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.
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2001-02-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
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:…
Chaos Theory: Implications for Nonlinear Dynamics in Counseling.
ERIC Educational Resources Information Center
Stickel, Sue A.
The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…
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
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.
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…
Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.
ERIC Educational Resources Information Center
Raw, Cecil J. G.; Stacey, Larry M.
1989-01-01
Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…
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.
Nonlinear system vibration---The appearance of chaos
Hunter, N.F. Jr.
1990-01-01
This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.
Nonlinear Perspectives on Family Process: Chaos and Catastrophe Theories.
ERIC Educational Resources Information Center
Ward, Margaret; Koopmans, Matthijs
This paper explores the principal features of nonlinear dynamical systems and applies the theory to parents' acceptance of a child adopted at an older age. Although family systems theories tend to be weak in addressing family change, chaos theory and catastrophe theory allow consideration of sudden, discontinuous change. If stable, the family may…
The edge of chaos: A nonlinear view of psychoanalytic technique.
Galatzer-Levy, Robert M
2016-04-01
The field of nonlinear dynamics (or chaos theory) provides ways to expand concepts of psychoanalytic process that have implications for the technique of psychoanalysis. This paper describes how concepts of "the edge of chaos," emergence, attractors, and coupled oscillators can help shape analytic technique resulting in an approach to doing analysis which is at the same time freer and more firmly based in an enlarged understanding of the ways in which psychoanalysis works than some current recommendation about technique. Illustrations from a lengthy analysis of an analysand with obsessive-compulsive disorder show this approach in action. PMID:27030426
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.
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.
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.
Shear-induced chaos in nonlinear Maxwell-model fluids.
Goddard, Chris; Hess, Ortwin; Balanov, Alexander G; Hess, Siegfried
2008-02-01
A generalized model for the behavior of the stress tensor in non-Newtonian fluids is investigated for spatially homogeneous plane Couette flow, showing a variety of nonlinear responses and deterministic chaos. Mapping of chaotic solutions is achieved through the largest Lyapunov exponent for the two main parameters: The shear rate and the temperature and/or density. Bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found. Suggested mechanisms for stability loss in these complex fluids include Hopf, saddle-node, and period-doubling bifurcations. PMID:18352126
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
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems
NASA Astrophysics Data System (ADS)
Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios
2015-11-01
We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.
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.
BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns
NASA Astrophysics Data System (ADS)
Grammaticos, B.
2004-02-01
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on `chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: `why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely `Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter. Moreover the relaxed, not too formal, style makes for easy reading. Given that I am writing this review just a few days before Christmas I cannot help thinking that this book could be a nice present for a physicist.
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)
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
2012-01-01
We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for hypothesis 1, and consistent with hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PMID:22563703
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
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).
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…
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)…
IUTAM chaos `97 - symposium on new applications of nonlinear and chaotic dynamics in mechanics
1997-12-31
It will be nearly twenty years since Feigenbaum`s landmark papers on period doubling and the modern beginnings of what is now called {open_quotes}Chaos Theory{close_quotes} in the popular press. From the very beginning, mechanics has been a central focus for modern nonlinear dynamical systems, from Lorenz`s pioneering work in 1963 on Rayleigh-Benard flow, to Holmes` theory of strange attractors in the buckling of structures in 1978. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the new {open_quotes}chaos theory{close_quotes} a mark of credibility, importance, and relevance that its earlier sister catastrophe theory did not achieve. The fact that mechanics straddles both physics and engineering also meant that mechanics became a pathway for direct application of chaos theory to applied problems such as aeroelastic instabilities, ship capsize, rattling and impact in machines, cable dynamics and many others. These applications were the subject of numerous conferences including two predecessors to this Symposium, Stuttgart in 1989 and London in 1993. This document contains abstracts of reports which were presented at the International Union of Theoretical and Applied Mechanics Symposium on Applications of Nonlinear and Chaotic Dynamics in Mechanics. Individual reports have been processed separately for the United States Department of Energy databases.
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}
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.
Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
NASA Astrophysics Data System (ADS)
Farshidianfar, A.; Saghafi, A.
2014-10-01
In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems.
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.
On cascades of bifurcations leading to chaos in several nonlinear dissipative systems of ODEs
NASA Astrophysics Data System (ADS)
Trebler, Andrey A.
2010-10-01
This paper considers several nonlinear dissipative systems of ordinary differential equations. The studied systems undergo a full analysis of corresponding singular points on a whole set of parameters' values variation. Specifically, types of singular points, boarders of stability regions, as well as presented local bifurcations, are determined. By using numerical methods a consideration of scenarios of transition to chaos in these systems with one bifurcation parameter variation is held. The aim of this research is a confirmation of a Feigenbaum-Sharkovskii-Magnitskii mechanism of transition to chaos unique for all dissipative systems of ODEs. As the result of analysis of one of the systems the lack of any chaotic behavior is shown with the help of Poincare sections.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Kinugawa, Hikaru; Ueda, Kazuhiro; Gotoda, Hiroshi
2015-11-01
We numerically study the nonlinear dynamics of flame front instability induced by radiative heat loss on the basis of dynamical systems theory. Our previous studies have shown that the radiative heat loss significantly produces the deterministic chaos of flame front temperature fluctuations throughout the period-doubling bifurcation known as Feigenbaum scenario, while its short-term behavior can be predicted using a local and global nonlinear predictors. The present study reports that the similar kind of bifurcation process clearly appears at the fuel concentration, and that the fuel concentration dynamics in the well-developed chaos region is much more complicated than that of the flame front temperature. Recurrence quatification analysis we adopted in the present study can quantify the significant changes in the dynamics in the chaos region that cannot be capture in the bifurcation diagram.
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.
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects.
Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu
2009-01-01
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340
Watts, C.A.
1993-09-01
In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
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.
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)
Blakely, Jonathan; Corron, Ned; Hayes, Scott; Pethel, Shawn
2007-03-01
Chaos is usually attributed only to nonlinear systems. Yet it was recently shown that chaotic waveforms can be synthesized by linear superposition of randomly polarized basis functions. The basis function contains a growing oscillation that terminates in a large pulse. We show that this function is easily realized when viewed backward in time as a pulse followed by ringing decay. Consequently, a linear filter driven by random pulses outputs a waveform that, when viewed backward in time, exhibits essential qualities of chaos, i.e. determinism and a positive Lyapunov exponent. This phenomenon suggests that chaos may be connected to physical theories whose framework is not that of a deterministic dynamical system. We demonstrate that synthesizing chaos requires a balance between the topological entropy of the random source and the dissipation in the filter. Surprisingly, using different encodings of the random source, the same filter can produce both Lorenz-like and R"ossler-like waveforms. The different encodings can be viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing the Lorenz and R"ossler paradigms of nonlinear dynamics. Thus, the language of deterministic chaos provides a useful description for a class of signals not generated by a deterministic system.
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.
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
Nonlinear inverse synthesis technique for optical links with lumped amplification.
Le, Son Thai; Prilepsky, Jaroslaw E; Turitsyn, Sergei K
2015-04-01
The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless path-averaged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital back-propagation. PMID:25968670
Chaos-based communications at high bit rates using commercial fibre-optic links.
Argyris, Apostolos; Syvridis, Dimitris; Larger, Laurent; Annovazzi-Lodi, Valerio; Colet, Pere; Fischer, Ingo; García-Ojalvo, Jordi; Mirasso, Claudio R; Pesquera, Luis; Shore, K Alan
2005-11-17
Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10(-7). The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions. PMID:16292256
Chaos-based communications at high bit rates using commercial fibre-optic links
NASA Astrophysics Data System (ADS)
Argyris, Apostolos; Syvridis, Dimitris; Larger, Laurent; Annovazzi-Lodi, Valerio; Colet, Pere; Fischer, Ingo; García-Ojalvo, Jordi; Mirasso, Claudio R.; Pesquera, Luis; Shore, K. Alan
2005-11-01
Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10-7. The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.
NASA Astrophysics Data System (ADS)
Hamid, Reza Abbasi; Ahmad, Gholami; Seyyed, Hamid Fathi; Ataollah, Abbasi
2014-01-01
In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester (MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation (PDB), saddle node bifurcation (SNB), Hopf bifurcation (HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.
Non-Linear Dynamics and Control of Chaos for a Tachometer
NASA Astrophysics Data System (ADS)
GE, Z.-M.; SHIUE, J.-S.
2002-06-01
The dynamic behaviors of a rotational tachometer with vibrating support are studied in the paper. Both analytical and computational results are used to obtain the characteristics of the system. The Lyapunov direct method is applied to obtain the conditions of stability of the equilibrium position of the system. The center manifold theorem determines the conditions of stability for the system in a critical case. By applying various numerical analyses such as phase plane, Poincaré map and power spectrum analysis, a variety of periodic solutions and phenomena of the chaotic motion are observed. The effects of the changes of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. By using Lyapunov exponents and Lyapunov dimensions, the periodic and chaotic behaviors are verified. Finally, various methods, such as the addition of a constant torque, the addition of a periodic torque, delayed feedback control, adaptive control, Bang-Bang control, optimal control and the addition of a periodic impulse are used to control chaos effectively.
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.
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.
Vibration and chaos control of non-linear torsional vibrating systems
NASA Astrophysics Data System (ADS)
El-Bassiouny, A. F.
2006-07-01
Vibration of a mechanical system is often an undesirable phenomenon, as it may cause damage, disturbance, discomfort and, sometimes, destruction of systems and structures. To reduce vibration, many methods can be used. The most famous method is using dynamic absorbers or dampers. In the present work, a non-linear elastomeric damper or absorber is used to control the torsional vibrations of the crankshaft in internal combustion engines, when subjected to both external and parametric excitation torques. The multiple time scale perturbation method is applied to determine the equations governing the modulation of both amplitudes and phases of the crankshaft and the absorber. These equations are used to determine the steady-state amplitudes and system stability. Numerical integration of the basic equations is applied to investigate the effects of the different parameters on system behavior. A comparison is made with the available published work. Some recommendations are given at the end of the work.
Tél, Tamás
2015-09-01
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion. PMID:26428572
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.
Chaos in driven Alfven systems
NASA Technical Reports Server (NTRS)
Hada, T.; Kennel, C. F.; Buti, B.; Mjolhus, E.
1990-01-01
The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.
Analysis of nonlinear vibration of a motor linkage mechanism system with composite links
NASA Astrophysics Data System (ADS)
Li, Zhaojun; Cai, Ganwei; Huang, Qibai; Liu, Shiqing
2008-04-01
This paper studies the nonlinear vibration of a three-phase AC motor-linkage mechanism system with links fabricated from three-dimensional braided composite materials. Taking the drive motor and the linkage mechanism as an integrated system, the dynamic equations of the system are established by the finite element method. The relation between the nonlinear vibration of the system and the parameters of the system is obtained by the method of multiple scales. Results show that not only the structural parameters, but also the electromagnetic parameters and the material parameters have significant effects on the nonlinear vibration of the system. Finally, a numerical example is presented.
ERIC Educational Resources Information Center
Jones, Rebecca
1994-01-01
In "Thriving on Chaos," author Tom Peters suggests that future managers will need the quick reactions of video game players. Patient observation may work better. Chaos theory teaches that random happenings cannot be controlled; the toughest, randomly caused problems have no solutions; a leader's vision or moral code cannot be imposed on others;…
NASA Astrophysics Data System (ADS)
Náraigh, LennonÓ
2015-08-01
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal nonlinear system that not only highlights the phenomena of linear transient growth, subcritical transition and global modes, but is also of potential interest in its own right in the field of nonlinear optics. The second is the fairly familiar inhomogeneous nonlinear complex Ginzburg-Landau (CGL) equation. The two-level model is exactly solvable for the nonlinear global mode and its stability, while for the spatially-extended CGL equation, perturbative solutions for the global mode and its stability are presented, valid for inhomogeneities with arbitrary scales of spatial variation and global modes of small amplitude, corresponding to a scenario near criticality. For other scenarios, a numerical iterative nonlinear eigenvalue technique is preferred. Two global modes of different amplitudes are revealed in the numerical approach. For both the two-level system and the nonlinear CGL equation, the analytical calculations are supplemented with direct numerical simulation, thus showing the fate of unstable global modes. For the two-level model this results in unbounded growth of the full nonlinear equations. For the spatially-extended CGL model in the subcritical regime, the global mode of larger amplitude exhibits a 'one-sided' instability leading to a chaotic dynamics, while the global mode of smaller amplitude is always unstable (theory confirms this). However, advection can stabilize the mode of larger amplitude.
"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…
Strange Attractors: Chaos Theory and Composition Studies.
ERIC Educational Resources Information Center
Hesse, Doug
Chaos theory provides a powerful lens for re-seeing a number of issues in composition studies ranging in scale from achieving a generative model for text production to articulating the very nature of the discipline. Chaos systems are nonlinear, have complex forms, manifest recursive symmetries between scale levels, have feedback mechanisms, and…
Sensitivity to initial conditions, entropy production, and escape rate at the onset of chaos
NASA Astrophysics Data System (ADS)
Fuentes, Miguel Angel; Sato, Yuzuru; Tsallis, Constantino
2011-08-01
We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in z-logistic maps for both positive and zero Lyapunov exponents. We unify these relations at chaos, where the Lyapunov exponent is positive, and at its onset, where it vanishes. Our result unifies, in particular, two already known cases, namely (i) the standard entropy rate in the presence of escape, valid for exponential functionality rates with strong chaos, and (ii) the Pesin-like identity with no escape, valid for the power-law behavior present at points such as the Feigenbaum one.
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
Optical chaos communications (Invited Paper)
NASA Astrophysics Data System (ADS)
Mirasso, Claudio R.; Poinsot, Stephane; Larger, Laurent; Peil, Michael; Fischer, Ingo
2005-06-01
We present recent results obtained for an optical chaos communications system using optoelectronic devices. These devices are used to improve privacy and security in information transmission. Two kind of chaos based emitters and receivers are described: a semiconductor laser subject to all-optical feedback and operating in a non-linear regime and a semiconductor laser subject to non-linear electro-optical feedback and operating in a linear regime. We show that both configuration give very good synchronization properties and are suitable for message enconding/decoding at bit rates as high as Gbit/s.
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
PT-Symmetry-Breaking Chaos in Optomechanics.
Lü, Xin-You; Jing, Hui; Ma, Jin-Yong; Wu, Ying
2015-06-26
We demonstrate PT-symmetry-breaking chaos in an optomechanical system, which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in the PT-symmetry-breaking phase. Moreover, this chaos is switchable by tuning the system parameters so that a PT-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser-triggered chaos and its potential applications in secret communication. PMID:26197125
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
NASA Astrophysics Data System (ADS)
Levine, Alex
Transiently cross linked networks of semiflexible filaments make up the principal structural component of the cell -- the cytoskeleton. This intracellular network, along with molecular motors, forms the basis for cellular control of morphology and force generation. In this talk, I report on investigations of the effect of transiently bound cross linkers on the structure and mechanics of semiflexible networks. Specifically, I address the role of Casimir or fluctuation-induced interactions between cross linkers in the formation of filament bundles. I report on the linear viscoelasticity of transiently cross-linked networks of bundles. Finally, I discuss the nonlinear mechanical response of such networks, where applied stress induces a persistent structural rearrangement of the network that can dramatically alter its nonlinear response to stresses subsequently applied.
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)
Hunt, Brian R.; Ott, Edward
2015-09-15
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.
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.
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
NASA Astrophysics Data System (ADS)
Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying
2016-03-01
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.
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
The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links
NASA Astrophysics Data System (ADS)
Carillo, Sandra; Fuchssteiner, Benno
1989-07-01
Explicit computation for a Kawamoto-type equation shows that there is a rich associated symmetry structure for four separate hierarchies of nonlinear integrodifferential equations. Contrary to the general belief that symmetry groups for nonlinear evolution equations in 1+1 dimensions have to be Abelian, it is shown that, in this case, the symmetry group is noncommutative. Its semisimple part is isomorphic to the affine Lie algebra A(1)1 associated to sl(2,C). In two of the additional hierarchies that were found, an explicit dependence of the independent variable occurs. Surprisingly, the generic invariance for the Kawamoto-type equation obtained in Rogers and Carillo [Phys. Scr. 36, 865 (1987)] via a reciprocal link to the Möbius invariance of the singularity equation of the Kaup-Kupershmidt (KK) equation only holds for one of the additional hierarchies of symmetry groups. Thus the generic invariance is not a universal property for the complete symmetry group of equations obtained by reciprocal links. In addition to these results, the bi-Hamiltonian formulation of the hierarchy is given. A direct Bäcklund transformation between the (KK) hierarchy and the hierarchy of singularity equation for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation is exhibited: This shows that the abundant symmetry structure found for the Kawamoto equation must exist for all fifth-order equations, which are known to be completely integrable since these equations are connected either by Bäcklund transformations or reciprocal links. It is shown that similar results must hold for all hierarchies emerging out of singularity hierarchies via reciprocal links. Furthermore, general aspects of the results are discussed.
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.
Reflective confocal laser scanning microscopy and nonlinear microscopy of cross-linked rabbit cornea
NASA Astrophysics Data System (ADS)
Krueger, Alexander; Hovakimyan, Marina; Ramirez, Diego F.; Stachs, Oliver; Guthoff, Rudolf F.; Heisterkamp, Alexander
2009-07-01
Cross-linking of the cornea with application of Ribovlavin and UV-A light is an evolving clinical treatment of the eye disease keratoconus. Despite the positive clinical track record of corneal cross-linking, the complex wound healing process after the treatment is still under investigation. In this study an animal model was used to clarify the state of wound healing 5 weeks after treatment. Cross-linked rabbit corneae were imaged with reflective confocal laser scanning and nonlinear microscopy, namely second harmonic imaging microscopy (SHIM) and two-photon excited autofluorescence. First results show that the NAD(P) H-autofluorescence of the corneal keratocytes and their scattering signal still show a signature of the treatment five weeks after the cross-linking procedure. The SHIM signals show the structural morphology of the fibrous collagen sheets in the stroma of the cornea. SHIM detected in the forward direction differs substantially from backward SHIM, but no signature of treatment was found in both detection channels of the SHIM signal.
Chaos in 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
NASA Astrophysics Data System (ADS)
Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P.; Paschereit, Christian O.
2015-02-01
This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.
Chaos in an imperfectly premixed model combustor
Kabiraj, Lipika Saurabh, Aditya; 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.
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.
Physics and applications of laser diode chaos
NASA Astrophysics Data System (ADS)
Sciamanna, M.; Shore, K. A.
2015-03-01
This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.
Proceedings of the 2nd Experimental Chaos Conference
NASA Astrophysics Data System (ADS)
Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep
1995-02-01
The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud
Tutorial: chaos theory--a primer for health care.
Sharp, L F; Priesmeyer, H R
1995-01-01
Chaos theory, also called nonlinear systems theory, provides new insights into processes previously thought to be unpredictable and random. It also provides a new set of tools that can be used to analyze common administrative and clinical data. This tutorial provides an introduction to chaos theory. Subsequent articles will address applications of those principles to the administrative activities of health care organizations, implications of those principles for clinical data, and application of chaos theory concepts to our understanding of organizational dynamics. PMID:10144786
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.
Nonlinear behavior of ionically and covalently cross-linked alginate hydrogels
NASA Astrophysics Data System (ADS)
Hashemnejad, Seyedmeysam; Zabet, Mahla; Kundu, Santanu
2015-03-01
Gels deform differently under applied load and the deformation behavior is related to their network structures and environmental conditions, specifically, strength and density of crosslinking, polymer concentration, applied load, and temperature. Here, we investigate the mechanical behavior of both ionically and covalent cross-linked alginate hydrogel using large amplitude oscillatory shear (LAOS) and cavitation experiments. Ionically-bonded alginate gels were obtained by using divalent calcium. Alginate volume fraction and alginate to calcium ratio were varied to obtain gels with different mechanical properties. Chemical gels were synthesized using adipic acid dihdrazide (AAD) as a cross-linker. The non-linear rheological parameters are estimated from the stress responses to elucidate the strain softening behavior of these gels. Fracture initiation and propagation mechanism during shear rheology and cavitation experiments will be presented. Our results provide a better understanding on the deformation mechanism of alginate gel under large-deformation.
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
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
Butterflies and Bifurcations: Can Chaos Theory Contribute to Our Understanding of Family Systems?
ERIC Educational Resources Information Center
Ward, Margaret
1995-01-01
Examines key "chaos" elements--operation of systems far from equilibrium, nonlinear causation and discontinuous change, patterns in apparent chaos, and self-organization--in relation to family systems theory. Although there are several parallels, chaos theory is better able to address change, inequity, and the occurrence of order and disorder in…
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…
An LPV framework for chaos synchronization in communication
NASA Astrophysics Data System (ADS)
Halimi, M.; Millérioux, G.
2014-06-01
This paper proposes a unified framework to achieve chaos synchronization of both classes of chaotic discrete-time systems, namely maps involving polynomial nonlinearities and piecewise linear maps. It is shown that all of those chaotic systems can be rewritten as a polytopic Linear Parameter Varying (LPV) system. A unified approach to tackle chaos synchronization problems encountered in communication is derived.
Conjugate pair of representations in chaos and quantum mechanics
NASA Astrophysics Data System (ADS)
Tomita, Kazuhisa
1987-07-01
Being based on the observation that a conjugate pair of representations, or dual logic, is a necessity under the presence of chaos, a new interpretation of quantum theory is proposed as describing proto-chaos. This chaos has to be a result of basic nonlinearity in the dynamic structure, of which, however, the nonchaotic phase seems to lie ourside the reach of experimental technique, thus the term proto-chaos. Nevertheless, assuming no extra degrees of freedom, the interpretation clarifies a number of riddles posed hitherto and throws some light on the overall hierarchical structure of our understanding and description of nature.
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.
Chaos, brain and divided consciousness.
Bob, Petr
2007-01-01
Modern trends in psychology and cognitive neuroscience suggest that applications of nonlinear dynamics, chaos and self-organization seem to be particularly important for research of some fundamental problems regarding mind-brain relationship. Relevant problems among others are formations of memories during alterations of mental states and nature of a barrier that divides mental states, and leads to the process called dissociation. This process is related to a formation of groups of neurons which often synchronize their firing patterns in a unique spatial maner. Central theme of this study is the relationship between level of moving and oscilating mental processes and their neurophysiological substrate. This opens a question about principles of organization of conscious experiences and how these experiences arise in the brain. Chaotic self-organization provides a unique theoretical and experimental tool for deeper understanding of dissociative phenomena and enables to study how dissociative phenomena can be linked to epileptiform discharges which are related to various forms of psychological and somatic manifestations. Organizing principles that constitute human consciousness and other mental phenomena from this point of view may be described by analysis and reconstruction of underlying dynamics of psychological or psychophysiological measures. These nonlinear methods in this study were used for analysis of characteristic changes in EEG and bilateral electrodermal activity (EDA) during reliving of dissociated traumatic and stressful memories and during psychopathological states. Analysis confirms a possible role of chaotic transitions in the processing of dissociated memory. Supportive finding for a possible chaotic process related to dissociation found in this study represent also significant relationship of dissociation, epileptiform discharges measured by typical psychopathological manifestations and characteristic laterality changes in bilateral EDA in patients with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519
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)
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.
Magnetic field induced dynamical chaos.
Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra
2013-12-01
In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples. PMID:24387560
Convection and chaos in fluids
Bhattacharjee, J.
1987-01-01
This book describes some of the progress made in understanding the phenomena of various hydrodynamic instabilities for the past 30 years. Among them the exact results for the onset of Rayleigh-Benard convection are discussed. Approximate techniques like the amplitude equations and few-mode truncations are treated at length. The reviews of the routes to chaos in dynamical systems and the characteristics of the chaotic state are also discussed here. Finally, certain features of the Taylor Couette instability and the effect of parametric modulation on hydrodynamic instabilities are also included. This book also discusses the results at all stages of experiments. Contents: Onset of Convection: Rayleigh-Benard Geometry for Simple Fluids; Amplitude Equations; Few-Mode Truncation: Lorentz Model; Characteristics of Chaotic Behavior, Routes to Chaos; On Experiments; Thermohaline Systems; Onset of Convection; Binary Liquids; Nonlinear Effects; Taylor-Couette flow; Magnetohydrodynamic Convection; Modulated Systems.
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…
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.
Kasimov, Aslan R; Faria, Luiz M; Rosales, Rodolfo R
2013-03-01
We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x = 0 for any t ≥ 0. Here, u(s)(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations. PMID:23521260
Chaos in the Belousov-Zhabotinsky reaction
NASA Astrophysics Data System (ADS)
Field, Richard J.
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...
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.
Chaos in plasma simulation and experiment
Watts, C.; Newman, D.E.; Sprott, J.C.
1993-09-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
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
Linking reduced breaking crest speeds to unsteady nonlinear water wave group behavior.
Banner, M L; Barthelemy, X; Fedele, F; Allis, M; Benetazzo, A; Dias, F; Peirson, W L
2014-03-21
Observed crest speeds of maximally steep, breaking water waves are much slower than expected. Our fully nonlinear computations of unsteadily propagating deep water wave groups show that each wave crest approaching its maximum height slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This previously noted crest slowdown behavior was validated as generic in our extensive laboratory and field observations. It is likely to occur in unsteady dispersive nonlinear wave groups in other natural systems. PMID:24702377
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
NASA Astrophysics Data System (ADS)
Akhmet, M. U.; Fen, M. O.
2013-10-01
We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney's, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. That is why we identify the extension of chaos through the replication as morphogenesis. To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functions, the generator and replicator of chaos, and precise description of ingredients for Devaney and Li-Yorke chaos in continuous dynamics. Appropriate simulations which illustrate the chaos replication phenomenon are provided. Moreover, in discussion form we consider inheritance of intermittency, replication of Shil'nikov orbits and quasiperiodical motions as a possible skeleton of a chaotic attractor. Chaos extension in an open chain of Chua circuits is also demonstrated.
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.
NASA Astrophysics Data System (ADS)
Singhrattna, N.; Babel, M. S.; Perret, S. R.
2009-10-01
The local hydroclimates get impacts from the large-scale atmospheric variables via atmospheric circulation. The developing of their relationships could enhance the understanding of hydroclimate variability. This study focuses on the Upper Chao Phraya River Basin in Thailand in which rainfall is influenced by the Indian Ocean and tropical Pacific Ocean atmospheric circulation. The Southwest monsoon from the Indian Ocean to Thailand is strengthened by the temperature gradient between land and ocean. Thus, the anomalous sea surface temperature (SST) is systematically correlated with the monthly rainfall and identified as the best predictor based on the significant relationships revealed by cross-correlation analysis. It is found that rainfall, especially during the monsoon season in the different zones of study basin, corresponds to the different SST indices. This suggests that the region over the ocean which develops the temperature gradient plays a role in strengthening the monsoon. The enhanced gradient with the SST over the South China Sea is related to rainfall in High Rainfall Zone (HRZ); however, the anomalous SST over the Indian Ocean and the equatorial Pacific Ocean are associated with rainfall in Normal and Low Rainfall Zone (NRZ and LRZ) in the study area. Moreover, the identified predictors are related to the rainfall with lead periods of 1-4 months for the pre-monsoon rainfall and 6-12 months for the monsoon and dry season rainfall. The study results are very useful in developing rainfall forecasting models and consequently in the management of water resources and extreme events.
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
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
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…
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.
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 Λ , the theory of gravity is Einstein's general relativity and the background is the standard flat Λ 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.
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.
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
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…
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…
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
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.
Spatiotemporal Communication with Synchronized Optical Chaos
NASA Astrophysics Data System (ADS)
García-Ojalvo, J.; Roy, Rajarshi
2001-05-01
We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wave fronts.
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.
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.
What Can We Learn from Chaos Theory? An Alternative Approach to Instructional Systems Design.
ERIC Educational Resources Information Center
You, Yeongmahn
1993-01-01
Explains chaos theory; compares a conventional instructional systems design (ISD) approach with chaos theory and dynamic nonlinear systems, including deterministic predictability and indeterministic unpredictability and negative and positive feedback; explores theoretical implications for developing an alternative ISD model; and recommends future…
NASA Astrophysics Data System (ADS)
Tauxe, L.
2002-12-01
When I finished graduate school I suppose I imagined myself as my dad. He worked hard, loved his job and family, made a good living. But I also saw myself as my mom - making a home, raising kids, cooking dinner, saving the world. I thought: I can handle being my mom and my dad. I can handle being a scientist and a mother. I can DO this.ÿ What I never imagined was the chaotic dynamic of the two career couple. The motions of bodies moving in response to the force of gravity cannot be predicted exactly if there are too many bodies. They dance in a jerky jumble, now faster, then slowly, bouncing, jostling, bumping and flying apart. Just so are the career trajectories of the two career couple. One rises up, the other, slower, pulls it down; overtaking, blocking preventing, now supporting, pulling along, now holding back - not moving, leap frogging, racing in opposite directions and snapping back together with a crack.ÿ The problem is non-linear. The outcome depends on feedback, whether positive or negative. The outcome cannot be predicted. Cannot be determined.ÿ Perhaps it cannot be done. Perhaps both husband and wife cannot be both mother and father. Too many mothers, too many fathers. Chaos.ÿ But I believe it can be done. Not like our mothers and fathers but a different way. And maybe our jerky paths will keep us sharp, make us work harder, and lead us through lives that at least cannot be described as dull.ÿ
Decrease of cardiac chaos in congestive heart failure
NASA Astrophysics Data System (ADS)
Poon, Chi-Sang; Merrill, Christopher K.
1997-10-01
The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.
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.
NASA Astrophysics Data System (ADS)
McHarris, Wm. C.
1999-10-01
The statistical nature of quantum mechanical transitions has often led to a comparison of half-lives of, say, nuclear transitions with the predictions of actuarial tables---although impossible to predict when an individual will transform, statistically one can obtain precise population predictions. For complex biological systems this is quite believable, but in ``simple" nuclear systems, the analogy is more questionable. Another way of looking at this is through feedback in non-linear systems. In many chaos games, e.g., varied, unpredictable starting points will always arrive at one or a few end points, but they take widely varying numbers of moves and routes to reach such end positions---this is the essence of chaotic attractors. Using the Uncertainty Principle to justify slightly varying initial states, one can play similar chaos games with quantum mechanical systems, and it is possible to arrive at the final destination(s) with predictable half-lives. Some simple examples of such transitions, as relating to nuclear transitions, will be presented.
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 Astrophysics Data System (ADS)
Chalhoub, N. G.; Kfoury, G. A.; Bazzi, B. A.
2006-03-01
Two robust nonlinear controllers along with a nonlinear observer have been developed in this study to control the rigid and flexible motions of a single-link robotic manipulator. The controllers and the observer have been designed based on a simplified model of the arm, which only accounts for the first elastic mode of the beam. The controllers consist of a conventional sliding mode controller (CSMC) and a fuzzy-sliding mode controller (FSMC). Moreover, the robust nonlinear observer has been designed based on the sliding mode methodology. The dynamic model, used in assessing the performances of the controllers and the observer, considers the first two elastic modes of the beam. The inclusion of the second elastic mode has been done to investigate the effects of unstructured uncertainties on the overall performance of the closed-loop system. The digital simulations have demonstrated the capability of the observer in yielding accurate estimates of the state variables in the presence of modeling uncertainties. Moreover, they served to prove the viability of using the observer to provide on-line estimates of the state variables for the computation of the control signals. The results have illustrated robust performances of the controllers and the observer in controlling the rigid and flexible motions of the manipulator in the presence of both structured and unstructured uncertainties. This was achieved irrespective of the differences in the initial conditions between the plant and the observer. Furthermore, the structural deformations, incurred by the beam at the onset of its movement, have been shown to be significantly reduced by fuzzy-tuning the η-control parameter. The results have demonstrated the superiority of the FSMC over the CSMC in producing less oscillatory and more accurate response of the angular displacement at the base joint, in damping out the unwanted vibrations of the beam, and in requiring significantly smaller control torques.
Exploiting chaos for applications
NASA Astrophysics Data System (ADS)
Ditto, William L.; Sinha, Sudeshna
2015-09-01
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Exploiting chaos for applications
Ditto, William L.; Sinha, Sudeshna
2015-09-15
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses
NASA Astrophysics Data System (ADS)
Simon, A.
2010-12-01
The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event triggered a debris flow which cutoff tributary channels to Glacier Creek and redirected Step and Loowit Creeks thereby forcing enhanced flow volumes through the main channel. Very coarse, armored bed materials were mobilized allowing for deep incision into the substrate. Incision continues today at slower rates but it is again the lateral shifting and widening of the channels that is dominant. Low and moderate flows undercut the toe of 30 m-high pyroclastic flow deposits causing significant erosion. As the channel continues to widen incision will attenuate non-linearly. Channels such as the multiple Step Creek channels will coalesce as narrow ridges erode by undercutting and mass failure much as reaches of lower Loowit Creek did in the late 1980’s. The resulting enlarged and over-widened sections will then again (as in downstream reaches) have lowered transporting power.
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.
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
Hung, Yu-Han; Hwang, Sheng-Kwang
2013-09-01
For radio-over-fiber links, microwave-modulated optical carriers with high optical modulation depth are preferred because high optical modulation depth allows generation of high microwave power after photodetection, leading to high detection sensitivity, long transmission distance, and large link gain. This study investigates the period-one nonlinear dynamics of semiconductor lasers for optical modulation depth improvement to achieve photonic microwave amplification through modulation sideband enhancement. In our scheme, only typical semiconductor lasers are required as the amplification unit. The amplification is achieved for a broad microwave range, from less than 25 GHz to more than 60 GHz, and for a wide gain range, from less than 10 dB to more than 30 dB. The microwave phase quality is mainly preserved while the microwave power is largely amplified, improving the signal-to-noise ratio up to at least 25 dB. The bit-error ratio at 1.25 Gbits/s is better than 10(-9), and a sensitivity improvement of up to at least 15 dB is feasible. PMID:23988956
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.
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. PMID:23515869
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
Parrondo’s 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 Parrondo’s 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 Parrondo’s paradox with “order” and “chaos", respectively, the PS algorithm leads to the generalized Parrondo’s 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.
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.
Migraine--new perspectives from chaos theory.
Kernick, D
2005-08-01
Converging from a number of disciplines, non-linear systems theory and in particular chaos theory offer new descriptive and prescriptive insights into physiological systems. This paper briefly reviews an approach to physiological systems from these perspectives and outlines how these concepts can be applied to the study of migraine. It suggests a wide range of potential applications including new approaches to classification, treatment and pathophysiological mechanisms. A hypothesis is developed that suggests that dysfunctional consequences can result from a mismatch between the complexity of the environment and the system that is seeking to regulate it and that the migraine phenomenon is caused by an incongruity between the complexity of mid brain sensory integration and cortical control networks. Chaos theory offers a new approach to the study of migraine that complements existing frameworks but may more accurately reflect underlying physiological mechanisms. PMID:16033380
Enacting a Chaos Theory Curriculum through Computer Interactions.
ERIC Educational Resources Information Center
Iseke-Barnes, Judith M.
1997-01-01
Examines human-computer interaction from two views of cognition: the representationist view and the enactivist perspective. A chaos-theory context is discussed from an enactivist stance. In this context, high school students manipulate nonlinear dynamic computer programs. Implications of the enactive stance for education and research are also…
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…
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.
Chaos theory and clinical pathways: a practical application.
Priesmeyer, H R; Sharp, L F; Wammack, L; Mabrey, J D
1996-01-01
Nonlinear analysis can improve the adaptive ability of clinical paths and aid in providing improved continuity of care. This article continues our exploration of the ways "chaos theory" can be applied in health care by focusing on clinical applications. It describes a specific application of nonlinear techniques to knee arthroplasty, but the generalized nature of the technique suggests it can be applied in many other settings. The approach offers an innovative means for both improved patient care and cost savings. PMID:10159143
Exploiting chaos for applications.
Ditto, William L; Sinha, Sudeshna
2015-09-01
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices. PMID:26428568
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.
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.
Solitons in the midst of chaos
NASA Astrophysics Data System (ADS)
Seghete, Vlad; Menyuk, Curtis R.; Marks, Brian S.
2007-10-01
A system of coupled nonlinear Schrödinger equations describes pulse propagation in weakly birefringent optical fibers. Soliton solutions of this system are found numerically through the shooting method. We employ Poincaré 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 in symmetric phase oscillator networks.
Bick, Christian; Timme, Marc; Paulikat, Danilo; Rathlev, Dirk; Ashwin, Peter
2011-12-01
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities. PMID:22243002
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 reversed-field-pinch plasma simulation and experiment
Watts, C.; Newman, D.E.; Sprott, J.C. )
1994-03-01
We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed-field-pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear-analysis techniques is used to identify low-dimensional chaos. These tools include phase portraits and 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 computer code, which models global RFP dynamics, and the dissipative trapped-electron-mode model, which models drift-wave turbulence. Data from both simulations show strong indications of low-dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low-dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate that the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
Relativistic chaos is coordinate invariant.
Motter, Adilson E
2003-12-01
The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents. PMID:14683170
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.
Noise tolerant spatiotemporal chaos computing.
Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L
2014-12-01
We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture. PMID:25554030
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.
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. PMID:25273218
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.
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
Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.
Zou, Yong; Donner, Reik V; Kurths, Jürgen
2012-03-01
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given. PMID:22462991
Chaos tool implementation for non-singer and singer voice comparison (preliminary study)
NASA Astrophysics Data System (ADS)
Dajer, Me; Pereira, Jc; Maciel, Cd
2007-11-01
Voice waveform is linked to the stretch, shorten, widen or constrict vocal tract. The articulation effects of the singer's vocal tract modify the voice acoustical characteristics and differ from the non-singer voices. In the last decades, Chaos Theory has shown the possibility to explore the dynamic nature of voice signals from a different point of view. The purpose of this paper is to apply the chaos technique of phase space reconstruction to analyze non- singers and singer voices in order to explore the signal nonlinear dynamic, and correlate them with traditional acoustic parameters. Eight voice samples of sustained vowel /i/ from non-singers and eight from singers were analyzed with "ANL" software. The samples were also acoustically analyzed with "Analise de Voz 5.0" in order to extract acoustic perturbation measures jitter and shimmer, and the coefficient of excess - (EX). The results showed different visual patterns for the two groups correlated with different jitter, shimmer, and coefficient of excess values. We conclude that these results clearly indicate the potential of phase space reconstruction technique for analysis and comparison of non-singers and singer voices. They also show a promising tool for training voices application.
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.
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.
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.
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.
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 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, 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.…
Nonlinear aspects of shock response in isolated accelerometers
Paez, T.L.; Hunter, N.
1992-04-01
Numerous investigations have studied the potential for chaotic vibrations of nonlinear systems. It has been shown for many simple nonlinear systems, that when they are excited severely enough, or with the appropriate parametric combinations, that they will execute chaotic vibrations. The present investigation considers the potential for the occurrence of chaos in a practical nonlinear system -- the isolated accelerometer. A simple, first order model is proposed for the isolated accelerometer, and it is shown that chaos can occur in the isolated accelerometer. A preliminary investigation into the bearing that this chaos potential has on the measurement of shock response is summarized. 7 refs.
Chaos in an impact oscillator constructed from undergraduate laboratory equipment.
NASA Astrophysics Data System (ADS)
Thomas, J.; Rhode, M. A.; Rollins, R. W.
1996-11-01
Bouncing effects in mechanical systems have drawn much attention as a limiting factor in the performance of various micro and macroscopic devices. As previously reported, a simulation of a ball bouncing on a periodically driven table, exhibits low dimensional deterministic chaos. By applying small changes in the drive frequency, we use a recently developed automated map based control scheme, to stabilize a period one orbit in such a system. We extend our studies to a system which is nonlinear between successive impacts. A simple mechanical, impact-driven, nonlinear pendulum constructed from easily available introductory physics laboratory equipment will be demonstrated. Period-doubling, high period orbits, and chaos are observed. Results from experiments and numerical simulations will be presented. Part C of program listing
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.
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.
Complex Gaussian Multiplicative Chaos
NASA Astrophysics Data System (ADS)
Lacoin, Hubert; Rhodes, Rémi; Vargas, Vincent
2015-07-01
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free Fields in dimension 2). Our main working assumption is that the real part and the imaginary part are independent. We also discuss applications in 2 D string theory; in particular we give a rigorous mathematical definition of the so-called Tachyon fields, the conformally invariant operators in critical Liouville Quantum Gravity with a c = 1 central charge, and derive the original KPZ formula for these fields.
NASA Technical Reports Server (NTRS)
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 Astrophysics Data System (ADS)
Ye, Mingxin; Xu, Lei; Ji, Liyong; Liu, Liying; Wang, Wencheng
The cyano and nitro groups were chosen as acceptor groups, and the substituent amino or ether groups as donor groups to the matrix. Polyurethane (PU) was modified by glycerol to increase the content of chromophore and to improve the stability of the nonlinearity. Tg and Tm were raised and solubility, film-forming ability and other physical properties were improved. The average functional groups of the reactant can be adjusted to ≥ 2 with polygroups and monogroups mixture. These poled polymers show high second-order optical nonlinearity and would have potential application in frequency-doubling or electro-optical controlling devices.
Giovacchini, P L
1990-01-01
There is a continuum from primitive, undifferentiated feelings that are simply the manifestations of homeostatic balance and imbalance to highly differentiated, pleasurable erotic feelings that characterize mature, intimate love relationships. Sensory reactions are elevated from simple reflex levels to highly complex, sophisticated affects that involve wide areas of the psyche. Thus, affects are associated with integration and organized psychic structure. Consequently they may function in various ways. Freud developed a continuum for anxiety as initially functioning as a conversion reaction enabling sexual feelings that cannot reach mentational levels or be consummated in erotic activity to be discharged. It reaches a final level of organization where it serves as a signal calling various defenses into play as emerging instinctual impulses threaten to upset psychodynamic equilibrium. I have focused on how affects, erotic feelings in particular, have an organizing function that binds a primitive inner agitation that occurs during what is called a prementational stage of the neonatal period. This is a stage that precedes psychological processes. Sexual feelings are generated as an attempt to bind inner chaos that stems from an amorphous, inchoate psychic state. Erotic feelings are experienced in order to smoothe inner tension. The patient tries but seldom achieves calm because the affective binding and structuralizing process, in itself, becomes painful and disruptive. I present several clinical incidents and also refer to so-called treatment relationships where the therapist absorbs the patient's chaos and then acts out sexually which leads to a total breakdown of the therapeutic setting. PMID:2354974
Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja
2014-11-01
We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal. PMID:25401887
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
Chaos in hydrodynamic BL Herculis models
NASA Astrophysics Data System (ADS)
Smolec, R.; Moskalik, P.
2014-06-01
We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.
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 Europa’s 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 Europa’s ice and ocean in light of active processes that may form a “chaos conveyor belt” that drives material exchange on Europa.
Energy Science and Technology Software Center (ESTSC)
2007-08-22
The CHAOS dchroot utilities is a set of software used to prepare and manage "alternate root" filesystems on Linux systems. These alternate roots can be used to provide an alternate set of system software for testing and compatibility purposes.
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 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 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
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.
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
Dynamical properties and chaos synchronization of improved Colpitts oscillators
NASA Astrophysics Data System (ADS)
Kengne, J.; Chedjou, J. C.; Kenne, G.; Kyamakya, K.
2012-07-01
In this paper, the dynamics and synchronization of improved Colpitts oscillators designed to operate in ultrahigh frequency range are considered. The model is described by a continuous time four-dimensional autonomous system with an exponential nonlinearity. The system is integrated numerically and various bifurcation diagrams and corresponding graphs of largest 1D Lyapunov exponent are plotted to summarize different scenarios leading to chaos. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes when monitoring the bias (i.e. power supply) in tiny ranges. In order to promote chaos-based synchronization designs of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. The suggested approach enables synchronization to be achieved via a scalar transmitted signal which represents a suitable feature for communication applications. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed technique.
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.
Explore the chaos behaviour of water quality variability: a case study at Huaihe River, China
NASA Astrophysics Data System (ADS)
Shi, Bi; Jiang, Jiping; Sivakumar, Bellie; Wang, Peng; Zhou, Weiwen
2015-04-01
Few studies investigated the nonlinear behaviour of water quality time series in natural surface waters. The work examines water quality time series in a Chinese River based on phase space reconstruction and optimal embedding dimension of chaos theories. It covers 3 regular water quality index (DO, CODMn, NH3-N) and 27 online monitoring stations. Through calculating and determining embedding dimension, m value, we analysis the chaotic characteristic of water quality variability in the river. Results shown the correlation dimension of typical water quality time series and the spatial variability. Reliability of dimension estimate and relationship between those chaos behaviours and impact factors were also discussed. It will improves the understanding of the nonlinear characteristics of water quality variation and chaos predication model.
Liang, Xiaojun; Kumar, Shiva
2014-12-01
A recursive perturbation theory to model the fiber-optic system is developed. Using this perturbation theory, a multi-stage compensation technique to mitigate the intra-channel nonlinear impairments is investigated. The technique is validated by numerical simulations of a single-polarization single-channel fiber-optic system operating at 28 Gbaud, 32-quadrature amplitude modulation (32-QAM), and 40 × 80 km transmission distance. It is found that, with 2 samples per symbol, the multi-stage scheme with eight compensation stages increases the Q-factor as compared with linear compensation by 4.5 dB; as compared with single-stage compensation, the computational complexity is reduced by a factor of 1.3 and the required memory for storing perturbation coefficients is decreased by a factor of 13. PMID:25606904
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 Poincaré 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
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
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.
Photonic Josephson effect, phase transitions, and chaos in optomechanical systems
Larson, Jonas; Horsdal, Mats
2011-08-15
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.
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
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.
Chaos, Complexity, and Earning Community: What Do They Mean for Education?
ERIC Educational Resources Information Center
Pouravood, Roland C.
1997-01-01
Ponders possible explanations for the connections among chaos, complexity, and a learning community. Challenges the Newtonian world model, suggests that the world operates in a complex, nonlinear, unpredictable pattern, and calls for a new science to understand this complexity. A true learning community values individual autonomy, risk taking,…
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
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.
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
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
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
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
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
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.
NASA Astrophysics Data System (ADS)
Valentini, F.; Vecchio, A.; Donato, S.; Carbone, V.; Briand, C.; Bougeret, J.; Veltri, P.
2014-06-01
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.
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.
Chaos, Communication, and Educational Technology.
ERIC Educational Resources Information Center
King, James W.
Chaos offers educational communications and technology new systems' tools and ideas; i.e., it provides the system with a deterministic "I don't know" state within which new activity patterns can be generated. Previous characterizations and paradigms of systems stated that simple systems behaved in simple ways, complex behaviors implied complex…
NASA Technical Reports Server (NTRS)
Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.
2001-01-01
The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!
ERIC Educational Resources Information Center
Bright, Jim E. H.; Pryor, Robert G. L.
2011-01-01
The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…
Chao Formalism & Kondratenko Crossing Tests
NASA Astrophysics Data System (ADS)
Raymond, R. S.; Chao, A. W.; Krisch, A. D.; Leonova, M. A.; Morozov, V. S.; Sivers, D. W.; Wong, V. K.; Gebel, R.; Lehrach, A.; Lorentz, B.; Maier, R.; Prasuhn, D.; Schnase, A.; Stockhorst, H.; Hinterberger, F.; Ulbrich, K.; Kondratenko, A. M.
2007-06-01
We recently started testing Chao's proposed new matrix formalism for describing the spin dynamics due to a single spin resonance; this seems to be the first generalization of the Froissart-Stora equation since it was published in 1960. The Chao matrix formalism allows one to calculate analytically the polarization's behavior inside a resonance, which is not possible using the Froissart-Stora equation. We recently tested some Chao formalism predictions using a 1.85 GeV/c polarized deuteron beam stored in COSY. We swept an rf dipole's frequency through 200 Hz while varying the distance from the sweep's end frequency to an rf-induced spin resonance's central frequency. While the Froissart-Stora formula can make no prediction in this case, the data seem to support the Chao formalism. We also started investigating the new Kondratenko method to preserve beam polarization during a spin resonance crossing; the method uses 3 rapid changes of the crossing rate near the resonance. With a proper choice of crossing parameters, Kondratenko Crossing may better preserve the polarization than simple fast crossing. We tested Kondratenko's idea using 2.1 GeV/c polarized protons stored in COSY; the frequency of a ferrite rf dipole was swept though an rf-induced spin resonance using Kondratenko's crossing shape. We have not yet observed a significant advantage of Kondratenko Crossing over simple fast crossing. We plan to study it further by choosing better crossing parameters and a smaller momentum spread.
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.
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.
Observing chaos for quantum-dot microlasers with external feedback.
Albert, Ferdinand; Hopfmann, Caspar; Reitzenstein, Stephan; Schneider, Christian; Höfling, Sven; Worschech, Lukas; Kamp, Martin; Kinzel, Wolfgang; Forchel, Alfred; Kanter, Ido
2011-01-01
Chaos presents a striking and fascinating phenomenon of nonlinear systems. A common aspect of such systems is the presence of feedback that couples the output signal partially back to the input. Feedback coupling can be well controlled in optoelectronic devices such as conventional semiconductor lasers that provide bench-top platforms for the study of chaotic behaviour and high bit rate random number generation. Here we experimentally demonstrate that chaos can be observed for quantum-dot microlasers operating close to the quantum limit at nW output powers. Applying self-feedback to a quantum-dot microlaser results in a dramatic change in the photon statistics wherein strong, super-thermal photon bunching is indicative of random-intensity fluctuations associated with the spiked emission of light. Our experiments reveal that gain competition of few quantum dots in the active layer enhances the influence of self-feedback and will open up new avenues for the study of chaos in quantum systems. PMID:21694714
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.
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. PMID:27036182
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.
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.
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.
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.
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.
Chaos over chaos: A new approach for satellite communication
NASA Astrophysics Data System (ADS)
Marinho, Cleverson M. P.; Macau, Elbert E. N.; Yoneyama, Takashi
2005-07-01
The chaotic dynamics can be exploited for the implementation of efficient and simple communication systems. Chaos communication explores chaotic synchronization to transmit information appropriately codified on the chaotic invariant set. This work studied control techniques and chaos synchronization, taking advantage of the chaotic evolution of the Chua circuit operating in double scroll regime and Lorenz system. Two forms were approached to taking advantage of peculiar characteristics of chaotic systems to transmit information. The first form uses small perturbation to encode the information in the symbolic dynamics of the double scroll system. The second one uses chaotic oscillations to mask the codified chaotic signal. The performance of the system is investigated, as well as its behavior when used to transmit information over a model of a real channel with limited bandwidth.
Characteristic Spaces Emerging from Primitive Chaos
NASA Astrophysics Data System (ADS)
Ogasawara, Yoshihito; Oishi, Shin'ichi
2014-01-01
This paper describes the emergence of two characteristic notions, nondegenerate Peano continuum and Cantor set, by the exploration of the essence of the existence of primitive chaos from a topological viewpoint. The primitive chaos is closely related to vital problems in physics itself and leads to chaotic features under natural conditions. The nondegenerate Peano continuum represents an ordinarily observed space, and the existence of a single nondegenerate Peano continuum guarantees the existence of infinite varieties of the primitive chaos leading to the chaos. This result provides an explanation of the reason why we are surrounded by diverse chaotic behaviors. Also, the Cantor set is a general or universal notion different from the special set, the Cantor middle-third set, and the existence of a single Cantor set guarantees infinite varieties of the primitive chaos leading to the chaos. This analogy implies the potential of the Cantor set for the method of new recognizing physical phenomena.
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…
Experimental study on chaos of a liquid-filled tank under vertical excitation
Okazaki, K.; Watanabe, K.; Tani, J.
1995-11-01
This paper is concerned with an experimental study on the chaos of a partially liquid-filled cylindrical tank under vertical excitation. The test cylinder made of polyester film was harmonically excited with constant displacement amplitude. It has been well known that the partially liquid-filled cylindrical tank under periodic vertical excitation gives rise to the parametoric resonance. As the excitation amplitude increases, the nonlinear response characteristics of soft and hard spring types as well as chaos were found to appear in this system. The occurrence of chaos was recognized by the time history, Poincare map, phase trajectory, and power spectrum. Furthermore, the sloshing and chaotic motion of the liquid surface were found to appear in the lower frequency range than the parametric resonance and chaotic motion of the cylindrical shell wall.
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.
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.
Route to chaos in optomechanics.
Bakemeier, L; Alvermann, A; Fehske, H
2015-01-01
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period-doubling bifurcations that leads to chaos and state the experimentally observable signatures in the optical spectrum. In addition to the semiclassical dynamics, we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and replace the classically chaotic motion. In this way observation of the dynamical signatures makes it possible to pin down the crossover from quantum to classical mechanics. PMID:25615468
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.
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.
NASA Astrophysics Data System (ADS)
Porta, G.; Tamellini, L.; Lever, V.; Riva, M.
2014-12-01
We present an inverse modeling procedure for the estimation of model parameters of sedimentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likelihood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quantified through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approximations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored.
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.
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
Controlling chaos in balanced neural circuits with input spike trains
NASA Astrophysics Data System (ADS)
Engelken, Rainer; Wolf, Fred
The cerebral cortex can be seen as a system of neural circuits driving each other with spike trains. Here we study how the statistics of these spike trains affects chaos in balanced target circuits.Earlier studies of chaos in balanced neural circuits either used a fixed input [van Vreeswijk, Sompolinsky 1996, Monteforte, Wolf 2010] or white noise [Lajoie et al. 2014]. We study dynamical stability of balanced networks driven by input spike trains with variable statistics. The analytically obtained Jacobian enables us to calculate the complete Lyapunov spectrum. We solved the dynamics in event-based simulations and calculated Lyapunov spectra, entropy production rate and attractor dimension. We vary correlations, irregularity, coupling strength and spike rate of the input and action potential onset rapidness of recurrent neurons.We generally find a suppression of chaos by input spike trains. This is strengthened by bursty and correlated input spike trains and increased action potential onset rapidness. We find a link between response reliability and the Lyapunov spectrum. Our study extends findings in chaotic rate models [Molgedey et al. 1992] to spiking neuron models and opens a novel avenue to study the role of projections in shaping the dynamics of large neural circuits.
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.…
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)
Cracks, ridges, and chaos: Europa un bel posto per vivere
NASA Astrophysics Data System (ADS)
Greenberg, R.; Tufts, B. R.; Hoppa, G. V.; Geissler, P.; Riley, J.
1999-09-01
The tidal-tectonic processes that appear to have governed Europa's geology require an ocean linked to the surface through a very thin crust, and provide a variety of evolving environmental niches, hospitable to life. The two dominant surface renewal processes that have alternated at various places and times throughout the geological history are melt-through (producing chaotic terrain) and tectonics (making cracks, ridges and bands); either process erases what was there before. Sequences and orientations of regional scale lineaments correlate with tidal stress patterns suggesting that there is a liquid ocean under the ice crust and rotation is non-synchronous. Subsequent diurnal tidal working of cracks creates ridges, by pumping liquid from below, and squeezing or spattering slush to the surface, with some distortion of the lip of the crack by the daily pounding. Strike-slip displacement and cycloidal cracking are driven by diurnal tides. Cracks can form bands if dilated by regional extension, perhaps also driven by tides. The same model of liquid water under a thin ice shell explains the characteristics of chaos areas as the result of melt-through from below. Chaos areas are wide-ranging in size (up to 1300 km across), location, and age. Pre-existing ridges resist melt-through and can form chaos boundaries or causeways or chains of rafts. Subsequent cracks and ridges can mask older chaos areas. Melt-through explains how compression can accommodate dilation along bands without leaving a trace. Surface colorants correlate with locations where ocean water reached the surface. As a result of tides, liquid water regularly bathed crustal cracks and surfaces with heat and whatever nutrients are included in the oceanic chemistry, creating a variety of potentially habitable crustal environments, as well as addressing requirements for life in the ocean itself. The processes described here were recent, and thus may continue today. In any particular niche, conditions have gradually changed, providing any organisms with the need for adaptation and opportunity for evolution.
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…
Structures of chaos in open reaction systems.
Ivanović-Šašić, A Z; Marković, V M; Anić, S R; Kolar-Anić, Lj Z; Cupić, Ž D
2011-12-01
By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions. PMID:21993658
Application of Artificial Neural Networks and Chaos in Chemical Processes
NASA Astrophysics Data System (ADS)
Otawara, Kentaro
1995-01-01
An artificial neural network (ANN) and chaos, conceived and developed independently, are beginning to play essential roles in chemical engineering. Nonetheless, the ANN possesses an appreciable number of deficiencies that need be remedied, and the capability of the ANN to explore and tame chaos or an irregularly behaving system is yet to be fully realized. The present dissertation attempts to make substantial progress toward such ends. The problem of controlling the temperature of an industrial reactor carrying out semibatch polymerization has been solved by an innovative adaptive hybrid control system comprising an ANN and fuzzy expert system (FES) complemented by two supervisory ANN's. The system enhances the strength and compensates for the weaknesses of both the ANN and FES. The system, named dual ANN (DANN), has been proposed for characterizing the nonlinear nature of chaotic time -series data. Its capability to approximate the behavior of a chaotic system has been found to far exceed that of a conventional ANN. A novel approach has been devised for training an ANN through the modified interactive training (MIT) mode. This mode of training has been demonstrated to substantially outperform a conventional interactive training (CIT) mode. A method has been established for synchronizing chaos by resorting to an ANN. This method is capable of causing to be coherent the trajectories of systems whose deterministic governing equations are insufficiently known. This requires training the ANN with a time series and a common driving signal or signals. Examples are given for chaos generated by difference as well as differential equations. An alternative to the OGY method has been proposed for controlling chaos; it meticulously perturbs an accessible parameter of the chaotic system. A single, highly precise ANN suffices to render stable any of an infinite number of unstable periodic orbits embedded in a chaotic or strange attractor. A method for estimating sub-Lyapunov exponents or conditional Lyapunov exponents is presented; it has been developed by exploiting the learning capability of an ANN. For some chaotic systems, the sub-Lyapunov exponents determined by the method are in good accord with the theoretical values.
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.
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)
Soe, Ni Ni; Nakagawa, Masahiro
2008-04-01
This paper presents the novel approach to evaluate the effects of different motor activation tasks of the human electroencephalogram (EEG). The applications of chaos and fractal properties that are the most important tools in nonlinear analysis are been presented for four tasks of EEG during the real and imaginary motor movement. Three subjects, aged 23-30 years, participated in the experiment. Correlation dimension (D2), Lyapunov spectrum (λi), and Lyapunov dimension (DL) are been estimated to characterize the movement related EEG signals. Experimental results show that these nonlinear measures are good discriminators of EEG signals. There are significant differences in all conditions of subjective task. The fractal dimension appeared to be higher in movement conditions compared to the baseline condition. It is concluded that chaos and fractal analysis could be powerful methods in investigating brain activities during motor movements.
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.
NASA Astrophysics Data System (ADS)
Luo, Shaohua; Sun, Quanping; Cheng, Wei
2016-04-01
This paper addresses chaos control of the micro-electro- mechanical resonator by using adaptive dynamic surface technology with extended state observer. To reveal the mechanism of the micro- electro-mechanical resonator, the phase diagrams and corresponding time histories are given to research the nonlinear dynamics and chaotic behavior, and Homoclinic and heteroclinic chaos which relate closely with the appearance of chaos are presented based on the potential function. To eliminate the effect of chaos, an adaptive dynamic surface control scheme with extended state observer is designed to convert random motion into regular motion without precise system model parameters and measured variables. Putting tracking differentiator into chaos controller solves the `explosion of complexity' of backstepping and poor precision of the first-order filters. Meanwhile, to obtain high performance, a neural network with adaptive law is employed to approximate unknown nonlinear function in the process of controller design. The boundedness of all the signals of the closed-loop system is proved in theoretical analysis. Finally, numerical simulations are executed and extensive results illustrate effectiveness and robustness of the proposed scheme.
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.
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.
Cryptography with Chaos and Shadowing
NASA Astrophysics Data System (ADS)
Smaoui, Nejib; Kanso, Ali
2009-11-01
A novel approach to encrypt a message using chaos and shadowing is presented. The approach is based on two steps: First, a numerical chaotic orbit of the logistic map is used in the shadowing algorithm of Smaoui & Kostelich [Intern. J. Computer. Math. (1998) 70] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, Baptista's algorithm [Phys. Lett. A (1998) 240] is used on the finite number of maps to encrypt each character of the message. It is shown that the use of the shadowing method in the encryption process enhances the security level.
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.
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.
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 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.
Transitions to chaos in two-dimensional double-diffusive convection
NASA Technical Reports Server (NTRS)
Knobloch, E.; Moore, D. R.; Toomre, J.; Weiss, N. O.
1986-01-01
The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.
Markov transitions and the propagation of chaos
Gottlieb, A.
1998-12-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.
Quantifying chaos for ecological stoichiometry.
Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2010-09-01
The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model. PMID:20887045
The route to chaos for the Kuramoto-Sivashinsky equation
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1991-01-01
The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609 .... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.
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.
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.
Applied chaos theory - A paradigm for complexity
NASA Astrophysics Data System (ADS)
Cambel, Ali B.
It is still not entirely clear, whether chaos theory will furnish solutions to problems posed by complex systems upon the development of a mathematics that is descriptive of complexity, in the same way that calculus is descriptive of continuously-varying processes. The present survey of the current understanding of chaos discusses the characteristics of complexity, the metaquantification of complexity, the anatomy of open and closed systems and structures, fixed-point and strange attractors, the mathematics of rapid growth, the discrete logistic equation, the role of entropy considerations, and the diagnostics and control of chaos.
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.
Nonlinear properties of relativistically intense laser in plasmas
Qiao Bin; Lai, C. H.; Zhou, C. T.; He, X. T.; Wang, X. G.; Yu, M. Y.
2007-11-15
Nonlinear characteristics including spatial chaos and patterns associated with relativistically intense laser-plasma interaction are studied theoretically and numerically using a model relativistic nonlinear Schroedinger equation. It is shown that in the phase space irregular homoclinic orbit crossings exist. The latter are verified and investigated numerically. The spatial chaos and complex patterns of the laser wave field can be attributed to the relativistic electron mass variation as well as the ponderomotive-force driven electron-density modulation. The formation of complex patterns results from stochastic partition of energy in the Fourier modes.
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
Experimental phase synchronization of chaos in a plasma discharge
NASA Astrophysics Data System (ADS)
Ticos, Catalin Mihai
2002-01-01
We demonstrate, for the first time, experimental phase synchronization in a chaotic plasma discharge. The nonlinear light and current discharge oscillations lock up in frequency with an external, low amplitude, periodic pacing signal, while their amplitude remains chaotic. Real-time observation of phase synchronization is made possible through a real-time sampling procedure, and the regions of synchronized/desynchronized states are presented. A set of equations is suggested to model the real plasma circuit. An experimental plasma system is driven with an information signal from a CD-player. With the plasma in the periodic regime, optical detection of the light emitted by the discharge allows the information signal to be heard from a loudspeaker. That does not happen when the plasma is chaotic, in which case we hear a noise-like hiss, typical of chaos. Modulation is observed in the periodic driven plasma, but it is not obvious when the plasma is chaotic. This procedure may be used as an encryption technique. Experimental phase synchronization of chaos is demonstrated for two different coupled oscillators: a plasma discharge and the Chua electronic circuit. Phase slips of 2pi are observed in the phase difference of the two oscillators, depending on the coupling strength. A power law indicates that an unstable-stable pair bifurcation crisis is responsible for the synchronization-desynchronization transition.
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.
Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Cantrell, Sean A.
2015-01-01
The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.
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)
Chaos in schizophrenia associations, reality or metaphor?
Bob, Petr; Susta, Marek; Chladek, Jan; Glaslova, Katerina; Palus, Milan
2009-09-01
There is evidence that schizophrenic associations display "chaotic", random-like behavior and decreased predictability. The evidence suggests a hypothesis that the "chaotic" mental disorganization could be explained within the concept of nonlinear dynamics and complexity in the brain that may cause chaotic neural organization. Testing of the hypothesis in the present study was performed using nonlinear analysis of bilateral electrodermal activity (EDA) during resting state and an association test in 56 schizophrenic patients and 44 healthy participants. EDA is a suitable measure of brain and autonomic activity reflecting neurobiological changes in schizophrenia that may indicate changes in nonlinear neural dynamics related to associative process. The results show that quantitative indices of chaotic dynamics (the largest Lyapunov exponents) calculated from EDA signals recorded during rest and the association test are significantly higher in schizophrenia patients than in the control group and increase during the test in comparison to the resting state. The difference was confirmed by statistical methods and using surrogate data testing that rejected an explanation within the linear statistical framework. The results provide supportive evidence that pseudo-randomness of schizophrenic associations and less predictability could be linked to increased complexity of nonlinear neural dynamics, although certain limitations in data interpretation must be taken into account. PMID:19166884
Common prescriptions for psychology derived from dialectical materialism and chaos theory.
Gilgen, A R
2000-04-01
During the entire Soviet period (1917-1991), Russian psychologists labored to create a psychology which would be consonant with Marxist-Leninist assumptions derived from dialectical materialism. Some of their early prescriptions, in particular those put forward by Konstantin N. Kornilov in the 1920s and early 1930s, are identical to strategies being advanced by contemporary American psychologists who propose that chaos theory and nonlinear meta-modeling techniques in general, given advances in computer and television technologies, can be designed for research capable of dealing with the complexities, nonlinearities, self-organizational processes, and abrupt transformations characteristic of human psychological functioning. PMID:10840901
Exploring Career Chaos: Patterns of Belief.
ERIC Educational Resources Information Center
Gibb, Stephen
1998-01-01
Allies the application of chaos theory to career development with phenomenological perspectives exploring people's beliefs. Suggests that this approach reveals that interactive belief systems underlie seemingly random career behavior. (SK)
Finite size scaling of domain chaos
Cross, M. C.; Louie, M.; Meiron, D.
2001-04-01
Numerical studies of the domain chaos state in a model of rotating Rayleigh-Benard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the predicted divergence near onset.
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)
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.
A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction
NASA Astrophysics Data System (ADS)
Györgyi, László; Field, Richard J.
1992-02-01
CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws1-3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov-Zhabotinsky (BZ) reaction4-6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator7 (which cannot produce chaos).
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.
Rotational chaos in dissipative systems
NASA Astrophysics Data System (ADS)
Casdagli, Martin
1988-01-01
An investigation is made into chaotic attractors arising from a quasiperiodic transition to chaos, using a quantity called the rotation interval. The rotation interval describes the short term rotation rates available to the attractor. We present algorithms to calculate it given an appropriate map, differential equation or time series. We find that the rotation interval has a very robust parameter dependence: its endpoints are almost always phase locked. Our numerical ideas are based on the theory of dissipative twist maps, which is reviewed. This theory is also used to prove a theorem about the non-existence of certain strange attractors in nearly conservative systems. Finally, an investigation is made into the relationship between the rotation interval and topological entropy, and the breakup of invariant circles.
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.
Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán
2013-04-01
The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five). PMID:23679502
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.
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.
Embracing Chaos and Complexity: A Quantum Change for Public Health
Resnicow, Kenneth; Page, Scott E.
2008-01-01
Public health research and practice have been guided by a cognitive, rational paradigm where inputs produce linear, predictable changes in outputs. However, the conceptual and statistical assumptions underlying this paradigm may be flawed. In particular, this perspective does not adequately account for nonlinear and quantum influences on human behavior. We propose that health behavior change is better understood through the lens of chaos theory and complex adaptive systems. Key relevant principles include that behavior change (1) is often a quantum event; (2) can resemble a chaotic process that is sensitive to initial conditions, highly variable, and difficult to predict; and (3) occurs within a complex adaptive system with multiple components, where results are often greater than the sum of their parts. PMID:18556599
Different routes to chaos in the Ti:sapphire laser
Kovalsky, Marcelo G.; Hnilo, Alejandro A.
2004-10-01
Kerr-lens mode-locked, femtosecond Ti:sapphire lasers can operate in two coexistent pulsed modes of operation, named P1 (transform limited output pulses) and P2 (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter's space, and the embedding and correlation dimensions of the attractors (and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.
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).
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.
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.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2016-05-01
We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.
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
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.
Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos
NASA Astrophysics Data System (ADS)
Sivakumar, B.; Berndtsson, R.; Olsson, J.; Jinno, K.; Kawamura, A.
Sivakumar et al. (2000a), by employing the correlation dimension method, provided preliminary evidence of the existence of chaos in the monthly rainfall-runoff process at the Gota basin in Sweden. The present study verifies and supports the earlier results and strengthens such evidence. The study analyses the monthly rainfall, runoff and runoff coefficient series using the nonlinear prediction method, and the presence of chaos is investigated through an inverse approach, i.e. identifying chaos from the results of the prediction. The presence of an optimal embedding dimension (the embedding dimension with the best prediction accuracy) for each of the three series indicates the existence of chaos in the rainfall-runoff process, providing additional support to the results obtained using the correlation dimension method. The reasonably good predictions achieved, particularly for the runoff series, suggest that the dynamics of the rainfall-runoff process could be understood from a chaotic perspective. The predictions are also consistent with the correlation dimension results obtained in the earlier study, i.e. higher prediction accuracy for series with a lower dimension and vice-versa, so that the correlation dimension method can indeed be used as a preliminary indicator of chaos. However, the optimal embedding dimensions obtained from the prediction method are considerably less than the minimum dimensions essential to embed the attractor, as obtained by the correlation dimension method. A possible explanation for this could be the presence of noise in the series, since the effects of noise at higher embedding dimensions could be significantly greater than that at lower embedding dimensions.
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.
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
Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence
NASA Technical Reports Server (NTRS)
Lipsitz, L. A.; Goldberger, A. L.
1992-01-01
The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.
Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure
NASA Technical Reports Server (NTRS)
Maestrello, L.
2000-01-01
Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.
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…
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…
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…
Generic superweak chaos induced by Hall effect
NASA Astrophysics Data System (ADS)
Ben-Harush, Moti; Dana, Itzhack
2016-05-01
We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.
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
Quantum chaos in nanoelectromechanical systems
NASA Astrophysics Data System (ADS)
Gusso, André; da Luz, M. G. E.; Rego, Luis G. C.
2006-01-01
We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate’s surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian orthogonal ensemble or the Gaussian unitary ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.
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
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
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
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. PMID:26465514
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.
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
Simultaneous bidirectional message transmission in a chaos-based communication scheme
NASA Astrophysics Data System (ADS)
Vicente, Raúl; Mirasso, Claudio R.; Fischer, Ingo
2007-02-01
We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. By coupling two semiconductor lasers through a partially transparent optical mirror, delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel.
Nonlinear magnetization dynamics under circularly polarized field.
Bertotti, G; Serpico, C; Mayergoyz, I D
2001-01-22
Exact analytical results are presented for the nonlinear large motion of the magnetization vector in a body with uniaxial symmetry subject to a circularly polarized field. The absence of chaos, the existence of pure time-harmonic magnetization modes with no generation of higher-order harmonics, and the existence of quasiperiodic magnetization modes with spontaneous breaking of the rotational symmetry are proven. Application to ferromagnetic resonance and connection with the Stoner-Wohlfarth model are discussed. PMID:11177922
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.
Teaching Deterministic Chaos through Music.
ERIC Educational Resources Information Center
Chacon, R.; And Others
1992-01-01
Presents music education as a setting for teaching nonlinear dynamics and chaotic behavior connected with fixed-point and limit-cycle attractors. The aim is not music composition but a first approach to an interdisciplinary tool suitable for a single-session class, at either the secondary or undergraduate level, for the introduction of these…
Transition to chaos of thermocapillary convection
NASA Astrophysics Data System (ADS)
Li, Kai; Tang, Ze Mei; Aa, Yan; Hu, Wen-Rui
Transition of fluid convection to chaos in dissipative dynamical systems is a subject of great interest for both its theoretical and practical aspects in the fluid mechanics. Extensive studies have shown that there are several routes of the buoyant natural convection to chaos depending on parameters of the dissipative dynamical systems such as the Rayleigh number, the Prandtl number and geometry aspect. Another important type of natural convection is thermocapillary convection driven by the surface-tension gradient prominent in fluid systems with interface in the microgravity condition or in small-scaled terrestrial configurations (The relative importance of the gravity effect to the capillary effect is scaled by the static Bond number, , and the dynamic Bond number, , the geometrical scale of the system in the terrestrial experiments, therefore, was significantly reduced to make the capillary effect dominant). The thermocapillary convection has become one of the fundamental subjects in the microgravity fluid physics and space fluid/heat management. However, most studies now available were focused on the onset of oscillatory thermocapillary convection, the initial regime of the route to chaos. A complete route to chaos in such a new sort of dissipative system is still an attractive open question, especially in the experimental study. In present study, the route to chaos of the thermocapillary convection has been investigated. Several routes to chaos, e.g. period oscillatory convection to quasi-period oscillatory convection with 2 to 3 major frequencies, a series of successive period doubling bifurcations and their combination, of the thermocapillary flow is reported through the temperature measurements and the corresponding real time analysis of frequency spectra accomplished by Fast-Fourier-Transformation (FFT) or numerically. The corresponding phase diagrams are also provided.
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.
Cultural chaos in the trenches: staff perspectives.
Untied, P
1999-03-01
When a hospital is acquired by a large health care organization, there are many challenges, for both the hospital and the organization. When the differences in culture are not addressed effectively by management at the time of acquisition, this can result in cultural chaos for the staff and a lengthened transition time. In this article, a staff member shares the observations, opinions, and feelings she experienced during such a time of cultural chaos between two well-respected organizations. Her opinions and observations are juxtaposed with the lives of two amalgamated fictionalized characters. PMID:10373980
On chaos synchronization and secure communication.
Kinzel, W; Englert, A; Kanter, I
2010-01-28
Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. PMID:20008407
Synchronization of Chaos in a Food Chain
NASA Astrophysics Data System (ADS)
Singh, Anuraj; Gakkhar, Sunita
2010-10-01
The three species ratio-dependent food chain (Holling-Tanner type) model is investigated by Gakkhar and Naji is known to have chaotic behavior for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.
Stochastic Finite Element Analysis using Polynomial Chaos
NASA Astrophysics Data System (ADS)
Drakos, S.; Pande, G. N.
2016-03-01
This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.
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.
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.
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
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.
Bifurcation, chaos, and scan instability in dynamic atomic force microscopy
NASA Astrophysics Data System (ADS)
Cantrell, John H.; Cantrell, Sean A.
2016-03-01
The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force "stiffness," the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model with frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.
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.
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
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.
Topological approximation of the nonlinear Anderson model.
Milovanov, Alexander V; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t→+∞. The second moment of the associated probability distribution grows with time as a power law ∝ t^{α}, with the exponent α=1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport. PMID:25019865
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…
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.
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…
Still Another Approach to Administration: Chaos Theory.
ERIC Educational Resources Information Center
Griffiths, Daniel E.; And Others
1991-01-01
Uses chaos systems concepts to analyze a case study of rapid growth and conflict in a southwestern school district. Difficulties arising from the need for very precise initial measurements, data forms adaptable to pattern modeling, and precise meanings for chaotic systems concepts limit chaotic theory's application to educational administration…
Chaos and Change in a Suicidal Family.
ERIC Educational Resources Information Center
Chamberlain, Linda
1995-01-01
The concepts evolving from chaos theory can help clinicians identify patterns in family interactions that are critical for transformations to occur. This article explores a specific case example from such a perspective. Observation of how suicidal behavior becomes part of a pattern of family interaction offers a framework for clinicians to observe…
Chaos Theory in the Arts and Design.
ERIC Educational Resources Information Center
McWhinnie, Harold J.
This paper explores questions associated with chaos theory as it relates to problems in the arts. It reviews the work of several scholars including Minai, Eckersley, Pickover, the Kirsches, and the Molnars. The document directs special attention toward three basic areas in art and design education, which are: (1) the integration of the computer…
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.
How to Generate Chaos at Home.
ERIC Educational Resources Information Center
Smith, Douglas
1992-01-01
Describes an electronic circuit that can function as a prototype for chaotic systems. Specific applied voltages produce chaotic signals that can be viewed with an oscilloscope or be made audible with a home stereo system. Provides directions for assembly with typical costs, mathematical basis of chaos theory, and experimental extensions. (JJK)
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.
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
[Chaos theory: a fascinating concept for oncologists].
Denis, F; Letellier, C
2012-05-01
The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. PMID:22401775
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.
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,…
Chaos theory: a new paradigm for psychotherapy?
Lonie, I
1991-12-01
Thomas Kuhn's concept of paradigm as central to the functioning of a mature science is linked with Johnson-Abercrombie's recognition that perception itself is shaped by the schemata available to the subject. The rapidly advancing field of non-linear mathematics, in offering conceptual forms to represent complex events, may provide a useful framework in which to place various psychodynamic formulations about the development of the personality, and suggests the possibility of a new approach to research concerning the efficacy of psychotherapy. Dan Stern's latest concept of "moments" as the basic unit in structuring the personality, leading to the complex representational patterns and feed-back loops he terms "RIGS" may be viewed in this context. The paradigm may be extended to include such concepts as Peterfreund's linkage of psychodynamic theorising with aspects of information theory generated by the study of computers, and with Sullivan's concepts of repetitive patterns of behaviour recognisable, and changing, throughout the course of a therapy. PMID:1793425
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
NASA Astrophysics Data System (ADS)
Zhang, Hailong; Zhang, Ning; Min, Fuhong; Yan, Wei; Wang, Enrong
2016-03-01
Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.
Controlling Chaos, Targeting, and Transport.
NASA Astrophysics Data System (ADS)
Bollt, Erik Matthew Arnold
1995-01-01
The sensitivity that defines chaotic dynamics makes accessible a wide range of behaviors using arbitrarily small control signals. "Controlling chaos" attempts to cause large changes in the dynamics using only small perturbations. In targeting, one attempts to find a fast path from an initial condition {bf a} to a target point {bf b} by exploiting the fact that transport times for a chaotic system are highly sensitive to initial conditions and parameter values. The main difficulty is finding the switching points, the times and places to apply judiciously chosen perturbations. I present a new technique to find rough orbits (epsilon chains) that rapidly achieve a desired transport. The strategy is to build the epsilon chain from segments of a long orbit. In two-dimensional maps, long orbits have recurrences in neighborhoods where faster orbits must also pass. Long orbits of higher dimensional maps are likely to have recurrences, albeit less frequently. The recurrences are used as switching points between segments. If a local hyperbolicity condition is satisfied, then a nearby shadow orbit might be constructed. In one example, I show that transport times for the standard map can typically be reduced by a factor of 10^4. In another example, I apply the technique to the restricted three-body problem from which I find a low energy Earth-Moon transfer orbit which requires 38% less characteristic velocity than a comparable Hohmann transfer orbit. In yet another example, a symbol dynamics model has a closed-form expression for the optimal transporting orbit from near {bf a} to near {bf b}. I compare the optimal orbit to the targeted orbit resulting from removing recurrences, which also takes a particularly simple form in symbol dynamics. The techniques developed here do not require a closed-form representation of the map. Using the standard map as an example, I demonstrate that predictions from a time series may be sufficient for targeting. Finally, as a contribution to the understanding of barriers in high-dimensional Hamiltonian maps, I present a technique to investigate the breakup of invariant tori with fixed frequency of a four-dimensional generalization of the complex, semi-standard map.
Swanstrom, Lee L.; Park, Adrian; Arregui, Marty; Franklin, Morris; Smith, C Daniel; Blaney, Christina
2006-01-01
Background: Since 1993, there has been an increase in the number of postgraduate fellowships in minimally invasive and gastrointestinal (GI) surgery; from 9 in 1993 to more than 80 in 2004. Early on, there was no supervision or accreditation of these fellowships, and they varied widely in content, structure, and quality. This was widely recognized as being a bad situation for fellow applicants and reflected poorly on the specialties of minimally invasive (MI) and GI surgery. In an effort to bring order to this chaotic situation, the Minimally Invasive Surgery Fellowship Council (MISFC) was founded in 1997. Method: In 2003, the MISFC was incorporated with 77 founding member programs. The goal of the MISFC was to develop guidelines for high-quality fellowship training, to provide a forum for the directors of MI and GI fellowships to exchange ideas, formulate training curricula; to establish uniform application and selection dates; and to create an equitable computerized match system for applicants. Results: In 2004, the MISFC has increased to 95 members representing 154 postgraduate fellowship positions. The majority of these positions are primarily laparoscopic in focus, but other aspects of GI surgery including bariatric, general GI, flexible endoscopy, and hepatopancreatobiliary are also represented. Uniform application and selection dates were agreed on in 2001; and in 2003, the Council established a computerized Match, administered by the National Resident Match Program, which was used for the 2004 fellowship selection. A total of 113 positions were open for the match. A total of 248 applicants formally applied to MISFC programs and 130 participated in the match. Ninety-nine positions matched on the December 10th match day, and the remaining 14 programs successfully filled on the following scramble day. Seventeen applicants did not match to a program. Post match polling of program directors and applicants documented a high degree of compliance, usability, and satisfaction with the process. Conclusion: The MISFC has been successful at realizing its goals of bringing order to the past chaos of the MIS and GI fellowship situation. Its current iteration, the Fellowship Council, is in the process of introducing an accreditation process to further ensure the highest quality of postgraduate training in the fields of GI and endoscopic surgery. PMID:16552191
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.
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.
The role of self-consistent Lagrangian chaos in Benard convection in an annulus
Finn, J.M.; Hermiz, K. )
1993-11-01
The nonlinear behavior of the two-dimensional Benard problem with periodic boundary conditions in the horizontal direction is studied with particular emphasis on the role of self-consistent chaotic advection. The results show a complex interplay between vortices driven by the Benard (Rayleigh--Taylor) instability and shear flow, which is driven by the vortices [J. Drake [ital et] [ital al]., Phys. Fluids B [bold 4], 4881 (1992)] and which causes their decay. Chaotic advection occurs in the transition from the low Rayleigh number (Ra) regime to the high Ra regime [J. Finn, Phys. Fluids B [bold 5], 415 (1993)]. For the former, vortex flow and shear flow coexist, possibly with slow relaxation oscillations. In the high Ra regime there are vortices localized near the upper and lower boundaries with a shear flow in between. As Ra is decreased from the high Ra regime, these vortices broaden, eventually overlapping, causing self-consistent Lagrangian chaos. This onset of chaos is responsible for several properties of the transition state between the low Ra and the high Ra regimes, most notably the damping of the relaxation oscillations involving vortex and shear flow. It is also observed that the Nusselt number Nu has a peak with respect to Ra in this transition regime characterized by Lagrangian chaos. In the low Ra regime, on the other hand, the relaxation oscillations are on a much slower time scale than the eddy turnover time and the Lagrangian behavior is described by separatrix crossing.
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
Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation
NASA Astrophysics Data System (ADS)
Makarov, D. V.; Kon'kov, L. E.
2015-03-01
The motion of a randomly driven quantum nonlinear pendulum is considered. Utilizing a one-step Poincaré map, we demonstrate that the classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study the influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. The transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.
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 Forecasting for the Classification of Natural Time Series
NASA Astrophysics Data System (ADS)
Sugihara, George
1994-09-01
There is a growing trend in the natural sciences to view time series as products of dynamical systems. This viewpoint has proven to be particularly useful in stimulating debate and insight into the nature of the underlying generating mechanisms. Here I review some of the issues concerning the use of forecasting in the detection of nonlinearities and possible chaos, particularly with regard to stochastic chaos. Moreover, it is shown how recent attempts to measure meaningful Lyapunov exponents for ecological data are fundamentally flawed, and that when observational noise is convolved with process noise, computing Lyapunov exponents for the real system will be difficult. Such problems pave the way for more operational definitions of dynamic complexity (cf. Yao & Tong, this volume). Aside from its use in the characterization of chaos, nonlinear forecasting can be used more broadly in pragmatic classification problems. Here I review a recent example of nonlinear forecasting as it is applied to classify human heart rhythms. In particular, it is shown how forecast nonlinearity can be a good discriminator of the physiological effects of age, and how prediction-decay may discriminate heart-disease. In so doing, I introduce a method for characterizing nonlinearity using `S-maps' and a method for analysing multiple short time series with composite attractors.
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
2015-07-15
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.
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.
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 ℏ 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.
Are earthquakes an example of deterministic chaos?
NASA Technical Reports Server (NTRS)
Huang, Jie; Turcotte, Donald L.
1990-01-01
A simple mass-spring model is used to systematically examine the dynamical behavior introduced by fault zone heterogeneities. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by elastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. A simple static/dynamic friction law is used. When the system is symmetric, cyclic behavior is observed. For an asymmetric system, where the frictional forces for the two blocks are not equal, the solutions exhibit deterministic chaos. Chaotic windows occur repeatedly between regions of limit cycles on bifurcation diagrams. The model behavior is similar to that of the one-dimensional logistic map. The results provide substantial evidence that earthquakes are an example of deterministic chaos.
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.
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.
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.
Ergodic chaos-based communication schemes
NASA Astrophysics Data System (ADS)
Leung, H.; Yu, H.; Murali, K.
2002-09-01
Recent studies have shown the applicability of synchronized chaotic systems to the area of communications in different ways. At the same time synchronization based signal recovery and estimation of parameters severely suffer due to the presence of channel noise. By exploiting the ergodic properties of chaotic signals effectively, a simple technique called the mean-value method is introduced. This method is shown to be capable of estimating chaos system parameters from the transmitted chaotic signal efficiently for a low signal-to-noise ratio. A suitable demodulator has been designed for ergodic chaotic parameter modulation scheme for digital signal communication. Further, the mean-value technique incorporates a noncoherent receiver to recover analog information signal from the chaos masked signal efficiently. It is found that the proposed chaotic masking scheme is robust even in the presence of strong noise. In addition, this scheme has the potential advantage of a very simple hardware realization, which promises enhanced signal recovery performances.
Chaos theory perspective for industry clusters development
NASA Astrophysics Data System (ADS)
Yu, Haiying; Jiang, Minghui; Li, Chengzhang
2016-03-01
Industry clusters have outperformed in economic development in most developing countries. The contributions of industrial clusters have been recognized as promotion of regional business and the alleviation of economic and social costs. It is no doubt globalization is rendering clusters in accelerating the competitiveness of economic activities. In accordance, many ideas and concepts involve in illustrating evolution tendency, stimulating the clusters development, meanwhile, avoiding industrial clusters recession. The term chaos theory is introduced to explain inherent relationship of features within industry clusters. A preferred life cycle approach is proposed for industrial cluster recessive theory analysis. Lyapunov exponents and Wolf model are presented for chaotic identification and examination. A case study of Tianjin, China has verified the model effectiveness. The investigations indicate that the approaches outperform in explaining chaos properties in industrial clusters, which demonstrates industrial clusters evolution, solves empirical issues and generates corresponding strategies.
Common Chaos in Arbitrarily Complex Feedback Networks
NASA Astrophysics Data System (ADS)
Mestl, Thomas; Bagley, R. J.; Glass, Leon
1997-07-01
A class of differential equations, which captures the logical structure of discrete time logical switching networks composed of many elements, displays deterministic chaos if each element has many inputs. Statistical features of the dynamics are approximated by using a mean field Langevin-type equation with a random telegraph signal as a stochastic forcing function, and also by considering a random walk on an N-dimensional hypercube.
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.
Chaos in the lowest Landau level
Emery, V.J.
1991-01-01
The problem of a few electrons in the lowest Landau level is discussed. Low-lying states of the three-and four-electron problems are constructed. In the classical limit, the three-body problem is integrable but there is numerical evidence of chaotic motion in the four-body problem. Consequences of classical chaos for the statistics of energy levels are described and the possibility of carrying out relevant experiments in semiconductor heterostructures is discussed. 9 refs.
Chaos: 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.
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.
Input-dependent Suppression of Chaos in Recurrent Neural Networks
NASA Astrophysics Data System (ADS)
Rajan, K.; Abbott, L. F.; Sompolinsky, H.
2010-03-01
Neuronal responses arise from an interaction between spontaneous activity and responses driven by external inputs. Experiments studying cortical circuits reveal a striking similarity between the magnitude and complexity of intrinsic and input-generated activity. How does a network generating complex activity remain sensitive to external inputs? This seems unlikely for a network in which input-driven responses add linearly to ongoing activity generated by stochastic noise generators. We developed a mean-field theory and used recurrent network models to distinguish between this type of external noise and chaotic background generated by strong coupling within the circuit. As a result of a highly nonlinear relationship between input- and internally generated activity, we show that intrinsic noise is sensitive to the amplitude and the spatiotemporal structure of the input. We find that input not only drives responses, it also actively suppresses spontaneous activity, leading to a phase transition in which the chaotic background is absent. Although the power spectrum of the spontaneous activity falls exponentially from zero, the phase transition reveals a resonant frequency at which relatively a weak input suppresses chaos. As long as the input drives the system across the phase transition, a spontaneously active network can work with coupling strong enough to allow large signal amplification and selectivity without the complex background interfering with sensory processing.
Endogenous rhythms and chaos in crassulacean acid metabolism.
Lüttge, U; Beck, F
1992-08-01
Endogenous free-running regular circadian oscillations of net CO2 exchange in the crassulacean-acidmetabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie under constant external conditions in continuous light have been shown to change to irregular non-predictable (chaotic) time behaviour as irradiance or temperature are raised above a critical level. A model of CAM has been constructed with pools of major metabolites of varying concentrations, flows of metabolites leading to exchange between pools, metabolite transformations determined by chemical reactions, and feedback regulations. The model is described by a system of coupled non-linear differential equations. It shows stable rhythmicity in normal dark-light cycles and in continuous light and, like the K. daigremontiana leaves in the experiments, a change to chaos as irradiance is increased. The maintenance of endogenous oscillations in the model is brought about by a hysteresis switch or beat oscillator between two stable oscillation modes. In CAM these stable modes are vacuolar malate accumulation and remobilization. The model shows that the physical nature of the beat oscillator in the leaves can be explained by the balance between active and passive transport at the tonoplast. PMID:24178196
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.
Investigating chaos in river stage and discharge time series
NASA Astrophysics Data System (ADS)
Khatibi, Rahman; Sivakumar, Bellie; Ghorbani, Mohammad Ali; Kisi, Ozgur; Koçak, 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.
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.
NASA Astrophysics Data System (ADS)
Li, Feng; Kutz, J. Nathan; Wai, P. K. A.
2012-04-01
We consider the nonlinear dynamics of multiwavelength laser cavities with saturable transmitter and saturating homogeneous gain using a simple and general discrete model. Saturable transmitter is an intensity dependent loss in which the transmittance decreases when the incident optical power increases. We determine the condition under which the saturable transmitter will generate behaviors such as stable steady-state lasing states, periodic lasing states, and chaotic lasing states. Indeed, for sufficiently large power, steady-state operation is first destabilized through a Hopf bifurcation which generates periodic lasing solutions. This is followed by a sequence of period doubling bifurcations to chaotic lasing. The bifurcation structure leading to chaos is characterized by three key methods of dynamical systems: a Feigenbaum series, the calculation of Lyapunov exponents and the computation of the correlation dimension of the system. We found that even single wavelength operation can exhibit complex nonlinear dynamics if the loss element is a saturable transmitter.
NASA Astrophysics Data System (ADS)
Kuznetsov, S. P.
2016-03-01
Equations are derived for a parametric chaos generator containing three oscillatory circuits and a variable-capacitance diode (varactor) and are reduced to equations for slow amplitudes of parametrically interacting modes. With allowance for quadratic nonlinearity, the problem is reduced to a system of three first-order differential equations for Pikovsky-Rabinovich-Trakhtengerts real amplitudes with a Lorenz-type attractor. In a more accurate description of nonlinearity of the varactor, the equations for slow amplitudes are complex-valued, which leads to the loss of robustness of chaotic dynamics, which is typical of the Lorenz attractor. The results of numerical calculations (portraits of attractors and Lyapunov exponents) in models with different approximation levels are compared.
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.
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.
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
Chaos Theory as a Lens for Advancing Quality Schooling.
ERIC Educational Resources Information Center
Snyder, Karolyn J.; Acker-Hocevar, Michele; Wolf, Kristen M.
Chaos theory provides a useful mental model for guiding change as leaders garner the energy from unpredictable events for realizing transformation goals. The paper considers chaos theory as a framework for managing school change toward Total Quality Management work cultures. Change is possible to manage when plans are made and then followed by a…
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: 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…
C. Y. Chao, Pair Creation and Pair Annihilation
NASA Astrophysics Data System (ADS)
Li, Bing An; Yang, C. N.
C. Y. Chao's contribution to physicists' acceptance of QED in 1933-1934 through his experiments of 1930 is analyzed. It is pointed out that Blackett and Occhialini's key suggestion of 1933 about hole theory was based on identifying Chao's "additional scattered rays" (1930) as due to pair annihilation.
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…
C. Y. Chao, Pair Creation and Pair Annihilation
NASA Astrophysics Data System (ADS)
Li, Bing An; Yang, C. N.
2013-05-01
C. Y. Chao's contribution to physicists' acceptance of QED in 1933-1934 through his experiments of 1930 is analyzed. It is pointed out that Blackett and Occhialini's key suggestion of 1933 about hole theory was based on identifying Chao's "additional scattered rays" (1930) as due to pair annihilation.
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 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.
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.
Elimination of spiral chaos by periodic force for the Aliev-Panfilov model
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu; Fujimoto, Takefumi
2003-06-01
Spiral chaos appears in the two-dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of the spiral chaos is most effective when the frequency of the periodic force is close to that of the breathing motion.
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.
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
Bose-Hubbard Hamiltonian: Quantum chaos approach
NASA Astrophysics Data System (ADS)
Kolovsky, Andrey R.
2016-03-01
We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose-Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.
Order and the ubiquitous occurrence of chaos
NASA Astrophysics Data System (ADS)
Fokas, A. S.; Bountis, T.
1996-02-01
For a large class of ODE's, which includes the Van der Pol equation, we determine analytically the asymptotic location of the singularities in the complex t-plane. By integrating these ODE's numerically we show that if the singularities are dense, which is the generic case, the solution is chaotic, in the sense of sensitive dependence on initial conditions. In the exceptional case that the singularities are not dense, the solution exhibits order (taxis). Chaos is ubiquitous even for first order ODE's in complex t.
Feigenbaum graphs at the onset of chaos
NASA Astrophysics Data System (ADS)
Luque, Bartolo; Lacasa, Lucas; Robledo, Alberto
2012-11-01
We analyze the properties of networks obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such entropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.
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.
Nonlinearity of TCP and instability with RED
NASA Astrophysics Data System (ADS)
La, Richard J.; Ranjan, Priya; Abed, Eyad H.
2002-07-01
Recently researchers have proposed active queue management (AQM) mechanisms as a means of better managing congestion at the bottlenecks inside the network. Random Early Detection (RED) mechanism has been proposed to control the average queue size at the congested routers. It has been shown that the interaction between an RED gateway and TCP connections can lead to period doubling bifurcation and chaos. In this paper we extend this model and study the interaction of the RED gateway with TCP and UDP connections, using a discrete-time model. First, we show that the presence of UDP traffic does much more than simply taking away the available capacity from the TCP connections. In fact it fundamentally changes the dynamics of the system. Second, with the help of bifurcation diagrams, we demonstrate the existence of nonlinear phenomena, such as oscillations and chaos, as the parameters of the RED mechanism are varied. Further, the presence of UDP traffic tends to stabilize the system in the sense that bifurcations and chaos are delayed in the parameter region. We investigate the impact of various system parameters on the stability of the system, present numerical results, and validate our analysis through ns-2 simulation.
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.
Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation
NASA Technical Reports Server (NTRS)
Moon, H. T.; Goldman, M. V.
1984-01-01
The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.
Zeeman catastrophe machines as a toolkit for teaching chaos
NASA Astrophysics Data System (ADS)
Nagy, Péter; Tasnádi, Péter
2014-01-01
The investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics in the basic course of mechanics taught to engineering students. In this paper, it will be demonstrated that the Zeeman machine can be a versatile and motivating tool for students to acquire introductory knowledge about chaotic motion via interactive simulations. The Zeeman catastrophe machine is a typical example of a quasi-static system with hysteresis. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple, the experimental investigation and the theoretical description can be connected intuitively. Although the Zeeman machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman machine, a wide range of chaotic properties of the simple systems can be demonstrated, such as bifurcation diagrams, chaotic attractors, transient chaos, Lyapunov exponents and so on. This paper is organically linked to our website (http://csodafizika.hu/zeeman) where the discussed simulation programs can be downloaded. In a second paper, the novel construction of a network of Zeeman machines will be presented to study the properties of cooperative systems.
Responses of spatiotemporal chaos to oscillating forces
NASA Astrophysics Data System (ADS)
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, Mp(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, Mp(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 Mp(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 Mp(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 Mp(t ) .
Chaos and structure of level densities
Moller, Peter; Aberg, Sven; Uhrenholt, Henrik; Ickhikawa, Takatoshi
2008-01-01
The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.
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.
Chaos suppression in gas-solid fluidization
Pence, D.V.; Beasley, D.E.
1997-07-01
The present study examines the effect of an opposing oscillatory flow on local, instantaneous heat transfer and pressure in a laboratory scale gas-fluidized bed. The experimental facility models a Pulsed Atmospheric Fluidized Bed Combustor (PAFBC), a hybrid combustor concept that couples a pulsed combustor with an atmospheric bubbling fluidized bed. Time-varying data were acquired at eight angular positions around a horizontal cylinder submerged in a monodisperse distribution of particles having a weight mean diameter of 345 {micro}m. Total flow rates employed in the present study ranged from 10 to 40% greater than the flow required for minimum fluidization. Spectral analyses of local, instantaneous heat flux and pressure clearly indicate that the bed hydrodynamics were significantly altered by the opposing secondary flow. The behavior of time-varying local pressure and heat transfer in fluidized beds in the absence of a secondary flow is consistent with deterministic chaos. Kolmogorov entropy estimates from local, instantaneous pressure suggest that the degree of chaotic behavior was substantially suppressed for operating conditions with low primary and secondary flow rates, and a secondary flow forcing frequency of 15 Hz. In contrast, entropy estimates from measurements of local, instantaneous heat transfer suggest no clear indication of chaos suppression for these operating conditions.
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.
Chaos control: The problem of a bouncing ball revisited
NASA Astrophysics Data System (ADS)
Vargas, M. Cristina; Huerta, D. A.; Sosa, Victor
2009-09-01
The problem of a body bouncing on a periodically oscillating surface is revisited to demonstrate chaos control. When the bouncing body is magnetic, it is possible to modify its behavior by adding a magnetic driving force. The mechanism of chaos control may be understood by means of a mechanical analysis which shows that the main result of applying the driving force is to shift the bifurcation diagram in such a way that chaotic behavior is replaced by periodic behavior and vice versa. A simple experiment is presented, along with a numerical simulation, that provides insight into chaos control.
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.
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.
NASA Astrophysics Data System (ADS)
Zavrazhina, T. V.
2007-10-01
A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ℝ2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.
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.
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.
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.
Theory for the experimental observation of chaos in a rotating waterwheel
NASA Astrophysics Data System (ADS)
Kolá, Miroslav; Gumbs, Godfrey
1992-01-01
We study the chaos for a set of coupled, nonlinear partial-differential equations that originate from the equation of motion and the Fourier transform of the mass-conservation equation for the Malkus waterwheel. Dissipation for this system is produced by an adjustable brake. The braking force, proportional to the angular velocity of the wheel, is responsible for the appearance of chaos. The variation of the moment of inertia with time is taken into account. In the large-time limit, the moment of inertia of the composite system, consisting of the wheel and water, tends to a constant, and the three controlling equations of the set of coupled limit equations reduce to a special case of the Lorenz equations, in which the Rayleigh number ρ (here characterizing the distribution of water inflow along the perimeter of the wheel) can also assume negative values. Chaotic attractors of the higher harmonics of the water density have been investigated. Boundaries between various regimes of the wheel's limit behavior (uniform rotation, periodic reversals of spin, chaotic reversals) in the Lorenz parameter space have been found. The Lorenz parameter space has thus been explored in considerably more detail than by previous authors.
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).].
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
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.
Numerical and experimental exploration of phase control of chaos.
Zambrano, Samuel; Allaria, Enrico; Brugioni, Stefano; Leyva, Immaculada; Meucci, Riccardo; Sanjuán, Miguel A F; Arecchi, Fortunato T
2006-03-01
A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally. PMID:16599742
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.
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.
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.
Fibonacci order in the period-doubling cascade to chaos
NASA Astrophysics Data System (ADS)
Linage, G.; Montoya, Fernando; Sarmiento, A.; Showalter, K.; Parmananda, P.
2006-12-01
In this contribution, we describe how the Fibonacci sequence appears within the Feigenbaum scaling of the period-doubling cascade to chaos. An important consequence of this discovery is that the ratio of successive Fibonacci numbers converges to the golden mean in every period-doubling sequence and therefore the convergence to ϕ, the most irrational number, occurs in concert with the onset of deterministic chaos.
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.
Synchronization of chaos in fully developed turbulence.
Lalescu, Cristian C; Meneveau, Charles; Eyink, Gregory L
2013-02-22
We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions. PMID:23473150
Overview of classical and quantum Hamiltonian chaos
NASA Astrophysics Data System (ADS)
Casati, G.
Classical and quantum Hamiltonian chaos is considered, with attention focused on systems acted on by an external periodic perturbation, since they allow - in principle - for continuous spectra and moreover are amenable to experimental investigation. The first and most popular model introduced to study the appearance of chaotic motion in quantum systems is the delta-function kicked rotator, as described in Casati, Chirikov, Izrailev and Ford (1979). The main features of the classical and quantum motion of this model are illustrated. The hydrogen atom under a microwave field is considered, and an interesting phenomenon - transition to quantum delocalization (where the quantum packet delocalizes and indefinite 'diffusion' takes place as the perturbation strength increases above a critical value called the quantum delocalization border) - is examined.