacy of Hsp70-conjugates in contrast enhancement of the glioma in comparison to non-conjugated nanoparticles. High contrast enhancement of the glioma was provided by the accumulation of the SPION-Hsp70 particles in the glioma tissue (as shown by the histological assay). Biodistribution analysis by NLR-M2 measurements evidenced the many-fold increase (~40) in the tumor-to-normal brain uptake ratio in the Hsp70-conjugates treated animals. Biodistribution pattern of Hsp70-decorated nanoparticles differed from that of non-conjugated SPIONs. Coating of the magnetic nanoparticles with Hsp70 protein enhances the tumor-targeting ability of the conjugates that could be applied in the MR imaging of the malignant brain tumors.
A novel 2D wavelength-time chaos code in optical CDMA system
NASA Astrophysics Data System (ADS)
Zhang, Qi; Xin, Xiangjun; Wang, Yongjun; Zhang, Lijia; Yu, Chongxiu; Meng, Nan; Wang, Houtian
2012-11-01
Two-dimensional wavelength-time chaos code is proposed and constructed for a synchronous optical code division multiple access system. The access performance is compared between one-dimensional chaos code, WDM/chaos code and the proposed code. Comparison shows that two-dimensional wavelength-time chaos code possesses larger capacity, better spectral efficiency and bit-error ratio than WDM/chaos combinations and one-dimensional chaos code.
Luo, Shaohua; Wu, Songli; Gao, Ruizhen
2015-07-01
This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation. PMID:26232953
NASA Astrophysics Data System (ADS)
Luo, Shaohua; Wu, Songli; Gao, Ruizhen
2015-07-01
This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.
Asymptotic average shadowing property, almost specification property and distributional chaos
NASA Astrophysics Data System (ADS)
Wang, Lidong; Wang, Xiang; Lei, Fengchun; Liu, Heng
2016-01-01
It is proved that a nontrivial compact dynamical system with asymptotic average shadowing property (AASP) displays uniformly distributional chaos or distributional chaos in a sequence. Moreover, distributional chaos in a system with AASP can be uniform and dense in the measure center, that is, there is an uncountable uniformly distributionally scrambled set consisting of such points that the orbit closure of every point contains the measure center. As a corollary, the similar results hold for the system with almost specification property.
Theoretical models for chronotherapy: periodic perturbations in funnel chaos type.
Betancourt-Mar, Juvencio Alberto; Nieto-Villar, Jose Manuel
2007-04-01
In this work, the Rssler system is used as a model for chrono therapy. We applied a periodic perturbation to the y variable to take the Rssler system from a chaotic behavior to a simple periodic one, varying the period and amplitude of forcing. Two types of chaos were considered, spiral and funnel chaos. As a result, the periodical windows reduced their areas as the funnel chaos character increased in the system. Funnel chaos, in this chrono therapy model, could be considered as a later state of a dynamical disease, more irregular and difficult to suppress. PMID:17658922
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.
Comments on microcausality, chaos, and gravitational observables
NASA Astrophysics Data System (ADS)
Marolf, Donald
2015-12-01
Observables in gravitational systems must be non-local so as to be invariant under diffeomorphism gauge transformations. But at the classical level some such observables can nevertheless satisfy an exact form of microcausality. This property is conjectured to remain true at all orders in the semiclassical expansion, though with limitations at finite ? or {{\\ell }}{Planck}. We also discuss related issues concerning observables in black hole spacetimes and comment on the senses in which they do and do not experience the form of chaos identified by Shenker and Stanford. In particular, in contrast to the situation in a reflecting cavity, this chaos does not afflict observables naturally associated with Hawking radiation for evaporating black holes.
Chaos in a Hydraulic Control Valve
NASA Astrophysics Data System (ADS)
Hayashi, S.; Hayase, T.; Kurahashi, T.
1997-08-01
In this paper we have studied the instability and chaos occurring in a pilot-type poppet valve circuit. The system consists of a poppet valve, an upstream plenum chamber, a supply pipeline and an orifice inserted between the pelnum and the pipeline. Although the poppet valve rests on the seat stably for a supply pressure lower than the cracking pressure, the circuit becomes unstable for an initial disturbance beyond a critical value and develops a self-excited vibration. In this unstable region, chaotic vibration appears at the period-doubling bifurcation. We have investigated the stability of the circuit and the chaotic phenomenon numerically, and elucidated it by power spectra, a bifurcation diagram and Lyapunov exponent calculations, showing that the phenomenon follows the Feigenbaum route to chaos.Copyright 1997 Academic Press Limited
Experimental chaos detection in the Duffing oscillator
NASA Astrophysics Data System (ADS)
Eyebe Fouda, J. S. Armand; Bodo, Bertrand; Djeufa, Guy M. D.; Sabat, Samrat L.
2016-04-01
This paper presents a comparative study of four algorithms namely the maximal Lyapunov exponent (MLE), 0-1 test, conditional entropy of ordinal patterns (CPE) and recently developed permutation largest slope entropy (PLSE) algorithm for experimental chaos detection in the Duffing oscillator. We consider an electrical model of the Duffing oscillator and its equivalent electronic circuit for generating the data to validate the effectiveness of the algorithms. The performance of the PLSE is compared with the 0-1 test and the CPE algorithms on the data set obtained from the simulated circuit; and with the MLE for the data collected from the experimental circuit. The experimental data are acquired using a digital oscilloscope with 1 MHz sampling frequency. From the comparison of the experimental spectra of the four methods with the analog phase portraits of the real system, it appears that the PLSE is the more reliable algorithm for chaos detection from experimental data.
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.
Estimating model parameters by chaos synchronization.
Tao, Chao; Zhang, Yu; Du, Gonghuan; Jiang, Jack J
2004-03-01
Using chaos synchronization and a proposed iterative method of parameter adaptation, we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters. This parameter adaptation method can be applied to a spatiotemporal chaotic system with a one-way-coupled map lattice. As a biomedical application, this method is capable of estimating the asymmetric tension parameter of a vocal fold model. PMID:15089389
Chaos and Coarse Graining in Statistical Mechanics
NASA Astrophysics Data System (ADS)
Castiglione, Patrizia; Falcioni, Massimo; Lesne, Annick; Vulpiani, Angelo
2008-08-01
1. Basic concepts of dynamical systems theory; 2. Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond; 3. Coarse graining, entropies and Lyapunov exponents at work; 4. Foundation of the statistical mechanics and dynamical systems; 5. On the origin of irreversibility; 6. The role of chaos in non-equilibrium statistical mechanics; 7. Coarse-graining equations in complex systems; 8. Renormalization-group approaches; Index.
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.
Controlling spatiotemporal chaos in coupled map lattices
Zhu, KaiEn; Chen, Tianlun
2001-06-01
A simple method is presented for controlling spatiotemporal chaos in coupled map lattices to a homogeneous state. This method can be applied to many kinds of models such as coupled map lattices (CML), one-way open CML (the open-flow model), and globally coupled map. We offer the stability analysis of the homogeneous state. Simple and sufficient conditions are obtained for controlling the above mentioned models. Our theoretical results agree well with numerical simulations.
Detecting chaos in irregularly sampled time series.
Kulp, C W
2013-09-01
Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars. PMID:24089946
Chaos, dynamical structure and climate variability
Stewart, H.B.
1995-09-01
Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.
Investigating chaos in river stage and discharge time series
NASA Astrophysics Data System (ADS)
Khatibi, Rahman; Sivakumar, Bellie; Ghorbani, Mohammad Ali; Kisi, Ozgur; Koak, Kasim; Farsadi Zadeh, Davod
2012-01-01
SummaryThe existence of chaotic behaviour in the river stage and discharge time series observed at the Sogutluhan hydrometric station, Turkey, is investigated. Five nonlinear dynamic methods are employed: (1) phase space reconstruction; (2) False Nearest Neighbour (FNN) algorithm; (3) correlation dimension method; (4) Lyapunov exponent method; and (5) local approximation method. These methods have their bases on data embedding, nearest neighbour search, dimensionality analysis, system divergence/convergence, and local approximation and have varying levels of sophistication in conceptualisation and implementation. They provide either direct identification of chaotic behaviour or at least facilitate identification through system reconstruction, complexity determination (especially in terms of dimensionality), and prediction (including predictability horizon). As the discharge data used in this study are produced by rating directly gauged stage time series, it becomes feasible to investigate any interference triggered by chaotic signals with the rating. The results indicate the existence of low-dimensional chaos in the two time series. They also suggest that the rating of the stage time series to obtain the discharge time series amplifies significantly the fluctuations in the latter in the presence of chaotic signals.
Chaos synchronization by resonance of multiple delay times
NASA Astrophysics Data System (ADS)
Martin, Manuel Jimenez; D'Huys, Otti; Lauerbach, Laura; Korutcheva, Elka; Kinzel, Wolfgang
2016-02-01
Chaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single-delay networks, the number of synchronized sublattices is determined by the greatest common divisor (GCD) of the network loop lengths. We demonstrate analytically the GCD condition in networks of iterated Bernoulli maps with multiple delay times and complement our analytic results by numerical phase diagrams, providing parameter regions showing complete and sublattice synchronization by resonance for Tent and Bernoulli maps. We compare networks with the same GCD with single and multiple delays, and we investigate the sensitivity of the correlation to a detuning between the delays in a network of coupled Stuart-Landau oscillators. Moreover, the GCD condition also allows detection of time-delay resonances, leading to high correlations in nonsynchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators.
Stabilization of stochastic cycles and control of noise-induced chaos
NASA Astrophysics Data System (ADS)
Bashkirtseva, Irina
2014-04-01
We consider a nonlinear control system forced by stochastic disturbances. The problem addressed is a design of the feedback regulator which stabilizes a limit cycle of the closed-loop deterministic system and synthesizes a required dispersion of random states of the forced cycle for the corresponding stochastic system. To solve this problem, we develop a method based on the stochastic sensitivity function technique. The problem of a synthesis of the required stochastic sensitivity for cycles by feedback regulators is reduced to the solution of the linear algebraic equation for the gain matrix of the regulator. For this matrix, in the general n-dimensional case, a full parametric representation is found. An attractive case of nonlinear 3D systems which exhibit both regular and chaotic regimes is studied in detail. To construct a regulator, we use a new technique based on a singular decomposition of the assigned stochastic sensitivity matrix. Explicit formulas for parameters of this regulator synthesizing the required stochastic sensitivity for 3D-cycle are obtained. The constructiveness of the developed theory is shown on the example of the stabilization of the cycle for stochastic Lorenz model which exhibits a noise-induced transition to chaos. Using our technique for this model we provide a required small sensitivity for stochastically forced cycle and suppress chaos successfully.
Mixed-mode oscillations and chaos in return maps of an oscillatory chemical reaction
NASA Astrophysics Data System (ADS)
Blagojević, S. N.; Čupić, Ž.; Ivanović-Šašić, A.; Kolar-Anić, Lj.
2015-12-01
The return maps, as an element of mathematical phenomenology appropriate for general examinations of complex dynamic states of the oscillatory systems were used to detect and explain the evolution of mixed-mode oscillations and chaos in a six-dimensional nonlinear reaction system of the Bray-Liebhafsky (BL) reaction, a well-studied nonlinear chemical reaction system that exhibits complex dynamic behavior. For this purpose principally different Poincaré sections were applied and different transition scenarios between periodic and aperiodic states were examined by numerical simulations. It is shown that emergence of new periodic patterns can be detected by return maps already within chaotic windows. Besides, we also show that the higher dimensionality of manifold gives the impression of having several layers of manifolds.
Implications of chaos, scale-invariance, and fractal statistics in geology
NASA Technical Reports Server (NTRS)
Turcotte, D. L.
1990-01-01
A set of three nonlinear total differential equations (Lorenz equations) exhibiting deterministic chaos is considered, and it is shown that these equations demonstrate that deterministic equations with deterministic initial conditions can yield stocastic solutions with fractal statistics. The logistic map, fractal distributions, and fragmentation are discussed. It is pointed out that well-defined fractal distributions of earthquakes are found both regionally and globally, and that the general applicability of the fractal relation for seismicity can provide the basis for a quantitative seismic hazard assessment. It is suggested that the governing physics of erosional topography is nonlinear and may be related to a fractal distribution of storms and floods that generate and renew erosional feature such as gullies and drainage systems.
A new method for line spectra reduction similar to generalized synchronization of chaos
NASA Astrophysics Data System (ADS)
Yu, Xiang; Zhu, Shijian; Liu, Shuyong
2007-10-01
Line spectra in the radiated noise of marine vessels are the most visible signs, which can be detected, tracked and identified by enemy's passive sonar, and hence it is of great significance to reduce the line spectra for improving the acoustic stealth of marine vessels. In this paper, a driving parameter scheme using an external chaotic signal to drive a nonlinear vibration isolation system (VIS) of onboard machinery is presented to make the chaotic motion in the nonlinear VIS persistent, which is similar to generalized synchronization of chaos in some sense. In this way, the line spectra in the radiated noise can be reduced effectively because the response spectrum of a chaotic system under harmonic excitations is a continuous and reduced one. Numerical simulations are carried out and the results confirm the effectiveness of this method. The maximum conditional Lyapunov exponent is calculated numerically and its negative value indicates the stability of this driving parameter control scheme.
Adaptive anti control of chaos for robot manipulators with experimental evaluations
NASA Astrophysics Data System (ADS)
Moreno-Valenzuela, Javier
2013-01-01
Roughly speaking, anti control of chaos consists in injecting a chaotic behavior to a system by means of a control scheme. This note introduces a new scheme to solve the anti control of chaos for robot manipulators. The proposed controller uses an adaption law to estimate the robot parameters on line. Thus, the controller does not require any knowledge of the physical parameters of the manipulator, such as masses, lengths of the links, moments of inertia, etc. The new scheme is based in the velocity field control paradigm, hence the specification of a chaotic system to define a desired velocity field is required. Experimental results in a two degrees-of-freedom direct-drive robot illustrate the practical feasibility of the introduced theory. In order to achieve anti control of chaos of our experimental system, two different chaotic attractors are used: the Genesio-Tesi system and a Jerk-type system. Results showed that the controller is able to inject the chaotic behavior to the robot while the robot parameters are estimated on line.
Chaos and order in non-integrable model field theories
Campbell, D.K.; Peyrard, M.
1989-01-01
We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.
NASA Astrophysics Data System (ADS)
Badea, Cristian; Gordon, Richard
2004-04-01
Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction.
Badea, Cristian; Gordon, Richard
2004-04-21
Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction. PMID:15152685
Nonlinear Control of Heart Rate Variability in Human Infants
NASA Astrophysics Data System (ADS)
Sugihara, George; Allan, Walter; Sobel, Daniel; Allan, Kenneth D.
1996-03-01
Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation >= 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation <= 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A. L., Rigney, D. R. & West, B. J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.
Nonlinear control of heart rate variability in human infants.
Sugihara, G; Allan, W; Sobel, D; Allan, K D
1996-01-01
Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation greater than or equal to 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation > or = to 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A.L., Rigney, D.R. & West, B.J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states. PMID:8637921
Nonlinear deterministic modeling of highly varying loads
O`Neill-Carrillo, E.; Heydt, G.T.; Kostelich, E.J.; Venkate, S.S.; Sundaram, A.
1999-04-01
Typically, the modeling of highly varying, nonlinear loads such as electric arc furnaces has involved stochastic techniques. This paper presents the use of chaotic dynamics to describe the operation of nonlinear loads. Included is a discussion of the Lyapunov exponents, a measure of chaotic behavior. The alternate approach is applied to electric arc furnaces. A tuning mode is described to develop the parameters of a chaotic model. This model is trained to have time and frequency responses that are tuned to match the current from the arc furnace under study. The simulated data are compared to actual arc furnace data to validate the model. This model is used to assess the impact of various highly varying nonlinear loads that exhibit chaos in power systems.
Quantum manifestations of classical nonlinear resonances
NASA Astrophysics Data System (ADS)
Wisniacki, Diego A.; Schlagheck, Peter
2015-12-01
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
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
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
Analysis of Discovery of Chaos: Social and Cognitive Aspects.
ERIC Educational Resources Information Center
Kim, J. B.
The purpose of this study was to examine Edward Lorenz's psychological processes and other environmental aspects in the discovery of chaos at that time. The general concept of chaos is discussed based on relations with previous scientific theories such as Newtonian physics and quantum mechanics. The constraints of discovery in terms of available
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
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
Master Teachers: Making a Difference on the Edge of Chaos
ERIC Educational Resources Information Center
Chapin, Dexter
2008-01-01
The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…
The Chaos Theory of Careers: A User's Guide
ERIC Educational Resources Information Center
Bright, Jim E. H.; Pryor, Robert G. L.
2005-01-01
The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…
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…
Chaos formation by sublimation of volatile-rich substrate: Evidence from Galaxias Chaos, Mars
NASA Astrophysics Data System (ADS)
Pedersen, G. B. M.; Head, J. W.
2011-01-01
Galaxias Chaos deviates significantly from other chaotic regions due to the lack of associated outflow channels, lack of big elevation differences between the chaos and the surrounding terrain and due to gradual trough formation. A sequence of troughs in different stages is observed, and examples of closed troughs within blocks suggest that the trough formation is governed by a local stress field rather than a regional stress field. Moreover, geomorphic evidence suggests that Galaxias Chaos is capped by Elysium lavas, which superpose an unstable subsurface layer that causes chaotic tilting of blocks and trough formation. Based on regional mapping we suggest a formation model, where Vastitas Borealis Formation embedded between Elysium lavas is the unstable subsurface material, because gradual volatile loss causes shrinkage and differential substrate movement. This process undermines the lava cap, depressions form and gradually troughs develop producing a jigsaw puzzle of blocks due to trough coalescence. Observations of chaos west of Elysium Rise indicate that this process might have been widespread along the contact between Vastitas Borealis Formation and Elysium lavas. However, the chaotic regions have probably been superposed by Elysium/Utopia flows to the NW of Elysium Rise, and partly submerged with younger lavas to the west.
Ferroelectrics Nonlinearity to Realize Chaotic Circuits
NASA Astrophysics Data System (ADS)
Fortuna, L.; Frasca, M.; Graziani, S.
2003-08-01
In this paper the possibility of observing chaotic behaviour in an electronic circuit including a nonlinear ferroelectrics has been investigated. The ferroelectrics constitutes the medium interposed between the two plates of a capacitor, and is obtained by successive vapour deposition of Strontium, Tantalum and Bismuth on Platinum substrates in small areas. The device is characterized by a nonlinear hysteretic behaviour observed by estimating the output voltage by using a Sawyer-Tower configuration. Different circuits showing chaos and based on hysteretic behaviour of the nonlinearities have been reported in literature. In particular, in the circuit reported in [1] the nonlinearity consists of a piecewise linear resistor, only the two tracts with positive slope are effectively involved in the dynamics and an hysteretic behaviour switching between these two linear segments of the nonlinearity can be addressed as responsible of the emergence of iperchaos in the circuit. Starting from the chaos generator reported in [1], the following dimensionless equations have been developed: where f(x) is the nonlinearity due to the hysteresis of the ferroelectrics capacitor. The functional f(x) constitutes a simple model of the ferroelectrics device and is defined by two functions (the upper curve and the lower curve based on experimental data on the ferroelectrics). Chaotic solutions of system (1) were searched for, by performing numerical integration with respect to different values of the parameters. Finally, the circuit implementing equations (1) has been realized. Experimental results show that for a suitable range of parameter a chaotic attractor emerges. Fig. 1 shows the projection of the attractor onto the phase plane x1-x2. The paper addresses the possibility of exploiting the rich dynamics of ferroelectrics hysteresis to obtain new chaotic attractors with low cost circuits.
NASA Astrophysics Data System (ADS)
Yu, Zu-Guo; Xiao, Qian-Jun; Shi, Long; Yu, Jun-Wu; Vo, Anh
2010-06-01
Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation (CGR) of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq (analogous to specific heat) curves to be meaningful. Furthermore, the Dq curves of the measure μ based on their CGRs for different orders to link the functional protein sequences are almost identical if q >= 0. Finally, the Cq curves of all linked functional proteins resemble a classical phase transition at a critical point.
Detecting and disentangling nonlinear structure from solar flux time series
NASA Technical Reports Server (NTRS)
Ashrafi, S.; Roszman, L.
1992-01-01
Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.
Exploring Information Chaos in Community Pharmacy Handoffs
Chui, Michelle A; Stone, Jamie A
2013-01-01
Background A handoff is the process of conveying necessary information in order to transfer primary responsibility for providing safe and effective drug therapy to a patient from one community pharmacist to another, typically during a shift change. The handoff information conveyed in pharmacies has been shown to be unstructured and variable, leading to pharmacist stress and frustration, prescription delays, and medication errors. Objective The purpose of this study was to describe and categorize the information hazards present in handoffs in community pharmacies. Methods A qualitative research approach was used to elicit the subjective experiences of community pharmacists. Community pharmacists who float or work in busy community pharmacies were recruited and participated in a face to face semi-structured interview. Using a systematic content data analysis, the study identified five categories of information hazards that can lead to information chaos, a framework grounded in human factors and ergonomics. Results Information hazards including erroneous information and information overload, underload, scatter, and conflict, are experienced routinely by community pharmacists during handoff communication and can result in information chaos. The consequences of information chaos include increased mental workload, which can precipitate problematic prescriptions falling between the cracks. This can ultimately impact patient care and pharmacist quality of working life. Conclusions The results suggest that handoffs in community pharmacies result in information hazards. These information hazards can distract pharmacists from their primary work of assessing prescriptions and educating their patients. Further research on how handoffs are conducted can produce information on how hazards in the system can be eliminated. PMID:23665076
Beyond Benford's Law: Distinguishing Noise from Chaos
Li, Qinglei; Fu, Zuntao; Yuan, Naiming
2015-01-01
Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly. PMID:26030809
Topological organization of (low-dimensional) chaos
Tufillaro, N.B.
1992-12-01
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with &ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series.
Topological organization of (low-dimensional) chaos
Tufillaro, N.B.
1992-01-01
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series.
Chaos in classical D0-brane mechanics
NASA Astrophysics Data System (ADS)
Gur-Ari, Guy; Hanada, Masanori; Shenker, Stephen H.
2016-02-01
We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We verify that these approach a smooth limit as N → ∞. We show that a classical analog of scrambling occurs with fast scrambling scaling, t ∗ ˜ log S. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.
The Curious Shorelines of Gorgonum Chaos
NASA Technical Reports Server (NTRS)
Howard, A. D.; Moore, J. M.
2003-01-01
Level, bench-like platforms in the interior of the Gorgonum Chaos basin appear to be shorelines associated with an ancient lake. These shorelines, however, seem to lack the typical features of shorelines associated with wave and current transport and erosion, such as crescentic embayments, spits, barrier islands, and wave-cut cliffs. Rather, the lakefacing platform edges are commonly rounded and cumulate in planform, often evenly encircling presumed islands. We interpret these shorelines to have been formed by outward growth in a quiescent environment, possibly in ice-covered bodies of water and possibly, in part, as chemical precipitates.
Large fluctuations and nonlinear dynamics of birhythmicity
NASA Astrophysics Data System (ADS)
Kar, S.; Ray, D. S.
2004-07-01
Birhythmicity, which arises due to the simultaneous existence of two stable limit cycles, has been shown to be an interesting dynamical scenario in chemical reactions and biology. Here we present an extension of the Decroly-Goldbeter model for birhythmicity in glycolysis within a Hamiltonian structure incorporating the stochastic substrate injection rate, the critical controlling factor in glycolytic oscillations. Our analysis reveals several generic features of nonlinear dynamics of birhythmicity in the weak-noise limit, e.g., crossover of birhythmicity to monorhythmic behaviour, period-doubling bifurcations leading to chaos and noise-induced transition between attractors.
Study of nonlinear dynamics in magnetron by using circuitry model
NASA Astrophysics Data System (ADS)
Li, Daohui; Chen, Xiaodong
2012-03-01
A circuitry model is established to study the nonlinear dynamics of magnetron through solving a third order differential equation. The steady, oscillatory oscillation and even chaotic state have been observed when changing different control parameters, i.e., the anode current and the load. The observation of the anode current increase causing the magnetron to operate in chaos agrees well to that in the experiments conducted by other researchers.
Generalized synchronization of chaos in autonomous systems.
Alvarez-Llamoza, O; Cosenza, M G
2008-10-01
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other, but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables. Nor does it need to be active for all times for achieving generalized synchronization. The procedure is based on an analogy between a response map subject to an external drive acting with a probability p and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems. PMID:18999517
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.
RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM
Deck, Katherine M.; Winn, Joshua N.; Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin; Agol, Eric; Lissauer, Jack J.
2012-08-10
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only {approx}10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first-order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for {approx}4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large-scale orbital instabilities on the timescale of our integrations ({approx}200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.
Responses of spatiotemporal chaos to oscillating forces.
Iino, Misato; Hidaka, Yoshiki; Nugroho, Fahrudin; Anugraha, Rinto; Okabe, Hirotaka; Hara, Kazuhiro
2015-07-01
The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, M(p)(t), which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, M(p)(t) oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of M(p)(t) to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of M(p)(t) contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of M(p)(t). PMID:26274256
A New Approach for Controlling Chaos in Lorenz System
NASA Astrophysics Data System (ADS)
Sanayei, Ali
2009-09-01
Is there a need for chaos? In order to answer to this important question, first, we should answer to "what chaos is?" Does "chaos" mean anarchy and confusion, or it means "randomness"? In order to answer to the second question, one may briefly consider that "chaos" means "far from the equilibrium." It is true that in a random behavior, we have "far from the equilibrium" phenomenon, but in the chaotic behavior, however, the trajectory goes far from the equilibrium, but it moves in a bounded basin. Therefore, chaos differs from randomness. In order to answer to the first question, we distinguish two states from each other. Chaos could be dangerous in many states, e.g. for an aircraft in the sky. Therefore, we should control it and return the system from the chaotic mood. But, in some states it is useful. Suppose that we have a periode-2 behavior system. If we intend to change its period, what should we do? One of the best techniques in order to change a system behavior is reaching the system into the chaotic mood for a short time, and then, by controlling chaos which is based on the feedback law, we could return the system into the desired period. Further, the control of chaos is also a way to manipulate the natural systems that are already chaotic. In this paper, we can imagine each mentioned states for chaos. Our goal is the control of a very famous system in the chaotic mood, in order to stabilize it and change its behavior into the desired behavior. We will achieved to this goal using OGY method which is based on the discrete dynamical system concept, and find the stabilized state by a new approach which is based on the generalized Routh-Hurwitz criterion.
Wave analysis of ray chaos in underwater acoustics.
Sundaram, Bala; Zaslavsky, G. M.
1999-06-01
The dispersion of a wave packet in an acoustic medium is considered in the paraxial wave approximation, where the effective potential, due to variation of the speed of propagation, varies both with depth and propagation distance. The analysis of the resulting parabolic equation, similar to the Schrodinger equation, clearly demonstrates the role of ray chaos in enhancing the dispersion of the initial packet. However, wave coherence effects are also seen that suppress the effects of the ray chaos in a manner analogous to the effects of quantum chaos. (c) 1999 American Institute of Physics. PMID:12779844
Theory of the nucleus as applied to quantum chaos
Bunakov, V. E.
2014-12-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.
Error function attack of chaos synchronization based encryption schemes.
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. PMID:15003053
OPEN PROBLEM: Some open questions in 'wave chaos'
NASA Astrophysics Data System (ADS)
Nonnenmacher, Stéphane
2008-08-01
The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal.
Geometric criterion for chaos in collective dynamics of nuclei
NASA Astrophysics Data System (ADS)
Strnsk, Pavel; Cejnar, Pavel
2015-11-01
A local geometrical criterion for chaos, based on an embedding of a Hamiltonian system into an appropriately chosen curved space, is applied in the classical version of the Geometric Collective Model of nuclei. The criterion is shown to be equivalent with a simpler indicator of chaos based on the convexconcave change of equipotential curves. It is tested by comparing its predictions with a detailed numerical analysis of global dynamics. The results indicate a capacity of the method to estimate the energy of the onset of chaos, but also demonstrate convincing counterexamples that disprove its general applicability.
NASA Astrophysics Data System (ADS)
Zhang, Yu; Tao, Chao; Jiang, Jack J.
2006-06-01
In this paper, we apply an iterative parameter adaption scheme based on chaos synchronization to estimate system parameters of the asymmetric vocal folds from glottal area time series. The original asymmetric vocal-fold system associated with recurrent laryngeal paralysis shows chaotic vibrations with positive Lyapunov exponents. Aperiodic glottal area time series from the original system will be applied as the feedback variable coupling the simulative and the original vocal-fold systems. The parameter adaption technique based on chaos synchronization is employed to manipulate the simulative system parameters. The chaotic vibrations, system parameters, and the bifurcation diagram of the original vocal-fold system can be exactly reproduced in the simulative system, and the two chaotic systems can be synchronized. Furthermore, the effects of noise, sampling rate, and equation difference due to nonlinear spring terms on vocal-fold parameter estimations are investigated. Despite large noise perturbations, large equation differences, and low sampling rate, the parameter adaption scheme can effectively estimate the original vocal-fold system parameters. This study provides a theoretical base to apply chaos synchronization to estimate the vocal-fold system parameters from the glottal area data and show its potential application in laryngeal physiology.
Tyson, Reny B; Nowacek, Douglas P; Miller, Patrick J O
2007-09-01
Nonlinear phenomena or nonlinearities in animal vocalizations include features such as subharmonics, deterministic chaos, biphonation, and frequency jumps that until recently were generally ignored in acoustic analyses. Recent documentation of these phenomena in several species suggests that they may play a communicative role, though the exact function is still under investigation. Here, qualitative descriptions and quantitative analyses of nonlinearities in the vocalizations of killer whales (Orcinus orca) and North Atlantic right whales (Eubalaena glacialis) are provided. All four nonlinear features were present in both species, with at least one feature occurring in 92.4% of killer and 65.7% of right whale vocalizations analyzed. Occurrence of biphonation varied the most between species, being present in 89.0% of killer whale vocalizations and only 20.4% of right whale vocalizations. Because deterministic chaos is qualitatively and quantitatively different than random or Gaussian noise, a program (TISEAN) designed specifically to identify deterministic chaos to confirm the presence of this nonlinearity was used. All segments tested in this software indicate that both species do indeed exhibit deterministic chaos. The results of this study provide confirmation that such features are common in the vocalizations of cetacean species and lay the groundwork for future studies. PMID:17927399
The Induction of Chaos in Electronic Circuits Final Report-October 1, 2001
R.M.Wheat, Jr.
2003-04-01
This project, now known by the name ''Chaos in Electronic Circuits,'' was originally tasked as a two-year project to examine various ''fault'' or ''non-normal'' operational states of common electronic circuits with some focus on determining the feasibility of exploiting these states. Efforts over the two-year duration of this project have been dominated by the study of the chaotic behavior of electronic circuits. These efforts have included setting up laboratory space and hardware for conducting laboratory tests and experiments, acquiring and developing computer simulation and analysis capabilities, conducting literature surveys, developing test circuitry and computer models to exercise and test our capabilities, and experimenting with and studying the use of RF injection as a means of inducing chaotic behavior in electronics. An extensive array of nonlinear time series analysis tools have been developed and integrated into a package named ''After Acquisition'' (AA), including capabilities such as Delayed Coordinate Embedding Mapping (DCEM), Time Resolved (3-D) Fourier Transform, and several other phase space re-creation methods. Many computer models have been developed for Spice and for the ATP (Alternative Transients Program), modeling the several working circuits that have been developed for use in the laboratory. And finally, methods of induction of chaos in electronic circuits have been explored.
Chaos and microbial systems. Final project report, July 1989--July 1992
Kot, M.
1992-10-01
The field of nonlinear dynamics has generated a variety of new techniques for identifying order in seemingly chaotic systems. These techniques have led to new insights for several ecological and epidemiological systems, most notably childhood disease epidemics. To better test the efficacy and relevance of these new techniques to population biology research with two components namely a mathematical analysis of some simple microbial models with chaotic dynamics; and experimental (chemostat) population studies to evaluate the accuracy of these models. I have completed a thorough analysis of the forced double-Monod model and of the phase-locking route to chaos that it exhibits. I have also analyzed a simpler pulsed system with mass action kinetics and a period-doubling route to chaos. This research also motivated detailed analyses of discrete-time predator-prey and dispersal models, and a fast new method for computing fractal dimension. My colleagues and I have assembled a complete laboratory system to determine the appropriateness of the forced double-Monod model. We have tested assays for concentration and density and have performed a variety of diagnostic tests on this system. We have measured growth parameters for bacteria and for protozoa in chemostat.
Observation of Hamiltonian chaos and its control in wave particle interaction
NASA Astrophysics Data System (ADS)
Doveil, F.; Macor, A.; Assi, 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.
Probability density of the empirical wavelet coefficients of a noisy chaos
NASA Astrophysics Data System (ADS)
Garcin, Matthieu; Guégan, Dominique
2014-05-01
We are interested in the random empirical wavelet coefficients of a noisy signal when this signal is a unidimensional or multidimensional chaos. More precisely we provide an expression of the conditional probability density of such coefficients, given a discrete observation grid. The noise is assumed to be described by a symmetric alpha-stable random variable. If the noise is a dynamic noise, then we present the exact expression of the probability density of each wavelet coefficient of the noisy signal. If we face a measurement noise, then the noise has a non-linear influence and we propose two approximations. The first one relies on a Taylor expansion whereas the second one, relying on an Edgeworth expansion, improves the first general Taylor approximation if the cumulants of the noise are defined. We give some illustrations of these theoretical results for the logistic map, the tent map and a multidimensional chaos, the Hénon map, disrupted by a Gaussian or a Cauchy noise.
Mono- & Polyhydrated Sulfates in Aureum Chaos
NASA Technical Reports Server (NTRS)
2008-01-01
This image of layered deposits in Aureum Chaos was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on June 6, 2007 at 0347 UTC (11:47 p.m. EDT on June 5, 2007), near 3.5 degrees south latitude, 333.25 degrees east longitude. The CRISM 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 just over 10 kilometers (6 miles) wide at its narrowest point.
Aureum Chaos lies in the eastern part of the Valles Marineris canyon system, southwest of a 280 kilometer (174 mile) diameter, highly modified impact crater called Aram Chaos. Both regions hold examples of chaotic terrain that is characterized by randomly oriented, large-scale mesas and knobs. In this region of Mars, these features range in size from a few kilometers to tens of kilometers wide and tend to be heavily eroded. As its name implies, chaotic terrain is extremely irregular. It is most likely the result of collapsed surface material that settled when subsurface ice, water, or magma 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 cover an area riddled with knobs. The lower two images were constructed by draping CRISM images over topography and exaggerating the vertical scale to better illustrate the region's topography. The upper right is an infrared, false color image that reveals layered deposits of a light-colored material along the flanks of several knobs. The lower-left image reveals the mineralogical composition of these layers, with yellow representing monohydrated sulfates (sulfates with one water molecule incorporated into each molecule of the mineral) and blue polyhydrated sulfates (sulfates with multiple waters per mineral molecule). There are two possible explanations for the compositional banding. The first is deposition of mono- and polyhydrated sulfates in alternating layers. The second is deposition of just one sulfate type, and subsequently its alteration by weathering at the exposed, eroded surface. Further observations will better determine the origin of these complex banded sulfate deposits.
CRISM is one of six science instruments on NASA's Mars Reconnaissance Orbiter. Led by The Johns Hopkins University Applied Physics Laboratory, Laurel, Md., the CRISM team includes expertise from universities, government agencies and small businesses in the United States and abroad. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Mars Reconnaissance Orbiter and the Mars Science Laboratory for NASA's Science Mission Directorate, Washington. Lockheed Martin Space Systems, Denver, built the orbiter.
Extension of spatiotemporal chaos in glow discharge-semiconductor systems
Akhmet, Marat 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 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).].
The rate of entropy increase at the edge of chaos
NASA Astrophysics Data System (ADS)
Latora, V.; Baranger, M.; Rapisarda, A.; Tsallis, C.
2000-08-01
Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This connection is here generalized to a simple dissipative system, the logistic map, and especially to the chaos threshold of the latter, the edge of chaos. It is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon entropy is not appropriate. Instead, the non-extensive entropy Sq?(1-?i=1W piq)/(q-1), must be used. The latter contains a parameter /q, the entropic index which must be given a special value q*?1 (for /q=1 one recovers the usual entropy) characteristic of the edge-of-chaos under consideration. The same q* enters also in the description of the sensitivity to initial conditions, as well as in that of the multifractal spectrum of the attractor.
Quantum chaos in the Lorenz equations with symmetry breaking
Sarkar, S.; Satchell, J.S.
1987-01-01
The role of phase diffusion for quantum chaos in the quantum-mechanical model of the laser in the Haken limit is discussed. Fractal properties of the support of the asymptotic attracting probability distribution for the system are studied.
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
Filtering with Marked Point Process Observations via Poisson Chaos Expansion
Sun Wei; Zeng Yong; Zhang Shu
2013-06-15
We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.
A simple guide to chaos and complexity
Rickles, Dean; Hawe, Penelope; Shiell, Alan
2007-01-01
The concepts of complexity and chaos are being invoked with increasing frequency in the health sciences literature. However, the concepts underpinning these concepts are foreign to many health scientists and there is some looseness in how they have been translated from their origins in mathematics and physics, which is leading to confusion and error in their application. Nonetheless, used carefully, complexity science has the potential to invigorate many areas of health science and may lead to important practical outcomes; but if it is to do so, we need the discipline that comes from a proper and responsible usage of its concepts. Hopefully, this glossary will go some way towards achieving that objective. PMID:17933949
Rocks Exposed on Slope in Aram Chaos
NASA Technical Reports Server (NTRS)
2003-01-01
MGS MOC Release No. MOC2-550, 20 November 2003
This spectacular vista of sedimentary rocks outcropping on a slope in Aram Chaos was acquired by the Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) on 14 November 2003. Dark piles of coarse talus have come down the slopes as these materials continue to erode over time. Note that there are no small meteor impact craters in this image, indicating that erosion of these outcrops has been recent, if not on-going. This area is located near 2.8oS, 20.5oW. The 200 meter scale bar is about 656 feet across. Sunlight illuminates the scene from the lower right.
A simple guide to chaos and complexity.
Rickles, Dean; Hawe, Penelope; Shiell, Alan
2007-11-01
The concepts of complexity and chaos are being invoked with increasing frequency in the health sciences literature. However, the concepts underpinning these concepts are foreign to many health scientists and there is some looseness in how they have been translated from their origins in mathematics and physics, which is leading to confusion and error in their application. Nonetheless, used carefully, "complexity science" has the potential to invigorate many areas of health science and may lead to important practical outcomes; but if it is to do so, we need the discipline that comes from a proper and responsible usage of its concepts. Hopefully, this glossary will go some way towards achieving that objective. PMID:17933949
Deterministic chaos in accreting neutron star systems
NASA Astrophysics Data System (ADS)
Morfill, G. E.; Atmanspacher, H.; Demmel, V.; Scheingraber, H.; Voges, W.
This review contains a brief introduction to the terminology of deterministic chaos, and a summary of important properties and definitions of strange attractors. A method is described how to reconstruct the attractor from experimental data. Using synthetic data, the specific problems associated with the reconstruction are examined. As an observational example, analysis of data from the accreting neutron star system Her X-1 is described. Finally, the authors discuss the physical interpretation of these observations, the possible implications for the description of the system from a general point of view, the specific implication for the pulse shape and pulse to pulse variations, and possible approaches towards a better understanding of both accretion disc and accretion column.
Emergence of chaos in interacting communities
NASA Astrophysics Data System (ADS)
Ostilli, M.; Figueiredo, W.
2014-10-01
We introduce a simple dynamical model of two interacting communities whose elements are subject to stochastic discrete-time updates governed by only bilinear interactions. When the intra- and inter-couplings are cooperative, the two communities reach asymptotically an equilibrium state. However, when the intra- or inter-couplings are anti-cooperative, the system may remain in perpetual oscillations and, when the coupling values belong to certain intervals, two possible scenarios arise, characterized either by erratic aperiodic trajectories and high sensitiveness to small changes of the couplings, or by chaotic trajectories and bifurcation cascades. Quite interestingly, we find out that even a moderate consensus in one single community can remove the chaos. Connections of the model with interacting stock markets are discussed.
Food chain chaos due to transcritical point
NASA Astrophysics Data System (ADS)
Deng, Bo; Hines, Gwendolen
2003-06-01
Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincar map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincar map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.
Secure communication based on spatiotemporal chaos
NASA Astrophysics Data System (ADS)
Ren, Hai-Peng; Bai, Chao
2015-08-01
In this paper, we propose a novel approach to secure communication based on spatiotemporal chaos. At the transmitter end, the state variables of the coupled map lattice system are divided into two groups: one is used as the key to encrypt the plaintext in the N-shift encryption function, and the other is used to mix with the output of the N-shift function to further confuse the information to transmit. At the receiver end, the receiver lattices are driven by the received signal to synchronize with the transmitter lattices and an inverse procedure of the encoding is conducted to decode the information. Numerical simulation and experiment based on the TI TMS320C6713 Digital Signal Processor (DSP) show the feasibility and the validity of the proposed scheme. Project supported by the National Natural Science Foundation of China (Grant No. 61172070) and the Funds from the Science and Technology Innovation Team of Shaanxi Province, China (Grant No. 2013CKT-04).
Noodle-map chaos - A simple example
NASA Astrophysics Data System (ADS)
Roessler, O. E.; Hudson, J. L.; Farmer, J. D.
Chaos-generating folded two-dimensional maps can be generalized to higher dimensions in two ways: as folded-towel (or pancake) maps and as bent-walking-stick (or noddle) maps. The noodle case is of mathematical interest because the topologically one-dimensional attractors involved may, despite their thinness, be of the 'non-sink' type (that is, stand in a bijective relation to their domain of attraction). Moreover, Shtern recently showed that the well-known Kaplan-Yorke conjecture on the fractal dimensionality of chaotic attractors may fail in the case of noodle maps. We present here an explicit 3-variable noodle map with constant divergence (constant Jacobian determinant). The example is a higher analogue to the Henon diffeomorphism. A map of similar shape was recently found experimentally by Rob Shaw in a study of the irregularly dripping faucet.
Philosophical perspectives on quantum chaos: Models and interpretations
NASA Astrophysics Data System (ADS)
Bokulich, Alisa Nicole
2001-09-01
The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.
Chaos And Noise-driven Emergence Of Order From Disorder
NASA Astrophysics Data System (ADS)
Bucolo, Maide; Caponetto, Riccardo; Fortuna, Luigi; Frasca, Mattia; Rizzo, Alessandro
2005-11-01
This paper investigates several case studies in which noise signals or random sequences play an important role in the emergence of a self-organized behaviour or a paradoxal behaviour. We considered the effects induced by using either a chaotic signal instead of noise or a chaotic sequence instead of a random one. We show that in many cases noise and chaos have similar effects and in some cases chaos work better than noise.
Different routes from a matter wavepacket to spatiotemporal chaos
Rong Shiguang; Hai Wenhua; Xie Qiongtao; Zhong Honghua
2012-09-15
We investigate the dynamics of a quasi-one-dimensional Bose-Einstein condensate confined in a double-well potential with spatiotemporally modulated interaction. A variety of phenomena is identified in different frequency regimes, including the self-compression, splitting, breathing-like, and near-fidelity of the matter wavepacket, which are associated with different routes for the onset of spatiotemporal chaos. The results also reveal that chaos can retain space-inversion symmetry of the system.
Chaos in axially symmetric potentials with octupole deformation
Heiss, W.D.; Nazmitdinov, R.G.; Radu, S. Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049, Madrid )
1994-04-11
Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.
Generalized spectral decomposition for stochastic nonlinear problems
Nouy, Anthony Le Maitre, Olivier P.
2009-01-10
We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.
Particle chaos and pitch angle scattering
NASA Technical Reports Server (NTRS)
Burkhart, G. R.; Dusenbery, P. B.; Speiser, T. W.
1995-01-01
Pitch angle scattering is a factor that helps determine the dawn-to-dusk current, controls particle energization, and it has also been used as a remote probe of the current sheet structure. Previous studies have interpreted their results under the exception that randomization will be greatest when the ratio of the two timescales of motion (gyration parallel to and perpendicular to the current sheet) is closet to one. Recently, the average expotential divergence rate (AEDR) has been calculated for particle motion in a hyperbolic current sheet (Chen, 1992). It is claimed that this AEDR measures the degree of chaos and therefore may be thought to measure the randomization. In contrast to previous expectations, the AEDR is not maximized when Kappa is approximately equal to 1 but instead increases with decreasing Kappa. Also contrary to previous expectations, the AEDR is dependent upon the parameter b(sub z). In response to the challenge to previous expectations that has been raised by this calculation of the AEDR, we have investigated the dependence of a measure of particle pitch angle scattering on both the parameters Kappa and b(sub z). We find that, as was previously expected, particle pitch angle scattering is maximized near Kappa = 1 provided that Kappa/b(sub z) greater than 1. In the opposite regime, Kappa/b(sub z) less than 1, we find that particle pitch angle scattering is still largest when the two timescales are equal, but the ratio of the timescales is proportional to b(sub z). In this second regime, particle pitch angle scattering is not due to randomization, but is instead due to a systematic pitch angle change. This result shows that particle pitch angle scattering need not be due to randomization and indicates how a measure of pitch angle scattering can exhibit a different behavior than a measure of chaos.
Chaos and dynamics of spinning particles in Kerr spacetime
NASA Astrophysics Data System (ADS)
Han, Wenbiao
2008-09-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.
NASA Astrophysics Data System (ADS)
Hu, Jian; Liu, Long; Ma, Da-wei
2014-12-01
The permanent-magnet synchronous motor (PMSM) system, which is a nonlinear dynamic system, will demonstrate a variety of chaotic phenomena when its parameters or external inputs fall into a certain area, which will lead to a deterioration of its performance. Thus, chaos should be suppressed or eliminated. In this paper, the property of equilibrium points is analyzed, and the condition for the occurrence of a Hopf bifurcation in a PMSM system is given based on a mathematical model of the PMSM system with a bifurcation diagram, a Lyapunov exponent map and phase plane diagrams given. After the drawbacks of the existing control methods have been analyzed, a robust nonlinear feedback controller is designed to control the chaos in the PMSM system with a load torque disturbance. The object is to eliminate the chaos and to drive the system speed to a desired value, Numerical simulation proves the validity of this control method.
De, Sudipto K; Aluru, N R
2005-05-27
In this Letter, the formation of complex oscillations of the type 2n M oscillations per period at the Mth superharmonic excitation is reported for electrostatic microelectromechanical systems. A dc bias (beyond "dc symmetry breaking") and an ac signal (at the Mth superharmonic frequency) with an amplitude around "ac symmetry breaking" gives rise to M oscillations per period or period M response. On increasing the ac voltage, a cascade of period doubling bifurcations take place giving rise to 2n M oscillations per period. An interesting chaotic transition (1-band and 2-band chaos) is observed during the first period doubling bifurcation. The nonlinear nature of the electrostatic force is shown to be responsible for the reported observations. PMID:16090253