Linear and Nonlinear Dynamical Chaos
Chirikov, B V
1997-01-01
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together wit...
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Digital Communications Using Chaos and Nonlinear Dynamics
Larson, Lawrence E; Liu, Jia-Ming
2006-01-01
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...
Nonlinear Dynamics: Integrability, Chaos and Patterns
Energy Technology Data Exchange (ETDEWEB)
Grammaticos, B [GMPIB, Universite Paris VII, Tour 24--14, 5e etage, Case 7021, 75251 Paris (France)
2004-02-06
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
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
Nonlinear Dynamics and Chaos: Advances and Perspectives
Thiel, Marco; Romano, M. Carmen; Károlyi, György; Moura, Alessandro
2010-01-01
This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most important researchers. The first contribution in this book, "How did you get into Chaos?", is actually a collection of personal accounts by a number of distinguished scientists on how they entered the field of chaos and dynamical systems, featuring comments and recollections by James Yorke, Harry Swinney, Floris Takens, Peter Grassberger, Edward Ott, Lou Pecora, Itamar Procaccia, Michael Berry, Giulio Casati, Valentin Afraimovich, Robert MacKay, and last but not least, Celso Grebogi, to whom this volume is dedicated.
Chaos and Nonlinear Dynamics in a Quantum Artificial Economy
Gonçalves, Carlos Pedro
2012-01-01
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.
Contributions of plasma physics to chaos and nonlinear dynamics
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Applications of chaos and nonlinear dynamics in engineering - Vol 1
Rondoni, Lamberto; Banerjee, Santo
2011-01-01
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘r...
Applications of chaos and nonlinear dynamics in science and engineering
Rondoni, Lamberto; Mitra, Mala
Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever the quantitative modeling and analysis of complex, nonlinear phenomena are required, chaos theory and its methods can play a key role. This second volume concentrates on reviewing further relevant, contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such as the spread of epidemics; electronic circuits; chaos control in mechanical devices; secure communication; and digital watermarking. Featuring contributions from active and leading research groups, this collection is ideal both as a reference work and as a ‘recipe book’ full of tried and tested, successf...
Nonlinear dynamics and chaos in an optomechanical beam
Navarro-Urrios, D; Colombano, M F; Garcia, P D; Sledzinska, M; Alzina, F; Griol, A; Martinez, A; Sotomayor-Torres, C M
2016-01-01
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning between an optical resonance and the excitation laser. However, the interplay between such mechanisms could also enable unexpected physical phenomena to be used in new applications. In the present work, we exploit those non-linearities and their intercoupling with the mechanical degrees of freedom of a silicon OM nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser, namely its power and wavelength, we demonstrate accurate control for activating bi-dimensional and tetra-dimensional limit-cycles, a period doubling route and chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between bi-dimensional and tetra-dimensional limit-cycles, be...
Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences
Selvam, A M
2010-01-01
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm - sec to climate scales of thousands of kilometers - years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long - range correlations identified as self - organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the self-similar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and inco...
AUTO-EXTRACTING TECHNIQUE OF DYNAMIC CHAOS FEATURES FOR NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
CHEN Guo
2006-01-01
The main purpose of nonlinear time series analysis is based on the rebuilding theory of phase space, and to study how to transform the response signal to rebuilt phase space in order to extract dynamic feature information, and to provide effective approach for nonlinear signal analysis and fault diagnosis of nonlinear dynamic system. Now, it has already formed an important offset of nonlinear science. But, traditional method cannot extract chaos features automatically, and it needs man's participation in the whole process. A new method is put forward, which can implement auto-extracting of chaos features for nonlinear time series. Firstly, to confirm time delay τ by autocorrelation method; Secondly, to compute embedded dimension m and correlation dimension D;Thirdly, to compute the maximum Lyapunov index λmax; Finally, to calculate the chaos degree Dch of features extracting has important meaning to fault diagnosis of nonlinear system based on nonlinear chaos features. Examples show validity of the proposed method.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns
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
A unified theory of chaos linking nonlinear dynamics and statistical physics
Poon, Chi-Sang; Wu, Guo-Qiang
2010-01-01
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene expression or stock exchange to quantum chaos. Traditionally, deterministic chaos is characterized by "sensitive dependence on initial conditions" as indicated by a positive Lyapunov exponent. However, ambiguity arises when applying this criterion to real-world data that are corrupted by measurement noise or perturbed nonautonomously by exogenous deterministic or stochastic inputs. Here, we show that a positive Lyapunov exponent is surprisingly neither necessary nor sufficient proof of deterministic chaos, and that a nonlinear dynamical system under deterministic or stochastic forcing may exhibit multiple forms of nonautonomous chaos assessable by a noise titration assay. These findings lay the foundation for reliable analysis of low-dimensional chaos for complex systems modeling an...
Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.
Zausner, Tobi
2011-04-01
Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation.
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
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
Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
Energy Technology Data Exchange (ETDEWEB)
Farshidianfar, A.; Saghafi, A., E-mail: a.i.saghafi@gmail.com
2014-10-24
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. - Highlights: • This study deals with the prediction and control of chaos in a nonlinear gear system. • Melnikov analysis is extended to present a practical gear system to control the chaos. • The proposed system is effective to eliminate the homoclinic bifurcation and chaos. • This controller is proposed as a way of implementing the chaos control in gear system.
Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases.
Grenfell, B T; Kleczkowski, A; Gilligan, C A; Bolker, B M
1995-06-01
There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demographic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Directory of Open Access Journals (Sweden)
Geoff Boeing
2016-11-01
Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.
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.
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
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.
Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects
Directory of Open Access Journals (Sweden)
Jie-Yu Chen
2009-05-01
Full Text Available 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.
Reithmeier, Eduard
1991-01-01
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly fro...
Takatsuka, Kazuo
Nonlinear dynamics and chaos are studied in a system for which a complete set of equations of motion such as equations of Newton, Navier-Stokes and Van der Pol, is not available. As a very general system as such, we consider coupled classical spins (pendulums), each of which is under control by a fuzzy system that is designed to align the spin to an unstable fixed point. The fuzzy system provides a deterministic procedure to control an object without use of a differential equation. The positions and velocities of the spins are monitored periodically and each fuzzy control gives a momentum to its associated spin in the reverse directions. If the monitoring is made with an interval short enough, the spin-spin interactions are overwhelmed by the fuzzy control and the system converges to a state as designed. However, a long-interval monitoring induces dynamics of “too-late response”, and thereby results in chaos. A great variety of dynamics are generated under very delicate balance between the fuzzy control and the spin-spin interaction, in which two independent mechanisms of creating negative and positive “Liapunov exponents” interact with each other.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Detecting nonlinearity and chaos in epidemic data
Energy Technology Data Exchange (ETDEWEB)
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
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.
Nonlinearity, chaos, and complexity the dynamics of natural and social systems
Bertuglia, Cristoforo Sergio
2005-01-01
Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course. text. - ;Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed...
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
On nonlinear dynamics and control of a robotic arm with chaos
Directory of Open Access Journals (Sweden)
Felix J. L. P.
2014-01-01
Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.
Nonlinear dynamics analysis of a self-organizing recurrent neural network: chaos waning.
Directory of Open Access Journals (Sweden)
Jürgen Eser
Full Text Available Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.
Nonlinear dynamics analysis of a self-organizing recurrent neural network: chaos waning.
Eser, Jürgen; Zheng, Pengsheng; Triesch, Jochen
2014-01-01
Self-organization is thought to play an important role in structuring nervous systems. It frequently arises as a consequence of plasticity mechanisms in neural networks: connectivity determines network dynamics which in turn feed back on network structure through various forms of plasticity. Recently, self-organizing recurrent neural network models (SORNs) have been shown to learn non-trivial structure in their inputs and to reproduce the experimentally observed statistics and fluctuations of synaptic connection strengths in cortex and hippocampus. However, the dynamics in these networks and how they change with network evolution are still poorly understood. Here we investigate the degree of chaos in SORNs by studying how the networks' self-organization changes their response to small perturbations. We study the effect of perturbations to the excitatory-to-excitatory weight matrix on connection strengths and on unit activities. We find that the network dynamics, characterized by an estimate of the maximum Lyapunov exponent, becomes less chaotic during its self-organization, developing into a regime where only few perturbations become amplified. We also find that due to the mixing of discrete and (quasi-)continuous variables in SORNs, small perturbations to the synaptic weights may become amplified only after a substantial delay, a phenomenon we propose to call deferred chaos.
Medvedev, A P; Gavrilushkin, A P; Kiselev, S V; Shelepnev, A V; Smirnov, N A
2001-01-01
An examination of 39 patients with heart diseases was performed before and after operations by the method of geometrical analysis of the nonlinear chaos (fractal) variability of the cardiac rhythm on the basis of the apparatus-programmed complex "Poly-spectrum". Five-minute-long registrations of ECG were carried on. On the basis of the data of examination of 195 healthy volunteers the reference norm of this method parameters was determined. Reliably lower parameters were found in patients with the acquired valvular disease. A dynamic investigation of the geometrical nonlinear structure of the cardiac rhythm has shown the possibility to make a prognosis of early complications after prosthetics of the heart valves.
Nakamura, K.
Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r_{ij} on short scale and logarithmic in r_{ij} on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore ``the chaos in the three-body problem" in the context of vortices with inertia.
Music from chaos: nonlinear dynamical systems as generators of musical materials
Bidlack, Rick Aaron
1990-01-01
A body of scientific/mathematical theory arising from a description of the behavior of complex dynamical systems is explored in terms of its pertinence to and utility in musical schemes for the generation of melodic lines and textures. Such systems are known to model significant behavioral features of real-world phenomena, including turbulent or chaotic behavior. Many of the features of nonlinear dynamical systems that are intriguing from a mathematical point of view, especially the propertie...
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Institute of Scientific and Technical Information of China (English)
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
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.
Chaos and transient chaos in an experimental nonlinear pendulum
de Paula, Aline Souza; Savi, Marcelo Amorim; Pereira-Pinto, Francisco Heitor Iunes
2006-06-01
Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in an experimental nonlinear pendulum. The pendulum consists of a disc with a lumped mass that is connected to a rotary motion sensor. This assembly is driven by a string-spring device that is attached to an electric motor and also provides torsional stiffness to the system. A magnetic device provides an adjustable dissipation of energy. This experimental apparatus is modeled and numerical simulations are carried out. Free and forced vibrations are analyzed showing that numerical results are in close agreement with those obtained from experimental data. This analysis shows that the experimental pendulum has a rich response, presenting periodic response, chaos and transient chaos.
Directory of Open Access Journals (Sweden)
L. L. Adams
2011-01-01
Full Text Available Problem statement: Management is generally easy to define and measure. And, good managers tend to have many of the same characteristics and skill sets. Great leaders, on the other hand, have fewer shared characteristics. Some great leaders are great orators, for example, and yet many other great leaders are terrible public speakers. Great leaders tend to be very intuitive, but other characteristics consistent with great leadership are few indeed. So, the authors of this study had a conversation over several years that led to the reduction of variables to two variables that immediately showed a pattern in individual leadership. Approach: This study presents a practical leadership matrix model based on non-linear dynamics and chaos theory. Specifically, the authors searched for two or more leadership variables (characteristics that would create a definite pattern. The researchers intuitively believed that some combination of variables would set up a pattern just as attractors (strange or otherwise create patterns in data and show some of the characteristics of the system being studied. Over time a set of two main variables, loosely labeled as ethics and energy at first, were identified that created a leadership pattern for individuals. This study describes the process that led to the identification of the two main variables and then to the matrix herein presented. Results: This model, called The WELL by the authors, was created at first to explain political leadership, yet is showing applicability to all kinds of leadership. The WELL as presented is a theoretical construct, with only experiential and qualitative evidence at present to support the patterns inferred from the model. Conclusion: In addition to the extensive political experience of the authors the experience of public safety, mental health, military and academic professionals has been sought to validate the main conclusions shown in this study and to improve the
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
An exploration of dynamical systems and chaos
Argyris, John H; Haase, Maria; Friedrich, Rudolf
2015-01-01
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlar...
Nonlinear Physics Integrability, Chaos and Beyond
Lakshmanan, M
1997-01-01
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the important integrable nonlinear systems while motions which are sensitively dependent on initial conditions are associated with chaotic systems. Besides dramatically raising our perception of many natural phenomena, these concepts are opening up new vistas of applications and unfolding technologies: Optical soliton based information technology, magnetoelectronics, controlling and synchronization of chaos and secure communications, to name a few. These developments have raised further new interesting questions and potentialities. We present a particular view of some of the challenging problems and payoffs ahead in the next few decades by tracing the early historical events, summarizing the revolutionary era of 1950-70 when many important new ideas including solitons and chaos were ...
Dynamical chaos in chip-scale optomechanical oscillators
Wu, Jiagui; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Xia, Guangqiong; Wong, Chee Wei
2016-01-01
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here we report the first generation of dynamical chaos in silicon optomechanical oscillators, enabled by the strong and coupled nonlinearities of Drude electron-hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the complexity of chaos. The correlation dimension D2 is determined at ~ 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate about 2.94*the fundamental optomechanical oscillation. The corresponding nonlinear dynamical maps demonstrate the plethora of subharmonics, bifurcations, and stable regimes, along with distinct transitional routes into chaotic states. The chaos generation in our mesoscopic...
Nonlinear Dynamics and Chaos Applications for Prediction of Weather and Climate
Pethkar, J S
2001-01-01
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature of both short-term weather and long-term climate.It is of importance to quantify the total pattern of fluctuations for predictability studies. The power spectra of temporal fluctuations are broadband and exhibit inverse power law form with different slopes for different scale ranges. Inverse power-law form for power spectra implies scaling (self similarity) for the scale range over which the slope is constant. Atmospheric flows therefore exhibit multiple scaling or multifractal structure.Standard meteorological theory cannot explain satisfactorily the observed multifractal structure of atmospheric flows.Selfsimilar spatial pattern implies long-range spatial correlations. Atmospheric flows therefore exhibit long-range spatiotemporal correlations, namely,self-organized critic...
Sensitivity and chaos control for the forced nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation); Ryashko, Lev [Department of Mathematics, Ural State University, 620083 Ekaterinburg (Russian Federation)] e-mail: lev.ryashko@usu.ru
2005-12-01
This paper is devoted to study the problem of controlling chaos for forced nonlinear dynamic systems. We suggest a new control technique based on sensitivity analysis. With the help of approximation of nonequilibrium quasipotential, stochastic sensitivity function (SSF) is constructed. This function is used as basic tool of a quantitative description for a system response on the random external disturbances. The possibilities of SSF to predict chaotic dynamics for the periodic and stochastic forced Brusselator are shown. The problem of chaos control based on SSF is considered. A design of attractors with the desired features by feedback regulator is discussed. Analysis of controllability and effective technique for regulator synthesis is presented. An example of suppressing chaos for Brusselator is considered.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Utilizing nonlinearity of transistors for reconfigurable chaos computation
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.
Nonlinear feedback control of spatiotemporal chaos in coupled map lattices
Directory of Open Access Journals (Sweden)
Jin-Qing Fang
1998-01-01
Full Text Available We describe a nonlinear feedback functional method for study both of control and synchronization of spatiotemporal chaos. The method is illustrated by the coupled map lattices with five different connection forms. A key issue addressed is to find nonlinear feedback functions. Two large types of nonlinear feedback functions are introduced. The efficient and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed. Various numerical results of nonlinear control are given. We have not found any difficulty for study both of control and synchronization using nonlinear feedback functional method. The method can also be extended to time continuous dynamical systems as well as to society problems.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
Chaos in the fractional order nonlinear Bloch equation with delay
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 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 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
Chaos in attitude dynamics of spacecraft
Liu, Yanzhu
2013-01-01
Attitude dynamics is the theoretical basis of attitude control of spacecrafts in aerospace engineering. With the development of nonlinear dynamics, chaos in spacecraft attitude dynamics has drawn great attention since the 1990's. The problem of the predictability and controllability of the chaotic attitude motion of a spacecraft has a practical significance in astronautic science. This book aims to summarize basic concepts, main approaches, and recent progress in this area. It focuses on the research work of the author and other Chinese scientists in this field, providing new methods and viewpoints in the investigation of spacecraft attitude motion, as well as new mathematical models, with definite engineering backgrounds, for further analysis. Professor Yanzhu Liu was the Director of the Institute of Engineering Mechanics, Shanghai Jiao Tong University, China. Dr. Liqun Chen is a Professor at the Department of Mechanics, Shanghai University, China.
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
Senthilkumar, D. V.; Lakshmanan, M.
2004-01-01
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attain...
Radio lighting based on dynamic chaos generators
Dmitriev, Alexander; Gerasimov, Mark; Itskov, Vadim
2016-01-01
A problem of lighting objects and surfaces with artificial sources of noncoherent microwave radiation with the aim to observe them using radiometric equipment is considered. Transmitters based on dynamic chaos generators are used as sources of noncoherent wideband microwave radiation. An experimental sample of such a device, i.e., a radio lighting lamp based on a chaos microgenerator and its performance are presented.
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Chaos dynamic characteristics during mine fires
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Mine fires break out and continue in confmed scopes, studying mine fire dynamics characteristics is very usefulto prevent and control fire. The judgement index of fire chaos characteristics was introduced, chaos analysis of mine Fireprocess was described, and the reconstruction of phase space was also presented. An example of mine fire was calculated.The computations show that it is feasible to analyze mine fire dynamic characteristics with chaos theory, and indicate thatfire preoeas is a catastrophe, that is to say, the fire system changes from one state to another during mine fire
Traffic chaos and its prediction based on a nonlinear car-following model
Institute of Scientific and Technical Information of China (English)
Hui FU; Jianmin XU; Lunhui XU
2005-01-01
This paper discusses the dynamic behavior and its predictions for a simulated traffic flow based on the nonlinear response of a vehicle to the leading car's movement in a single lane.Traffic chaos is a promising field,and chaos theory has been applied to identify and predict its chaotic movement.A simulated traffic flow is generated using a car-following model(GM model),and the distance between two cars is investigated for its dynamic properties.A positive Lyapunov exponent confirms the existence of chaotic behavior in the GM model.A new algorithm using a RBF NN (radial basis function neural network) is proposed to predict this traffic chaos.The experiment shows that the chaotic degree and predictable degree are determined by the first Lyapunov exponent.The algorithm proposed in this paper can be generalized to recognize and predict the chaos of short-time traffic flow series.
Nonlinear dynamics: Challenges and perspectives
Indian Academy of Sciences (India)
M Lakshmanan
2005-04-01
The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators
Lakshmanan, M
1997-01-01
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.
非线性环型腔反馈激光系统的动力学特性及其混沌控制%Chaotic dynamics and chaos control in nonlinear laser systems
Institute of Scientific and Technical Information of China (English)
方锦清; 姚伟光
2001-01-01
Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed in this article mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for applications ( such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally.%以环型腔反馈激光系统为主，综述了非线性激光系统的混沌动力学特性；分析了延迟反馈方法控制混沌的原理和稳定性条件，实现了对多介质非线性激光系统中的混沌控制。同时概述了近年来非线性激光系统中混沌控制的最新进展，诸如空间小微扰法、偶然正比反馈技术等，讨论了混沌控制在提高激光器功率和性能、利用混沌进行秘密通讯和信息处理等方面的应用前景。
Chaos in a double driven dissipative nonlinear oscillator.
Adamyan, H H; Manvelyan, S B; Kryuchkyan, G Y
2001-10-01
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.
Dynamic system uncertainty propagation using polynomial chaos
Directory of Open Access Journals (Sweden)
Xiong Fenfen
2014-10-01
Full Text Available The classic polynomial chaos method (PCM, characterized as an intrusive methodology, has been applied to uncertainty propagation (UP in many dynamic systems. However, the intrusive polynomial chaos method (IPCM requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Dynamic system uncertainty propagation using polynomial chaos
Institute of Scientific and Technical Information of China (English)
Xiong Fenfen; Chen Shishi; Xiong Ying
2014-01-01
The classic polynomial chaos method (PCM), characterized as an intrusive methodology, has been applied to uncertainty propagation (UP) in many dynamic systems. However, the intrusive polynomial chaos method (IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method (NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
Institute of Scientific and Technical Information of China (English)
秦卫阳; 孙涛; 焦旭东; 杨永锋
2012-01-01
To realize the synchronization of nonlinear dynamical system,the general control method is unidirectional linear coupling.Research on function coupling of chaos synchronization is not enough,so there arises a question：for nonlinear dynamical system,if chaos synchronization is realized by linear coupling,whether can any type of function coupling always make the system go to chaos synchronization？ In this paper,a class of nonlinear dynamical system is considered and the relation between linear coupling and function coupling is investigated.It is proved that if linear coupling can make chaos synchronization,then any function satisfying some conditions can do so too.The condition is given and proved.Finally for Duffing system,three coupling functions are used to prove the analytical result.The simulation results show that the conclusion is correct.%非线性动力学系统的混沌同步,一般采用单向线性耦合的控制方式,对于函数耦合方式研究的比较少.这就存在一个问题,对于非线性动力学系统,在线性耦合实现混沌同步后,是否其他函数的耦合方式都可以实现混沌同步？本文对于一类非线性动力学系统,研究了其线性耦合同步与函数耦合同步的关系,证明当线性耦合实现同步后,函数在满足一定的条件下,可以通过函数耦合实现系统的混沌同步.最后对于Duffing系统采用两种函数耦合进行了仿真计算,证明了结论的正确性.
Chaos Cryptography with Dynamical Systems
Anderson, Robert; Morse, Jack; Schimmrigk, Rolf
2001-11-01
Cryptography is a subject that draws strength from an amazing variety of different mathematical fields, including such deep results as the Weil-Dwork-Deligne theorem on the zeta function. Physical theories have recently entered the subject as well, an example being the subject of quantum cryptography, motivated in part by Shor's insight into the vulnerability of prime number factorization based crypto systems. In this contribution we describe a cryptographic algorithm which is based on the dynamics of a class of physical models that exhibit chaotic behavior. More precisely, we consider dissipative systems which are described by nonlinear three-dimensional systems of differential equations with strange attractor surfaces of non-integer Lyapunov dimension. The time evolution of such systems in part of the moduli space shows unpredictable behavior, which suggests that they might be useful as pseudorandom number generators. We will show that this is indeed the case and illustrate our procedure mainly with the Lorenz attractor, though we also briefly mention the Rössler system. We use this class of nonlinear models to construct an extremely fast stream cipher with a large keyspace, which we test with Marsaglia's battery of DieHard tests.
Analysis of Bifurcation and Nonlinear Control for Chaos in Gear Transmission System
Directory of Open Access Journals (Sweden)
Wang Jingyue
2013-07-01
Full Text Available In order to study the bifurcation characteristics and control chaotic vibration of the gear transmission system. The complex dynamics characters of gear transmission system are studied. The dynamical equation and the state equation of gear transmission system are established according to Newton's rule. The route to chaos of the system is studied by the bifurcation diagram, phase portrait, time course diagram and Poincaré map. A method of controlling chaos by nonlinear feedback controller is developed to guide chaotic motions towards regular motions. Numerical simulation shows that with the increase of meshing stiffness, gear transmission system will be from the periodic motion to chaotic motion by doubling bifurcation, the effectiveness and feasibility of the strategy to get rid of chaos by stabilizing the related unstable periodic orbit.
Nonlinearity and Chaos in the Magnetopause Shear System
Institute of Scientific and Technical Information of China (English)
傅绥燕; 濮祖荫; 刘振兴
1994-01-01
Chaotic phenomena in the magnetopause boundary region are studied in the MHD framework by using the Fourier truncation method. The MHD system is considered as a one-dimensional current sheet with a co-existing velocity shear and continuous energy transfer. The nonlinearity of the system, the evolution processes and properties of its different attractors are analysed. The possible routs and parameter conditions for chaos onset are also investigated. Numerical solutions show that when the Reynolds number (R) and the magnetic Reynolds number (Km) are very large, chaos appears in the system and its onset may provide a physical mechanism leading to turbulent reconnection at the magnetopause.
Quantum dynamical entropies in discrete classical chaos
Energy Technology Data Exchange (ETDEWEB)
Benatti, Fabio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Cappellini, Valerio [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Zertuche, Federico [Instituto de Matematicas, UNAM, Unidad Cuernavaca, AP 273-3, Admon. 3, 62251 Cuernavaca, Morelos (Mexico)
2004-01-09
We discuss certain analogies between quantization and discretization of classical systems on manifolds. In particular, we will apply the quantum dynamical entropy of Alicki and Fannes to numerically study the footprints of chaos in discretized versions of hyperbolic maps on the torus.
The nonlinear universe chaos, emergence, life
Scott, A C
2007-01-01
Written in Alwyn Scott’s inimitable style – lucid and accessible – The Nonlinear Universe surveys and explores the explosion of activity in nonlinear science that began in the 1970s and 1980s and continues today. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science – and an appreciation of its implications – is essential for understanding scientific developments of the twenty-first century.
Complex chaos in the conditional dynamics of qubits
Kiss, T; Jex, I; Vymetal, S
2005-01-01
We analyse the consequences of measurement induced non-linearity for the dynamical behaviour of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex nonlinear map with one complex parameter. The map is a rational function of degree two leading to chaotic dynamics of the quantum state, in contrast to the usual notion of quantum chaos. The set of initial values with irregular behavior, the Julia set, has a nontrivial structure depending crucially on the parameter of the map. The family of maps labeled by the parameter can be characterized by the attractive fixed points. Each map with a fixed parameter can have at most two attractive cycles. This type of instability is also present in purification protocols based on conditional non-linear transformations of qubits.
Urban chaos and replacement dynamics in nature and society
Chen, Yanguang
2014-11-01
Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.
Chaos control applied to heart rhythm dynamics
Energy Technology Data Exchange (ETDEWEB)
Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)
2011-08-15
Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
Chaos in effective classical and quantum dynamics
Casetti, L; Modugno, M; Casetti, Lapo; Gatto, Raoul; Modugno, Michele
1998-01-01
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the classical model we observe chaotic orbits for any value of the external field, while in the quantum case chaos is strongly suppressed. A simple explanation of this behaviour is found in the change in the structure of the orbits induced by quantum corrections. Consistently with Heisenberg's principle, quantum fluctuations are forced away from zero, removing in the effective quantum dynamics a hyperbolic fixed point that is a major source of chaos in the classical model.
A monomial chaos approach for efficient uncertainty quantification on nonlinear problems
Witteveen, J.A.S.; Bijl, H.
2008-01-01
A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equation
A monomial chaos approach for efficient uncertainty quantification on nonlinear problems
Witteveen, J.A.S.; Bijl, H.
2008-01-01
A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear
Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit
Energy Technology Data Exchange (ETDEWEB)
Wang Jinzhi [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)]. E-mail: jinzhiw@pku.edu.cn; Duan Zhisheng [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China); Huang Lin [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)
2006-02-27
In this Letter a new method of chaos control for Chua's circuit and the modified canonical Chua's electrical circuit is proposed by using the results of dichotomy in nonlinear systems. A linear feedback control based on linear matrix inequality (LMI) is given such that chaos oscillation or hyperchaos phenomenon of circuit systems injected control signal disappear. Numerical simulations are presented to illustrate the efficiency of the proposed method.
Bifurcation and chaos in simple jerk dynamical systems
Indian Academy of Sciences (India)
Vinod Patidar; K K Sud
2005-01-01
In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this paper, we investigate the global dynamics of a special family of jerk systems $\\ddddot{x} = -Aẍ - ẋ$ + (), where () is a non-linear function, which are known to exhibit chaotic behaviour at some parameter values. We particularly identify the regions of parameter space with different asymptotic dynamics using some analytical methods as well as extensive Lyapunov spectra calculation in complete parameter space. We also investigate the effect of weakening as well as strengthening of the non-linearity in the () function on the global dynamics of these jerk dynamical systems. As a result, we reach to an important conclusion for these jerk dynamical systems that a certain amount of non-linearity is sufficient for exhibiting chaotic behaviour but increasing the non-linearity does not lead to larger regions of parameter space exhibiting chaos.
Chaos for Discrete Dynamical System
Directory of Open Access Journals (Sweden)
Lidong Wang
2013-01-01
Full Text Available We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.
Controlling chaos based on an adaptive nonlinear compensator mechanism
Institute of Scientific and Technical Information of China (English)
Tian Ling-Ling; Li Dong-Hai; Sun Xian-Fang
2008-01-01
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory.By using a designed nonlinear compensator mechanism,the system deterministic nonlinearity,parametric uncertainty and disturbance effect can be compensated effectively.The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example.From the Lyapunov stability theory,sufficient conditions for choosing control parameters to guarantee chaos control are derived.Several experiments are carried out,including parameter change experiments,set-point change experiments and disturbance experiments.Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
Nonlinear Dynamics and Control of Flexible Structures
1991-03-01
Freedom," Ph.D. Thesis, Department of Theoretical and Applied Mechanics, Cornell University, in preparation. 5I I URI Reorts Islam , Saiful and Mircea...Theoretical and Applied Mechanics I S. Islam Civil and Environmental Engineering I 2! I 3 URI Accomplishments 3 -Nonlinear Dynamics and Chaos in Flexible...Structures with Symmetry," 31 (1991) 265-285. Islam , S. and M. Grigoriu, "Nonlinear Random Vibration of Pin-Jointed Trusses with Imperfections," in
Introduction to modern dynamics chaos, networks, space and time
Nolte, David D
2015-01-01
The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile populations, or the synchronization of global economies are governed by universal principles just as profound as Newton's laws. Nonetheless, the conventional university physics curriculum reserves most of these topics for advanced graduate study. Two justifications are given for this situation: first, that the mathematical tools needed to understand these topics are beyond the skill set of undergraduate students, and second, that these are speciality topics with no common theme and little overlap. Introduction to Modern Dynamics dispels these myths. The structure of this book combines the three main topics of modern dynamics - chaos theory, dynamics on complex networks, and gener...
Wave Dynamical Chaos in Superconducting Microwave Cavities
Rehfeld, H; Dembowski, C; Gräf, H D; Hofferbert, R; Richter, A; Lengeler, Herbert
1997-01-01
During the last few years we have studied the chaotic behavior of special Euclidian geometries, so-called billiards, from the quantum or in more general sense "wave dynamical" point of view. Due to the equivalence between the stationary Schroedinger equation and the classical Helmholtz equation in the two-dimensional case (plain billiards), it is possible to simulate "quantum chaos" with the help of macroscopic, superconducting microwave cavities. Using this technique we investigated spectra of three billiards from the family of Pascal's Snails (Robnik-Billiards) with a different chaoticity in each case in order to test predictions of standard stochastical models for classical chaotic systems.
Nonlinear dynamics as an engine of computation.
Kia, Behnam; Lindner, John F; Ditto, William L
2017-03-06
Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear dynamics as an engine of computation
Kia, Behnam; Lindner, John F.; Ditto, William L.
2017-03-01
Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue 'Horizons of cybernetical physics'.
Teaching nonlinear dynamics through elastic cords
Energy Technology Data Exchange (ETDEWEB)
Chacon, R; Galan, C A; Sanchez-Bajo, F, E-mail: rchacon@unex.e [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)
2011-01-15
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wen-Biao
2010-01-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincar\\'e sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial condition...
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.
2013-08-05
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.
Urban chaos and replacement dynamics in nature and society
Chen, Yanguang
2011-01-01
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and numerical computation, we can demonstrate that the 1-dimensional map comes from a 2-dimensional two-group interaction map. By analogy with urbanization, a general theory of replacement dynamics is presented in this paper, and the replacement process can be simulated with the 2-dimansional map. If the rate of replacement is too high, periodic oscillations and chaos will arise, and the system maybe breaks down. The replacement theory can be used to interpret various complex interaction and conversion in physical and human systems. The replacement dynamics provides a new way of looking at Volterra-Lotka's predator-prey inte...
Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy
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.
Energy Technology Data Exchange (ETDEWEB)
Watts, Christopher A. [Univ. of Wisconsin, Madison, WI (United States)
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.
Bifurcation, chaos, and scan instability in dynamic atomic force microscopy
Energy Technology Data Exchange (ETDEWEB)
Cantrell, John H., E-mail: john.h.cantrell@nasa.gov [Research Directorate, NASA Langley Research Center, Hampton, Virginia 23681 (United States); Cantrell, Sean A., E-mail: scantrell@nlsanalytics.com [NLS Analytics, LLC, 375 Dundee Road, Glencoe, Illinois 60022 (United States)
2016-03-28
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.
Directory of Open Access Journals (Sweden)
Saul Hazledine
Full Text Available Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia, with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.
Rapid dynamical chaos in an exoplanetary system
Deck, Katherine M; Agol, Eric; Carter, Joshua A; Lissauer, Jack J; Ragozzine, Darin; Winn, Joshua N
2012-01-01
We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which we studied through numerical integrations of initial conditions that are consistent with observations of the system. The orbits are chaotic with a Lyapunov time of only ~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 ~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 (~200 million years). The long-lived subset of the allowed initial conditions are those that satisfy the Hill stability criterion by the largest margin. Any succes...
Universal properties of dynamically complex systems - The organization of chaos
Procaccia, Itamar
1988-06-01
The complex dynamic behavior of natural systems far from equilibrium is discussed. Progress that has been made in understanding universal aspects of the paths to such behavior, of the trajectories at the borderline of chaos, and of the nature of the complexity in the chaotic regime, is reviewed. The emerging grammar of chaos is examined.
Chaos control in a nonlinear pendulum using a semi-continuous method
Energy Technology Data Exchange (ETDEWEB)
Pereira-Pinto, Francisco Heitor I. E-mail: heitor@epq.ime.eb.br; Ferreira, Armando M. E-mail: armando@epq.ime.eb.br; Savi, Marcelo A. E-mail: savi@ufrj.br
2004-11-01
Chaotic behavior of dynamical systems offers a rich variety of orbits, which can be controlled by small perturbations in either a specific parameter of the system or a dynamical variable. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs) that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. At first, it is considered signals generated by numerical integration of the mathematical model. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method is employed with this aim. Finally, an analysis related to the effect of noise in controlling chaos is of concern. Results show situations where these techniques may be used to control chaos in mechanical systems.
Closed-loop suppression of chaos in nonlinear driven oscillators
Aguirre, L. A.; Billings, S. A.
1995-05-01
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
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.
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Energy Technology Data Exchange (ETDEWEB)
Bessa, Wallace M. [Universidade Federal do Rio Grande do Norte, Department of Mechanical Engineering, Campus Universitario Lagoa Nova, 59072-970 Natal, RN (Brazil)], E-mail: wmbessa@ufrnet.br; Paula, Aline S. de [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp27@gmail.com; Savi, Marcelo A. [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-10-30
Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. The idea that chaotic behavior may be controlled by small perturbations of physical parameters allows this kind of behavior to be desirable in different applications. In this work, chaos control is performed employing a variable structure controller. The approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling inaccuracies. The convergence properties of the closed-loop system are analytically proven using Lyapunov's direct method and Barbalat's lemma. As an application of the control procedure, a nonlinear pendulum dynamics is investigated. Numerical results are presented in order to demonstrate the control system performance. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.
Deterministic chaos in government debt dynamics with mechanistic primary balance rules
Lindgren, Jussi Ilmari
2011-01-01
This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich nonlinear behaviour and it can exhibit deterministic chaos with certain parameter regimes. Deterministic chaos means the existence of the butterfly effect which in turn is qualitatively very important, as it shows that even deterministic budget rules produce unpredictable behaviour of the debt-to-GDP ratio, as chaotic systems are extremely sensitive to initial conditions.
Energy Technology Data Exchange (ETDEWEB)
Duan Zhisheng [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: duanzs@pku.edu.cn; Wang Jinzhi; Yang Ying; Huang Lin [State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)
2009-04-30
This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur'e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the convergence of solutions are presented. Some latest results on analysis and control of nonlinear systems with multiple equilibria and applications to chaos control are reviewed. Finally, new chaotic oscillating phenomena are shown in a pendulum-like system and a new nonlinear system with an attraction/repulsion function.
Nonlinear dynamics and chaotic phenomena an introduction
Shivamoggi, Bhimsen K
2014-01-01
This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...
Control of Orbit and Control of Chaos in a Class of Dynamic System
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
The problem of control of orbit for the dynamic system ~ + x ( 1 -x ) ( x - a ) = 0 is discussed. Any unbounded orbit of the dynamic system can be controlled to become a bounded periodic orbit by adding a periodic stepexcitation to the system. By using a nonlinear feedback control law presented in this paper the chaos of the dynamicsystem with excitation and damping is stabilized. This method is more effectual than the linear feedback control
Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System
Institute of Scientific and Technical Information of China (English)
FANG JinQing; CHEN GuanRong; ZHOU LiuLai; WENG JiaQiang
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.
Chaos control of chaotic dynamical systems using backstepping design
Energy Technology Data Exchange (ETDEWEB)
Yassen, M.T. [Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)] e-mail: mtyassen@yahoo.com
2006-01-01
This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results.
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions
Institute of Scientific and Technical Information of China (English)
FangJin－Qing; MKAli
1997-01-01
In this paper the nonlinear feedback functional method is presented for study of synchronization of spatiotemporal chaos in coupled map lattices with five connection forms.Some of nonlinear feedback functions are given.The noise effect on synchronization and sporadic nonlinear feedback are discussed.
The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej
Energy Technology Data Exchange (ETDEWEB)
Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)
1995-12-31
The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.
Chaos control in passive walking dynamics of a compass-gait model
Gritli, Hassène; Khraief, Nahla; Belghith, Safya
2013-08-01
The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.
Nonlinear-dynamical arrhythmia control in humans.
Christini, D J; Stein, K M; Markowitz, S M; Mittal, S; Slotwiner, D J; Scheiner, M A; Iwai, S; Lerman, B B
2001-05-08
Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.
Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium
Chen, Jyh-Phen; Engelmann, Wolfgang; Baier, Gerold
1995-12-01
The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.
Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method
Energy Technology Data Exchange (ETDEWEB)
Souza de Paula, Aline [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp@ufrj.br; Savi, Marcelo Amorim [COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68503, 21.941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-12-15
Chaos control is employed for the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The extended time-delayed feedback control uses a continuous feedback loop incorporating information from previous states of the system in order to stabilize unstable orbits. This article deals with the chaos control of a nonlinear pendulum employing the extended time-delayed feedback control method. The control law leads to delay-differential equations (DDEs) that contain derivatives that depend on the solution of previous time instants. A fourth-order Runge-Kutta method with linear interpolation on the delayed variables is employed for numerical simulations of the DDEs and its initial function is estimated by a Taylor series expansion. During the learning stage, the UPOs are identified by the close-return method and control parameters are chosen for each desired UPO by defining situations where the largest Lyapunov exponent becomes negative. Analyses of a nonlinear pendulum are carried out by considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show the capability of the control procedure to stabilize UPOs of the dynamical system, highlighting some difficulties to achieve the stabilization of the desired orbit.
Nonlinear dynamics and quantitative EEG analysis.
Jansen, B H
1996-01-01
Quantitative, computerized electroencephalogram (EEG) analysis appears to be based on a phenomenological approach to EEG interpretation, and is primarily rooted in linear systems theory. A fundamentally different approach to computerized EEG analysis, however, is making its way into the laboratories. The basic idea, inspired by recent advances in the area of nonlinear dynamics and chaos theory, is to view an EEG as the output of a deterministic system of relatively simple complexity, but containing nonlinearities. This suggests that studying the geometrical dynamics of EEGs, and the development of neurophysiologically realistic models of EEG generation may produce more successful automated EEG analysis techniques than the classical, stochastic methods. A review of the fundamentals of chaos theory is provided. Evidence supporting the nonlinear dynamics paradigm to EEG interpretation is presented, and the kind of new information that can be extracted from the EEG is discussed. A case is made that a nonlinear dynamic systems viewpoint to EEG generation will profoundly affect the way EEG interpretation is currently done.
An Experimental Investigation of Secure Communication With Chaos Masking
Dhar, Sourav
2007-01-01
The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is generated from two chaos generators is masked with the massage signal to be transmitted, thus makes communication is more secure.
基于混沌理论的心音信号非线性动力学分析%Nonlinear dynamic analysis of heart sound signals based on chaos theory
Institute of Scientific and Technical Information of China (English)
丁晓蓉; 郭兴明; 钟丽莎
2012-01-01
In order to get more valuable information from the perspective of nonlinear dynamics, a method based on chaos theory was proposed to analyze the heart sound signals. The correlation dimension and largest Lyapunov exponent were calculated, besides, the recurrence plot and its quantification analysis parameters were obtained and used to study the heart sounds of 13 cases of normal people and 13 cases of patients with mitral stenosis. The results show that the difference between the chaotic features of the normal heart sounds and of the sounds with mitral stenosis is significant. Thus, the method can be applied to assist the diagnosis of mitral stenosis.%为了从非线性动力学的角度对心音进行分析,提出一种基于混沌理论的心音信号的分析方法.首先,计算心音信号的关联维数及最大Lyapunov指数,获取了心音信号递归图和递归定量分析参数;然后,通过13例健康人和13例二尖瓣狭窄病人的心音对其进行分析验证.结果表明:正常及二尖瓣狭窄心音信号的混沌特征具有显著差异,该方法为实现二尖瓣狭窄的早期辅助诊断提供了依据.
Energy Technology Data Exchange (ETDEWEB)
Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)
2015-09-15
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.
A Monomial Chaos Approach for Efficient Uncertainty Quantification in Computational Fluid Dynamics
Witteveen, J.A.S.; Bijl, H.
2006-01-01
A monomial chaos approach is proposed for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can still be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equ
Simulation of Chaos in Asymmetric Nonlinear Chua's Circuit
Institute of Scientific and Technical Information of China (English)
WANG Yu-fei; QIAO Shu-tong; JIANG Jian-guo
2008-01-01
In order to describe practical chaotic systems exactly, we presented a simple modified Chua's circuit,which contains an asymmetric nonlinear resistive element. Mathematical analysis was made, and simulation study was performed by MATLAB. By varying the value of linear resistor in the circuit, rich variety dynamical behaviors were observed, such as DC equilibrium point, Hopf bifurcation, period-doubling bifurcation,single-scroll strange attractor, periodic windows, and asymmetric double-scroll strange attractor. The extreme sensitivity in the state trajectory with respect to the initial conditions was exhibited; the special characteristic of asymmetric nonlinear Chua's circuit was found also.
Chaos and dynamics of spinning particles in Kerr spacetime
Han, Wenbiao
2008-09-01
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincaré sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity
Yin, Jiu-Li; Zhao, Liu-Wei; Tian, Li-Xin
2014-02-01
The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.
[Dynamic paradigm in psychopathology: "chaos theory", from physics to psychiatry].
Pezard, L; Nandrino, J L
2001-01-01
For the last thirty years, progress in the field of physics, known as "Chaos theory"--or more precisely: non-linear dynamical systems theory--has increased our understanding of complex systems dynamics. This framework's formalism is general enough to be applied in other domains, such as biology or psychology, where complex systems are the rule rather than the exception. Our goal is to show here that this framework can become a valuable tool in scientific fields such as neuroscience and psychiatry where objects possess natural time dependency (i.e. dynamical properties) and non-linear characteristics. The application of non-linear dynamics concepts on these topics is more precise than a loose metaphor and can throw a new light on mental functioning and dysfunctioning. A class of neural networks (recurrent neural networks) constitutes an example of the implementation of the dynamical system concept and provides models of cognitive processes (15). The state of activity of the network is represented in its state space and the time evolution of this state is a trajectory in this space. After a period of time those networks settle on an equilibrium (a kind of attractor). The strength of connections between neurons define the number and relations between those attractors. The attractors of the network are usually interpreted as "mental representations". When an initial condition is imposed to the network, the evolution towards an attractor is considered as a model of information processing (27). This information processing is not defined in a symbolic manner but is a result of the interaction between distributed elements. Several properties of dynamical models can be used to define a way where the symbolic properties emerge from physical and dynamical properties (28) and thus they can be candidates for the definition of the emergence of mental properties on the basis of neuronal dynamics (42). Nevertheless, mental properties can also be considered as the result of an
Dynamical topology and statistical properties of spatiotemporal chaos.
Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli
2012-12-01
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.
2012-01-01
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this co...
The Dynamics of Nonlinear Inference
Kadakia, Nirag
The determination of the hidden states of coupled nonlinear systems is frustrated by the presence of high-dimensionality, chaos, and sparse observability. This problem resides naturally in a Bayesian context: an underlying physical process produces a data stream, which - though noisy and incomplete - can in principle be inverted to express the likelihood of the underlying process itself. A large class of well-developed methods treat this problem in a sequential predict-and-correct manner that alternates information from the presumed dynamical model with information from the data. One might instead formulate this problem in a temporally global, non-sequential manner, which suggests new avenues of approach within an optimization context, but also poses new challenges in numerical implementation. The variational annealing (VA) technique is proposed to address these problems by leveraging an inherent separability between the convex and nonconvex contributions of the resulting functional forms. VA is shown to reliably track unobservable states in sparsely observed chaotic systems, as well as in minimally-observed biophysical neural models. Second, this problem can be formally cast in continuous time as a Wiener path integral, which then suggests classical solutions derived from Hamilton's principle. These solutions come with their own difficulties in that they comprise an unstable boundary-value problem. Accordingly, a further technique called Hamiltonian variational annealing is proposed, which again exploits an existing separability of convexity and nonlinearity, this time in a an enlarged manifold constrained by underlying symmetries. A running theme in this thesis is that the optimal estimate of a nonlinear system is itself a dynamical system that lives in an unstable, symplectic manifold. When this system is recast in a variational context, instability is manifested as nonconvexity, the central idea being that when this nonconvexity is incorporated in a systematic
Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods
Nayfeh, Ali H
1995-01-01
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
Zaslavsky, G. M.; Edelman, M.; Tarasov, V. E.
2007-12-01
We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l1+α, where l is a distance between oscillators and 0continuous limit, the system's dynamics is described by a fractional generalization of the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter α that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics, especially near α =2 and α =1. We study different spatiotemporal patterns of the dynamics depending on α and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.
Nonlinear Dynamical Analysis of Fibrillation
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
Dissipative Nonlinear Dynamics in Holography
Basu, Pallab
2013-01-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour 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 behaviour, 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 the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.
Zhang, Yongfang; Hei, Di; Lü, Yanjun; Wang, Quandai; Müller, Norbert
2014-03-01
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson- θ-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincaré map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
Partial dynamical symmetry and the suppression of chaos
Energy Technology Data Exchange (ETDEWEB)
Whelan, N.; Alhassid, Y. (Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06511 (United States)); Leviatan, A. (Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel))
1993-10-04
Partial dynamical symmetry is a situation in which the Hamiltonian does not have a certain symmetry yet a subset of its eigenstates does. It is shown that partial dynamical symmetry may cause suppression of chaos even in cases where the fraction of states which has the symmetry vanishes in the classical limit. The average entropy associated with the symmetry is a sensitive quantum measure of the partial symmetry and its effect on the chaotic dynamics.
Nonlinear laser dynamics from quantum dots to cryptography
Lüdge, Kathy
2012-01-01
A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research.By presenting both experimental and theoretical results, the distinguished authors consider solitary lase
Bubble nonlinear dynamics and stimulated scattering process
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
The onset of chaos in orbital pilot-wave dynamics.
Tambasco, Lucas D; Harris, Daniel M; Oza, Anand U; Rosales, Rodolfo R; Bush, John W M
2016-10-01
We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario.
The onset of chaos in orbital pilot-wave dynamics
Tambasco, Lucas D.; Harris, Daniel M.; Oza, Anand U.; Rosales, Rodolfo R.; Bush, John W. M.
2016-10-01
We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario.
Directory of Open Access Journals (Sweden)
Shaohua Luo
2016-04-01
Full Text Available 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.
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.
Dynamic Ice-Water Interactions Form Europa's Chaos Terrains
Blankenship, D. D.; Schmidt, B. E.; Patterson, G. W.; Schenk, P.
2011-12-01
Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. We present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. This model is consistent with key observations of chaos, predicts observables for future missions, and indicates that the surface is likely still active today[1]. We apply lessons from ice-water interaction in the terrestrial cryosphere to hypothesize a dynamic lense-collapse model to for Europa's chaos terrain. Chaos terrain morphology, like that of Conamara chaos and Thera Macula, suggests a four-phase formation [1]: 1) Surface deflection occurs as ice melts over ascending thermal plumes, as regularly occurs on Earth as subglacial volcanoes activate. The same process can occur at Europa if thermal plumes cause pressure melt as they cross ice-impurity eutectics. 2) Resulting hydraulic gradients and driving forces produce a sealed, pressurized melt lense, akin to the hydraulic sealing of subglacial caldera lakes. On Europa, the water cannot escape the lense due to the horizontally continuous ice shell. 3) Extension of the brittle ice lid above the lense opens cracks, allowing for the ice to be hydrofractured by pressurized water. Fracture, brine injection and percolation within the ice and possible iceberg toppling produces ice-melange-like granular matrix material. 4) Refreezing of the melt lense and brine-filled pores and cracks within the matrix results in raised chaos. Brine soaking and injection concentrates the ice in brines and adds water volume to the shell. As this englacial water freezes, the now water-filled ice will expand, not unlike the process of forming pingos and other "expansion ice" phenomena on Earth. The refreezing can raise the surface and create the oft-observed matrix "domes" In this presentation, we describe how catastrophic ice-water interactions on Earth have
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Synchronization of spatiotemporal chaos using nonlinear feedback functions
Directory of Open Access Journals (Sweden)
M. K. Ali
1997-01-01
Full Text Available Synchronization of spatiotemporal chaos is studied using the method of variable feedback with coupled map lattices as model systems. A variety of feedback functions are introduced and the diversity in their choices for synchronizing any given system is exemplified. Synchronization in the presence of noise and with sporadic feedback is also presented.
Solutions, bifurcations and chaos of the nonlinear Schrodinger equation with weak damping
Institute of Scientific and Technical Information of China (English)
彭解华; 唐驾时; 于德介; 颜家壬; 海文华
2002-01-01
Using the wave packet theory, we obtain all the solutions of the weakly damped nonlinear Schrodinger equation.These solutions are the static solution, and solutions of planar wave, solitary wave, shock wave and elliptic functionwave and chaos. The bifurcation phenomenon exists in both steady and non-steady solutions. The chaotic and periodicmotions can coexist in a certain parametric space region.
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Intrinsically localized chaos in discrete nonlinear extended systems
Martínez, P J; Falo, F; Mazo, J J
1999-01-01
The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.
Biometric Authentication System using Non-Linear Chaos
Directory of Open Access Journals (Sweden)
Dr.N.Krishnan
2010-08-01
Full Text Available A major concern nowadays for any Biometric Credential Management System is its potential vulnerability to protect its information sources; i.e. protecting a genuine user’s template from both internal and external threats. These days’ biometric authentication systems face various risks. One of the most serious threats is the ulnerability of the template's database. An attacker with access to a reference template could try to impersonate a legitimate user by reconstructing the biometric sample and by creating a physical spoof.Susceptibility of the database can have a disastrous impact on the whole authentication system. The potential disclosure of digitally stored biometric data raises serious concerns about privacy and data protection. Therefore, we propose a method which would integrate conventional cryptography techniques with biometrics. In this work, we present a biometric crypto system which encrypts the biometric template and the encryption is done by generating pseudo random numbers, based on non-linear dynamics.
Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback
Energy Technology Data Exchange (ETDEWEB)
Virte, Martin; Karsaklian Dal Bosco, Andreas; Wolfersberger, Delphine; Sciamanna, Marc [Supelec, OPTEL Research Group, Laboratoire Materiaux Optiques, Photonique et Systemes, EA-4423, 2 rue Edouard Belin, F-57070 Metz (France)
2011-10-15
A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Chaos and complexity in a simple model of production dynamics
Directory of Open Access Journals (Sweden)
I. Katzorke
2000-01-01
Full Text Available We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one-dimensional Bernoulli-type map, and demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system.
Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos
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.
Pinning control of spatio temporal chaos in nonlinear optics
Energy Technology Data Exchange (ETDEWEB)
Mendoza, C; Martinez-Mardones, J [Institute of Physics, Pontifical Catholic University of Valparaiso, 234-0025 Valparaiso (Chile); Ramazza, P L; Boccaletti, S [CNR- Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)], E-mail: caromendoza@gmail.com
2008-11-01
We have studied numerically the influence of the number of controllers in the control of a spatial pattern in an optical device. In this article, we focus on the liquid crystal light valve (LCLV) which is known to exhibit spatio-temporal chaotic states in some range of parameters. By applying a correcting term in the intensity proportional to the difference between the light intensity of the target pattern and the chaos state, the system is driven to the target pattern in finite time. In addition, we study the number of pinning points and their positions to reach the control of the pattern.
Bifurcation and Chaos Control for Nonlinear Laser Systems
Institute of Scientific and Technical Information of China (English)
2001-01-01
In recent years, complexity science, including various bifurcations ,chaos and turbulence, has become a great challenge in various interdisciplinary fields. It promises to have a major impact on many aspects of nature science and engineering, even social and economic science. Candidates of complex system include coupled laser systems, accelerator-driven clean nuclear power system, neural networks, cellular automata, living organism, human brain, chemical reactions and economic systems. This new and challenging research and development area has in effect become a scientific inter-discipline itself, involving systems and control engineers, theoretical and experimental
Universal quantification for deterministic chaos in dynamical systems
Selvam, A M
1993-01-01
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1 /sqr(tau) (=0.382) where tau is the golden mean. (c) The Feigenbaum's universal constants a and d are functions of k and, further, the expression 2(a**2) = (pie)*d quantifies the steady-state ordered emergence of the fractal geometry of the strange attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statist...
Gritli, Hassène; Belghith, Safya
2017-06-01
An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.
Controlling chaos in dynamical systems described by maps
Energy Technology Data Exchange (ETDEWEB)
Crispin, Y.; Marduel, C. [Embry-Riddle Aeronautical Univ., Daytona Beach, FL (United States)
1994-12-31
The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps.
Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation
Institute of Scientific and Technical Information of China (English)
SHI Peiming; LIU Bin; HOU Dongxiao
2009-01-01
Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
Delay driven spatiotemporal chaos in single species population dynamics models.
Jankovic, Masha; Petrovskii, Sergei; Banerjee, Malay
2016-08-01
Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can significantly influence population dynamics. In general, time delays may arise from inter- and intra-specific trophic interactions or population structure, however in the context of single species populations they are linked to more intrinsic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two different mathematical formulations. Firstly, we revisit the diffusive logistic equation in which the per capita growth is a function of some specified delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-differential model. Using the combination of analytical and numerical techniques, we investigate the effect of time delay on pattern formation. In particular, we show that for sufficiently large values of time delay the system's dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.
Computational complexity of symbolic dynamics at the onset of chaos
Lakdawala, Porus
1996-05-01
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.
Organized and Disorganized Chaos a New Dynamics in Peace Intelligence
Erçetin, Şefika Şule; Tekin, Ali; Açıkalın, Şuay Nilhan
"How to prevent wars" can be considered as reason behind the foundation of field international relations. In other words, after two devastating war humanity realized that we should learn peaceful coexistence. That's why last 50 years were dedicated to peace which have been the most controversial and gripping notion in all disciplines. Within this context, the notion of sustainable peace becomes more important in last years. On the other hand, chaos and its application in social life- actually our real universe gave insight people to understand social facts with dynamic systems and chaos theory. So, this chapter will be a new and fresh to have sustainable peace with peace intelligence. Peace intelligence is completely new phenomena which coined by Şefika Şule Erçetin.
Control of complex dynamics and chaos in distributed parameter systems
Energy Technology Data Exchange (ETDEWEB)
Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)
1995-12-31
This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.
Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser
Institute of Scientific and Technical Information of China (English)
XIE Xia; HUANG Hong-Bin; QIAN Feng; ZHANG Ya-Jun; YANG Peng; QI Guan-Xiao
2006-01-01
We derive equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The dynamic equations of such a system are derived by using the technique of quantum Langevin operators, and then are studied numerically under different driving conditions. The results show thgt under certain conditions the cascade twophoton laser can generate chaotic, period doubling, periodic, stable and bistable states. Chaos can be inhibited by atomic populations, atomic coherences, and injected classical field. In addition, no chaos occurs in optical bistability.
Nonlinear dynamic behaviors of ball bearing rotor system
Institute of Scientific and Technical Information of China (English)
WANG Li-qin; CUI Li; ZHENG De-zhi; GU Le
2009-01-01
Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing. Five-DOF dynamic equations of rotor supported by ball bearings were estimated. The Newmark-β method and Newton-Laphson method were used to solve the equations. The dynamic characteristics of rotor system were studied through the time response, the phase portrait, the Poincar? maps and the bifurcation diagrams. The results show that the system goes through the quasiperiodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions. The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases; the initial contact angle of ball bearing affects dynamic behaviors of the system obviously. The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.
Chaos and related nonlinear noise phenomena in Josephson tunnel junctions
Energy Technology Data Exchange (ETDEWEB)
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.
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
Non-linearity of Beam Halo-Chaos in the ADS
Institute of Scientific and Technical Information of China (English)
2001-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applicationsin industry, medicine, and national defense. This latter reviews some general features of complexities and their expressions in accelerator-driven clean nuclear power system (ADS).Complexity has become an important subject for study, especially in the field of nonlinear
The Chaos Dynamic of Multiproduct Cournot Duopoly Game with Managerial Delegation
Directory of Open Access Journals (Sweden)
Fang Wu
2014-01-01
Full Text Available Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.
Chaos Behaviour of Molecular Orbit
Institute of Scientific and Technical Information of China (English)
LIU Shu-Tang; SUN Fu-Yan; SHEN Shu-Lan
2007-01-01
Based on H(u)ckel's molecular orbit theory,the chaos and;bifurcation behaviour of a molecular orbit modelled by a nonlinear dynamic system is studied.The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.
CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM
Institute of Scientific and Technical Information of China (English)
王登刚; 刘迎曦; 李守巨
2002-01-01
A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature.Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regalarization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
Energy Technology Data Exchange (ETDEWEB)
Medvinsky, Alexander B., E-mail: medvinsky@iteb.ru [Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino 142290, Moscow Region (Russian Federation); Rusakov, Alexey V. [Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino 142290, Moscow Region (Russian Federation)
2011-06-15
Highlights: > We model community dynamics in stateless societies. > Intercommunity barter is shown to be a factor impacting the societies dynamics. > Increase in the human population growth rate can lead to appearance of chaos. > Secular and millennial cycles are found to arise as a result of the barter. - Abstract: The once abstract notions of dynamical chaos now appear naturally in various systems [Kaplan D, Glass L. Understanding nonlinear dynamics. New York: Springer; 1995]. As a result, future trajectories of the systems may be difficult to predict. In this paper, we demonstrate the appearance of chaotic dynamics in model human communities, which consist of producers of agricultural product and producers of agricultural equipment. In the case of a solitary community, the horizon of predictability of the human population dynamics is shown to be dependent on both intrinsic instability of the dynamics and the chaotic attractor sizes. Since a separate community is usually a part of a larger commonality, we study the dynamics of social systems consisting of two interacting communities. We show that intercommunity barter can lead to stabilization of the dynamics in one of the communities, which implies persistence of stable equilibrium under changes of the maximum value of the human population growth rate. However, in the neighboring community, the equilibrium turns into a stable limit cycle as the maximum value of the human population growth rate increases. Following an increase in the maximum value of the human population growth rate leads to period-doubling bifurcations resulting in chaotic dynamics. The horizon of predictability of the chaotic oscillations is found to be limited by 5 years. We demonstrate that the intercommunity interaction can lead to the appearance of long-period harmonics in the chaotic time series. The period of the harmonics is of order 100 and 1000 years. Hence the long-period changes in the population size may be considered as an
Nonlinear dynamics in atom optics
Energy Technology Data Exchange (ETDEWEB)
Chen Wenyu; Dyrting, S.; Milburn, G.J. [Queensland Univ., St. Lucia, QLD (Australia). Dept. of Physics
1996-12-31
In this paper theoretical work on classical and quantum nonlinear dynamics of cold atoms is reported. The basic concepts in nonlinear dynamics are reviewed and then applied to the motion of atoms in time-dependent standing waves and to the atomic bouncer. The quantum dynamics for the cases of regular and chaotic classical dynamics is described. The effect of spontaneous emission and external noise is also discussed. 104 refs., 1 tab., 21 figs.
Dynamic Feedback Controlling Chaos in Current-Mode Boost Converter
Institute of Scientific and Technical Information of China (English)
LU Wei-Guo; ZHOU Luo-Wei; LUO Quan-Ming
2007-01-01
A method for the control of chaos in the current-mode boost converter is presented by using the first-order dynamic feedback control. The feedback part consists of a resistance and a capacitance in series. The system to be controlled is treated as a third-order model, and then the discrete mapping model is obtained by using the data-sampling method. By analysing the position of the maximum norm eigenvalue, the stable range of feedback gain is ascertained out and its optimization is also carried out. Finally, the results of simulation and experiment confirm the correctness of the theoretical analysis and the validity of the proposed means.
Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology
Catsigeras, Eleonora
2011-01-01
We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics.
Energy Technology Data Exchange (ETDEWEB)
Mueller, B.
1997-09-22
The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.
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. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Chaos in fractional-order autonomous nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M.; Sprott, J.C
2003-03-01
We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0,1], based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, and a mechanical chaotic 'jerk' model. In both models, numerical simulations are used to demonstrate that for different types of model nonlinearities, and using the proper control parameters, chaotic attractors are obtained with system orders as low as 2.1. Consequently, we present a conjecture that third-order chaotic nonlinear systems can still produce chaotic behavior with a total system order of 2+{epsilon}, 1>{epsilon}>0, using the appropriate control parameters. The effect of fractional order on the chaotic range of the control parameters is studied. It is demonstrated that as the order is decreased, the chaotic range of the control parameter is affected by contraction and translation. Robustness against model order reduction is demonstrated.
Deterministic Chaos in Tropical Atmospheric Dynamics
Waelbroeck, H
1994-01-01
Abstract: We examine an 11-year data set from the tropical weather station of Tlaxcala, Mexico. We find that mutual information drops quickly with the delay, to a positive value which relaxes to zero with a time scale of 20 days. We also examine the mutual dependence of the observables and conclude that the data set gives the equivalent of 8 variables per day, known to a precision of $2\\%$. We determine the effective dimension of the attractor to be $D_{eff} \\approx 11.7$ at the scale $3.5\\% < R/R_{max} < 8\\%$. We find evidence that the effective dimension increases as $R/R_{max} \\to 0$, supporting a conjecture by Lorenz that the climate system may consist of a large number of weakly coupled subsystems, some of which have low-dimensional attractors. We perform a local reconstruction of the dynamics in phase space; the short-term predictability is modest and agrees with theoretical estimates. Useful skill in predictions of 10-day rainfall accumulation anomalies reflects the persistence of weather pattern...
Deterministic Chaos in Tropical Atmospheric Dynamics.
Waelbroeck, H.
1995-07-01
An 11-year dataset from the tropical weather station of Tlaxcala, Mexico, is examined. It is found that mutual information drops quickly with the delay, to a positive value that relaxes to zero with a timescale of 20 days. The mutual dependence of the observables is also examined and it is concluded that the dataset gives the equivalent of eight variables per day, known to a precision of 2%. It is determined that the effective dimension of the attractor is Deff 11.7 at the scale 3.5% < R/Rmax < 8%. Evidence is found that the effective dimension increases as R/Rmax 0, supporting a conjecture by Lorenz that the climate system may consist of a large number of weakly coupled subsystems, some of which have low-dimensional attractors. A local reconstruction of the dynamics in phase space is performed; the short-term predictability is modest and agrees with theoretical estimates. Useful skill in predictions of 10-day rainfall accumulation anomalies reflects the persistence of weather patterns, which follow the 20-day decay rate of the mutual information.
Ghosh, A. K.; Verma, P.
2011-03-01
Generation of chaos from nonlinear optical systems with an optical or electronic feedback has been studied for several years. Such chaotic signals have an important application in providing secure encryption in free-space optical communication systems. Lyapunov exponent is an important parameter for analysis of chaos generated by a nonlinear system. The Lyapunov exponent of a class of a nonlinear optical system showing a nonlinear transfer characteristics of the form sin2(x) is determined and calculated in this paper to understand the dependence of the chaotic response on the system parameters such as bias, feedback gain, input intensity and initial condition exciting the optical system. Analysis of chaos using Lyapunov exponent is consistent with bifurcation analysis and is useful in encrypting data signal.
Fuzzy chaos control for vehicle lateral dynamics based on active suspension system
Huang, Chen; Chen, Long; Jiang, Haobin; Yuan, Chaochun; Xia, Tian
2014-07-01
The existing research of the active suspension system (ASS) mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.
Nonlinear magnetization dynamics in nanosystems
Mayergoyz, Isaak D; Serpico, Claudio
2014-01-01
As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level. This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics. An advanced reference for the study and understanding of non
Intermittency at critical transitions and aging dynamics at the onset of chaos
Indian Academy of Sciences (India)
A Robledo
2005-06-01
We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order > 1, the dynamics rigorously obeys the Tsallis statistics. We account for the -indices and the generalized Lyapunov coefficients that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the onset of chaos with the appearance of a special value for the entropic index . The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.
Ikeda-like chaos on a dynamically filtered supercontinuum light source
Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent
2016-08-01
We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.
Synchronization of spatiotemporal chaos in a class of complex dynamical networks
Institute of Scientific and Technical Information of China (English)
Zhang Qing-Ling; Lü Ling
2011-01-01
This paper studies the synchronization of complex dynamical networks constructed by spatiotemporal chaotic systems with unknown parameters. The state variables in the systems with uncertain parameters are used to construct the parameter recognizers, and the unknown parameters are identified. Uncertain spatiotemporal chaotic systems are taken as the nodes of complex dynamical networks, connection among the nodes of all the spatiotemporal chaotic systems is of nonlinear coupling. The structure of the coupling functions between the connected nodes and the control gain are obtained based on Lyapunov stability theory. It is seen that stable chaos synchronization exists in the whole network when the control gain is in a certain range. The Gray-Scott models which have spatiotemporal chaotic behaviour are taken as examples for simulation and the results show that the method is very effective.
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Experimental mastering of nonlinear dynamics in circuits by sporadic pulses
Energy Technology Data Exchange (ETDEWEB)
Ruiz, P. [Instituto de Fisica de Cantabria IFCA (CSIC-UC), Santander (Spain); Gutierrez, J.M. [Department of Applied Mathematics and Computer Science, University of Cantabria, 39005 Santander (Spain)], E-mail: gutierjm@unican.es; Gueemez, J. [Department of Applied Physics, Universidad de Cantabria (Spain)
2008-05-15
We present some experimental evidence of mastering chaos (control and anticontrol) in nonlinear circuits using a simple impulsive method which does not require any knowledge about the system's dynamics. The method works by introducing instantaneous pulses in some system variables-in this paper the pulses are applied to a capacitor voltage-and, hence, is an additional plug-in that does not modify the system itself. When varying the mastering parameters (amplitude and frequency of pulses) we obtain a bifurcation structure similar to the one obtained when varying some system's parameters. Therefore, this device allows us investigating the dynamics of a given circuit providing us with a versatile component for performing both control or anticontrol of chaos. In particular, we show how a double-scroll chaotic system is stabilized in period three, single-scroll, period-4, period-2, period-1, fixed point, following an inverse bifurcation route as a function of the pulses amplitude (chaos control). It is also shown how a periodic Chua's circuit is driven to chaotic behavior (chaos anticontrol)
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Energy Technology Data Exchange (ETDEWEB)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás
2016-12-01
We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.
Quantum and wave dynamical chaos in superconducting microwave billiards
Energy Technology Data Exchange (ETDEWEB)
Dietz, B., E-mail: dietz@ikp.tu-darmstadt.de; Richter, A., E-mail: richter@ikp.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt (Germany)
2015-09-15
Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.
"Chaos" Theory: Implications for Educational Research.
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…
Chaos and non-linear phenomena in renal vascular control
DEFF Research Database (Denmark)
Yip, K P; Holstein-Rathlou, N H
1996-01-01
Renal autoregulation of blood flow depends on the functions of the tubuloglomerular feedback (TGF) system and the myogenic response of the afferent arteriole. Studies of the dynamic aspects of these control mechanisms at the level of both the single nephron and the whole kidney have revealed a va...
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
The "Chaos" Pattern in Piaget's Theory of Cognitive Development.
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.…
Alexandrov, D. V.; Bashkirtseva, I. A.; Ryashko, L. B.
2016-08-01
In this work, a non-linear dynamics of a simple three-dimensional climate model in the presence of stochastic forcing is studied. We demonstrate that a dynamic scenario of mixed-mode stochastic oscillations of the climate system near its equilibrium can be formed. As this takes place, a growth of noise intensity increases the frequency of interspike intervals responsible for the abrupt climate changes. In addition, a certain enhancement of stochastic forcing abruptly increases the atmospheric carbon dioxide and decreases the Earth's ice mass. A transition from order to chaos occurring at a critical noise is shown.
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Dynamics of vibrational chaos and entanglement in triatomic molecules: Lie algebraic model
Institute of Scientific and Technical Information of China (English)
Zhai Liang-Jun; Zheng Yu-Jun; Ding Shi-Liang
2012-01-01
In this paper,the dynamics of chaos and the entanglement in triatomic molecnlar vibrations are investigated.On the classical aspect,we study the chaotic trajectories in the phase space.We employ the linear entropy to examine the dynamical entanglement of the two bonds on the quantum aspect.The correspondence between the classical chaos and the quantum dynamical entanglement is also investigated.As an example,we apply our algebraic model to molecule H2O.
Research on Nonlinear Dynamics with Defense Applications
2006-04-01
numerical verifications, we have experimentally realized the scheme by using a Duffing -type of nonlinear electronic oscillator (originally developed by C...circuits In defense applications it may be desirable to induce chaos in nonlinear oscillators operating in a stable regime. Examples of such oscillators ...evolutions of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors. A brief account of the work has been
A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes
Energy Technology Data Exchange (ETDEWEB)
Choi, Minseok [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Sapsis, Themistoklis P. [Courant Institute of Mathematical Sciences, New York University, NY 10012 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2013-07-15
We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.
Directory of Open Access Journals (Sweden)
Ajit Desai
2010-01-01
Full Text Available Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. Uncertainties can occur due to any inherent randomness in the system or modeling limitations, and so forth. Uncertainties can play a significant role in the aeroelastic stability predictions in a nonlinear system. The analysis has been put in a stochastic framework, and the propagation of system uncertainties has been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection-based nonintrusive Polynomial Chaos approach is shown to be much faster than its classical Galerkin method based counterpart. Traditional Monte Carlo Simulation is used as a reference solution. Effect of system randomness on the bifurcation behavior and the flutter boundary has been presented. Stochastic bifurcation results and bifurcation of probability density functions are also discussed.
Device Applications of Nonlinear Dynamics
Baglio, Salvatore
2006-01-01
This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.
Energy Technology Data Exchange (ETDEWEB)
Siewe, M. Siewe [Laboratoire de Mecanique, Departement de Physique, Faculte des sciences, Universite de Yaounde I, B.P. 812, Yaounde (Cameroon)]. E-mail: msiewe@uycdc.uninet.cm; Kakmeni, F.M. Moukam [Laboratoire de Mecanique, Departement de Physique, Faculte des sciences, Universite de Yaounde I, B.P. 812, Yaounde (Cameroon) and Department of Physics, Faculty of science, University of Buea, P.O. Box 63, Buea (Cameroon)]. E-mail: fmoukam@uycdc.uninet.cm; Bowong, S. [Laboratoire de Mathematiques appliquees, Departement de Mathematiques et Informatique, Faculte des sciences, Universite de Douala, B.P. 24157, Douala (Cameroon)]. E-mail: sbowong@uycdc.uninet.cm; Tchawoua, C. [Laboratoire de Mecanique, Departement de Physique, Faculte des sciences, Universite de Yaounde I, B.P. 812, Yaounde (Cameroon)]. E-mail: ctchawoua@uycdc.uninet.cm
2006-07-15
In this paper, the problem of dynamics and chaos control of an electromechanical instrument which is used to record the motion of earth during and earthquake is studied. The amplitude of the fifth sub- and super-harmonic oscillations for the resonant states are obtained and discussed using the multiples time scales method. It is found that chaotic and periodic orbits of the system depend strongly of the value of the damping. The suppression of chaos using small amplitude damping signals is also investigated and the condition under which chaos suppression is possible is derived. Simulation results are presented to confirm analytical process.
Energy Technology Data Exchange (ETDEWEB)
Luo, Shaohua [School of Automation, Chongqing University, Chongqing 400044 (China); Department of Mechanical Engineering, Chongqing Aerospace Polytechnic, Chongqing, 400021 (China); Wu, Songli [Department of Mechanical Engineering, Chongqing Aerospace Polytechnic, Chongqing, 400021 (China); Gao, Ruizhen [School of Automation, Chongqing University, Chongqing 400044 (China)
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.
Selected topics in nonlinear dynamics and theoretical electrical engineering
Energy Technology Data Exchange (ETDEWEB)
Kyamakya, Kyandoghere; Chedjou, Jean Camberlain [Kalgenfurt Univ. (Austria); Halang, Wolfgang A.; Li, Zhong [Hagen Fernuniv. (Germany); Mathis, Wolfgang (eds.) [Leibniz Univ. Hannover (Germany). Inst. fuer Theoretische Elektrotechnik
2013-02-01
Post proceedings of Joint Conference INDS 2011 and ISTET 2011. Recent advances in nonlinear Dynamics and Synchronization as well as in Theoretical Electrical Engineering. Written by leading experts in the field. This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.
Experimental Control of Instabilities and Chaos in Fast Dynamical Systems
1997-06-01
is short (- 10 cm) [153]-[155]; these studies have more recently been considered from the chaos control viewpoint [42]. The apparatus required to...13] Christini, David J., and James A. Collins. Controlling Nonchaotic Neuronal Noise Using Chaos Control Techniques. Phys. Rev. Lett. 75:2782-2785
Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
J. Slezak
2008-09-01
Full Text Available In this detailed paper, several novel oscillator's configurations which consist only of five positive second generation current conveyors (CCII+ are presented and experimentally verified. Each network is able to generate the conservative chaotic attractors with the certain degree of the structural stability. It represents a class of the autonomous deterministic dynamical systems with two-segment piecewise linear (PWL vector fields suitable also for the theoretical analysis. Route to chaos can be traced and observed by a simple change of the external dc voltage. Advantages and other possible improvements are briefly discussed in the text.
Voglis, Nikos
2003-01-01
Galaxies and Chaos examines the application of tools developed for Nonlinear Dynamical Systems to Galactic Dynamics and Galaxy Formation, as well as to related issues in Celestial Mechanics. The contributions collected in this volume have emerged from selected presentations at a workshop on this topic and key chapters have been suitably expanded in order to be accessible to nonspecialist researchers and postgraduate students wishing to enter this exciting field of research.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces
Molz, F. J.; Murdoch, L. C.; Faybishenko, B.
2013-12-01
Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the
Genealogical tree of Russian schools on Nonlinear Dynamics
Prants, S V
2015-01-01
One of the most prominent feature of research in Russia and the former Soviet Union is so-called scientific schools. It is a collaboration of researchers with a common scientific background working, as a rule, together in a specific city or even at an institution. The genealogical tree of scientific schools on nonlinear dynamics in Russia and the former Soviet Union is grown. We use these terminology in a broad sense including theory of dynamical systems and chaos and its applications in nonlinear physics. In most cases we connect two persons if one was an advisor of the Doctoral thesis of another one. It is an analogue of the Candidate of Science thesis in Russia. If the person had no official advisor or we don't know exactly who was an advisor, we fix that person who was known to be an informal teacher and has influenced on him/her very much.
Energy Technology Data Exchange (ETDEWEB)
Yin, Jiuli, E-mail: yjl@ujs.edu.cn; Zhao, Liuwei
2014-11-07
In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams.
Chaotic behavior in nonlinear polarization dynamics
Energy Technology Data Exchange (ETDEWEB)
David, D.; Holm, D.D.; Tratnik, M.V. (Los Alamos National Lab., NM (USA))
1989-01-01
We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.
Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems
Directory of Open Access Journals (Sweden)
Huiling Xi
2014-11-01
Full Text Available In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.
Edge detection by nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Self-Organized Biological Dynamics and Nonlinear Control
Walleczek, Jan
2006-04-01
The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological
Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2011-01-01
Full Text Available An N-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in which N is divided into two groups and the other in which N is divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly and three-firm (triopoly models to shed light on roles of the number of the firms.
Experimental Chaos - Proceedings of the 3rd Conference
Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep
1996-10-01
The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio
A new method for parameter estimation in nonlinear dynamical equations
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
Nonlinear Dynamical Control of Lasers
1993-10-30
chaos and strange attractors," Reviews of Modem Physics, 57, 617 (1985). I I I 48. E. Ott, C. Grebogi , and J.A. Yorke, in Chaos. ed. D.K Campbell...American Institute of Physics, New York, 1990, pp. 153-172. I 49. E. Ott, C. Grebogi , and J.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990). 50. Troy...shinbrot, Edward Ott, Celso Grebogi , and James A. Yorke, ’Using Chaos to Direct Trajectories to Targets,’ Phys., Rev. Lett. 65, 3215 (1990). i 51. J. Singer
Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions
Rauch, Kevin P.; Holman, Matthew
1999-01-01
We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The physical mechanism of the halo-chaos formation for a high intensity proton beam in a periodic-fo cusing channel is analyzed using the transfer mahix theory and a qualiative analysis method.Particles-in-cell simula tims are further used to explore the mechanism of the beam halo-chaos fomation, which concerns not only with thc non linear effect of the beam space charge but also with the lransverse energy exchange belween the particles and the particle core. as well as the chaos generated by the nonlinear resonance ovcrlap. A nonlinear control method is proposed for con trolling tie haho-chaos. Simulation results show lhal the melhod is efhclivc. Somc potemlial applications of the halo chaos conlrol in experimenls are discussed.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
In the Wake of Chaos Unpredictable Order in Dynamical Systems
Kellert, Stephen H
1993-01-01
Chaos theory has captured scientific and popular attention. What began as the discovery of randomness in simple physical systems has become a widespread fascination with "chaotic" models of everything from business cycles to brainwaves to heart attacks. But what exactly does this explosion of new research into chaotic phenomena mean for our understanding of the world? In this timely book, Stephen Kellert takes the first sustained look at the broad intellectual and philosophical questions raised by recent advances in chaos theory—its implications for science as a source of knowledge a
Biped control via nonlinear dynamics
Hmam, Hatem M.
1992-09-01
This thesis applies nonlinear techniques to actuate a biped system and provides a rigorous analysis of the resulting motion. From observation of human locomotion, it is believed that the 'complex' dynamics developed by the aggregation of multiple muscle systems can be generated by a reduced order system which captures the rough details of the locomotion process. The investigation is begun with a simple model of a biped system. Since the locomotion process is cyclic in nature, we focus on applying the topologically similar concept of limit cycles to the simple model in order to generate the desired gaits. A rigorous analysis of the biped dynamics shows that the controlled motion is robust against dynamical disturbances. In addition, different biped gaits are generated by merely adjusting some of the limit cycle parameters. More dynamical and actuation complexities are then added for realism. First, two small foot components are added and the overall biped motion under the same control actuation is analyzed. Due to the physical constraints on the feet, it is shown using singular perturbation theory how the gross behavior of the biped dynamics are dictated by those of the reduced model. Next, an analysis of the biped dynamics under added nonlinear elasticities in the legs is carried out. Moreover, using a slightly modified model, forward motion is generated in the sagittal plane. At each step, a small amount of energy is consistently derived from the vertical plane and converted into a forward motion. Stability of the forward dynamics is guaranteed by appropriate foot placement. Finally, the robustness of the controlled biped dynamics is rigorously analyzed and illustrated through extensive computer simulations.
Hip actuations can be used to control bifurcations and chaos in a passive dynamic walking model.
Kurz, Max J; Stergiou, Nicholas
2007-04-01
We explored how hip joint actuation can be used to control locomotive bifurcations and chaos in a passive dynamic walking model that negotiated a slightly sloped surface (gammapassive dynamic walking model was capable of producing a chaotic locomotive pattern when the ramp angle was 0.01839 rad
Dynamical behaviors and chaos control in a discrete functional response model
Energy Technology Data Exchange (ETDEWEB)
Zhang Yue [Institute of Systems Science, Northeastern University, Shenyang 110004 (China)]. E-mail: zyueneu@sina.com; Zhang Qingling [Institute of Systems Science, Northeastern University, Shenyang 110004 (China)]. E-mail: qlzhang@mail.neu.edu.cn; Zhao Lichun [Department of Mathematics, Anshan Teachers College, Anshan 114005 (China); Yang Chunyu [Institute of Systems Science, Northeastern University, Shenyang 110004 (China)
2007-11-15
In this paper, the dynamical behaviors and chaos control are investigated in a discrete functional response model. It is verified that there are phenomena of the transcritical bifurcation, flip bifurcation, Hopf bifurcation types and chaos in the sense of Marotto's definition. Specifically, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one (i.e., an unstable fixed point of the chaotic system). Finally, numerical simulations not only show the consistency with theoretical analysis but also exhibit the complex dynamical behaviors.
The danger of wishing for chaos.
McSharry, Patrick
2005-10-01
With the discovery of chaos came the hope of finding simple models that would be capable of explaining complex phenomena. Numerous papers claimed to find low-dimensional chaos in a number of areas ranging from the weather to the stock market. Years later, many of these claims have been disproved and the fantastic hopes pinned on chaos have been toned down as research with more realistic objectives follows. The difficulty in calculating reliable estimates of the correlation dimension and the maximal Lyapunov exponent, two of the hallmarks of chaos, are explored. Given that nonlinear dynamics is a relatively new and growing field of science, the need for statistical testing is greater than ever. Surrogate data provides one possible approach but great care is needed in generating relevant surrogates and in interpreting the results. Examples of misleading applications and challenges for the future of research in nonlinear dynamics are discussed.
Jacquelin, E.; Adhikari, S.; Sinou, J.-J.; Friswell, M. I.
2015-11-01
Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken's transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken's transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken's method are enough. This latter result is improved if a generalization of Aitken's method (recursive Aitken's transformation, Shank's transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response.
Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering
Halang, Wolfgang; Mathis, Wolfgang; Chedjou, Jean; Li, Zhong
2013-01-01
This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.
Selected topics in nonlinear dynamics and theoretical electrical engineering
Halang, Wolfgang; Mathis, Wolfgang; Chedjou, Jean; Li, Zhong
2013-01-01
This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.
Improvements and applications of entrainment control for nonlinear dynamical systems.
Liu, Fang; Song, Qiang; Cao, Jinde
2008-12-01
This paper improves the existing entrainment control approaches and develops unified schemes to chaos control and generalized (lag, anticipated, and complete) synchronization of nonlinear dynamical systems. By introducing impulsive effects to the open-loop control method, we completely remove its restrictions on goal dynamics and initial conditions, and derive a sufficient condition to estimate the upper bound of impulsive intervals to ensure the global asymptotic stability. We then propose two effective ways to implement the entrainment strategy which combine open-loop and closed-loop control, and we prove that the feedback gains can be chosen according to a lower bound or be tuned with an adaptive control law. Numerical examples are given to verify the theoretical results and to illustrate their applications.
BOOK REVIEW: Microscopic Dynamics of Plasmas and Chaos
Elskens, Y.; Escande, D.
2003-04-01
Some of the key intellectual foundations of plasma physics are in danger of becoming a lost art. Fortunately, however, this threat recedes with the publication of this valuable book. It renders accessible those aspects of theoretical plasma physics that are best approached from the perspectives of classical mechanics, in both its early nineteenth century and late twentieth century manifestations. Half a century has elapsed since the publication of seminal papers such as those by Bohm and Pines (1951), van Kampen (1955), and Bernstein, Greene and Kruskal (1957). These papers served to address a fundamental question of physics - namely the relation between degrees of freedom that exist at the individual particle level of description, and those that exist at the collective level - in the plasma context. The authors of the present book have played a major role in the investigation of this question from an N-body standpoint, which can be divided into two linked themes. First, those topics that can be illuminated by analytical methods that lie in the tradition of classical mechanics that stretches back to Lagrange, Legendre and Hamilton. Second, those topics that benefit from the insights developed following the redevelopment of classical mechanics in relation to chaos theory in the 1980s and subsequently. The working plasma physicist who wishes to dig more deeply in this field is faced at present with a number of challenges. These may include a perception that this subfield is of limited relevance to mission-oriented questions of plasma performance; a perception of the research literature as being self-contained and inaccessible; and, linked to this, unfamiliarity with the mathematical tools. The latter problem is particularly pressing, given the limited coverage of classical mechanics in many undergraduate physics courses. The book by Elskens and Escande meets many of the challenges outlined above. The rewards begin early, by the end of the second chapter, with
Chaos in World Politics: A Reflection
Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.
Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.
Dynamics of hourly sea level at Hillarys Boat Harbour, Western Australia: a chaos theory perspective
Khatibi, Rahman; Ghorbani, Mohammad Ali; Aalami, Mohammad Taghi; Kocak, Kasim; Makarynskyy, Oleg; Makarynska, Dina; Aalinezhad, Mahdi
2011-11-01
Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed: low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delay-embedding theorem suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another, the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual insights provided by each model.
Terminal chaos for information processing in neurodynamics.
Zak, M
1991-01-01
New nonlinear phenomenon-terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated with higher level of cognitive processes such as generalization and abstraction.
Nonlinear dynamics of cardiovascular ageing
Energy Technology Data Exchange (ETDEWEB)
Shiogai, Y. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Stefanovska, A. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom); Faculty of Electrical Engineering, University of Ljubljana, Ljubljana (Slovenia); McClintock, P.V.E. [Physics Department, Lancaster University, Lancaster LA1 4YB (United Kingdom)], E-mail: p.v.e.mcclintock@lancaster.ac.uk
2010-03-15
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
Chaos in an imperfectly premixed model combustor
Energy Technology Data Exchange (ETDEWEB)
Kabiraj, Lipika, E-mail: lipika.kabiraj@tu-berlin.de; Saurabh, Aditya; Paschereit, Christian O. [Hermann Föttinger Institut, Technische Universität Berlin (Germany); Karimi, Nader [School of Engineering, University of Glasgow (United Kingdom); Sailor, Anna [University of Wisconsin-Madison, Madison 53706 (United States); Mastorakos, Epaminondas; Dowling, Ann P. [Department of Engineering, University of Cambridge (United Kingdom)
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.
STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL
Institute of Scientific and Technical Information of China (English)
WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing
2005-01-01
A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics, the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed. The result shows that through quasi-periodicity bifurcation the system is lost in chaos.
Are oil markets chaotic? A non-linear dynamic analysis
Energy Technology Data Exchange (ETDEWEB)
Panas, E.; Ninni, V. [Athens University of Economics and Business, Athens (Greece)
2000-10-01
The analysis of products' price behaviour continues to be an important empirical issue. This study contributes to the current literature on price dynamics of products by examining for the presence of chaos and non-linear dynamics in daily oil products for the Rotterdam and Mediterranean petroleum markets. Previous studies using only one invariant, such as the correlation dimension may not effectively determine the chaotic structure of the underlying time series. To obtain better information on the time series structure, a framework is developed, where both invariant and non-invariant quantities were also examined. In this paper various invariants for detecting a chaotic time series were analysed along with the associated Brock's theorem and Eckman-Ruelle condition, to return series for the prices of oil products. An additional non-invariant quantity, the BDS statistic, was also examined. The correlation dimension, entropies and Lyapunov exponents show strong evidence of chaos in a number of oil products considered. 30 refs.
Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System
Directory of Open Access Journals (Sweden)
M. M. El-Dessoky
2012-01-01
Full Text Available This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.
Chaos from simple models to complex systems
Cencini, Massimo; Vulpiani, Angelo
2010-01-01
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor
Physics and Applications of Laser Diode Chaos
Sciamanna, Marc
2015-01-01
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed 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.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo; Yang Chao-Ping
2005-01-01
A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced,and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)thorder as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a During-Holmes system with uncertainty.
A nonlinear dynamical system for combustion instability in a pulse model combustor
Takagi, Kazushi; Gotoda, Hiroshi
2016-11-01
We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.
Measurement of heart rate variability by methods based on nonlinear dynamics.
Huikuri, Heikki V; Mäkikallio, Timo H; Perkiömäki, Juha
2003-01-01
Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
A Self-Check System for Mental Health Care based on Nonlinear and Chaos Analysis
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.
RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.
Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research
Bianchi IX dynamics in bouncing cosmologies: homoclinic chaos and the BKL conjecture
Maier, Rodrigo; Damião Soares, Ivano; Valentino Tonini, Eduardo
2015-12-01
We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. The matter content is a pressureless perfect fluid restricted to the brane, with the embedding consistently satisfying the Gauss-Codazzi equations. The 4-dim Einstein equations on the brane reduce to a 6-dim Hamiltonian dynamical system with additional terms (due to the bulk-brane interaction) that avoid the singularity and implement nonsingular bounces in the model. We examine the complex Bianchi IX dynamics in its approach to the neighborhood of the bounce which replaces the cosmological singularity of general relativity. The phase space of the model presents (i) two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, (ii) two asymptotic de Sitter critical points at infinity, one acting as an attractor to late-time acceleration and (iii) a 2-dim invariant plane, which together organize the dynamics of the phase space. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders R × S 3, where R is a saddle direction and S 3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation the degrees of freedom of the dynamics are separated into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom associated with the center manifold S 3. The typical dynamical flow is thus an oscillatory mode about the orbits of the invariant plane. The stable and unstable cylinders are spanned by oscillatory orbits about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct simulations. The homoclinic intersection manifold has the topology of R × S 2 consisting of
Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates
Lahmiri, Salim
2017-01-01
This paper proposes a new methodology to investigate presence of chaos in exchange rate time series by combining wavelet transform and Lyapunov exponent estimation. In particular, stationary wavelet transform (SWT) is applied to exchange rate original time series for decomposition purpose. As a result, approximation and details coefficients are extracted. They are used to represent long and short term dynamics of the original exchange rate time series. Then, largest Lyapunov exponent is estimated for each type of dynamics to check for presence of chaos. Our methodology is applied to several Moroccan exchange rate time series. The empirical results show that, in general, the hypothesis of chaotic structure is accepted for currency levels but it is rejected for currency returns on both long and short dynamics. In addition, long and short dynamics exhibit different chaotic patterns in some exchange rate time series. Our approach may be useful to understand chaotic behaviour in original exchange rate time series.
Chacón, R.; García-Hoz, A. Martínez; Martínez, J. A.
2017-05-01
We study the effectiveness of locally controlling the impulse transmitted by parametric periodic excitations at inducing and suppressing chaos in starlike networks of driven damped pendula, leading to asynchronous chaotic states and equilibria, respectively. We found that the inducing (suppressor) effect of increasing (decreasing) the impulse transmitted by the parametric excitations acting on particular nodes depends strongly on their number and degree of connectivity as well as the coupling strength. Additionally, we provide a theoretical analysis explaining the basic physical mechanisms of the emergence and suppression of chaos as well as the main features of the chaos-control scenario. Our findings constitute proof of the impulse-induced control of chaos in a simple model of complex networks, thus opening the way to its application to real-world networks.
Corporate Investment Dynamic Control System Based on Chaos Cycle Perturbations
Directory of Open Access Journals (Sweden)
Yanyan Gao
2014-11-01
Full Text Available It exists some issues such as the low predict accuracy and a bad convergence performance to predict business investment with BP neural network algorithm. This paper presents a predictive model of business investment based on improved artificial bee colony and chaos periodic disturbance optimizing BP neural network algorithm. At first, use Boltzmann selection strategy and group behaviour control strategy to optimize the artificial bee colony algorithm, and then use the improved algorithm to transform BP neural network algorithm’s optimized parameters into optimization process of artificial bee colony algorithm to reduce the training error of the original algorithm. Finally, use chaotic optimized Logistic mapping enables BP neural network out of the local minimum point in the training process based on secondary chaotic cycle perturbation strategies. Simulation results show that the proposed predictive model of investment in the enterprise based on improved artificial bee colony and chaos periodic disturbance optimizing BP neural network algorithm shows higher predict accuracy and better convergence than normal BP neural network algorithm.
Numerical investigation of bubble nonlinear dynamics characteristics
Energy Technology Data Exchange (ETDEWEB)
Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo; Hu, Bo [Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001 (China); College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China); Zhang, Haoyang; Jiang, Wei [College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001 (China)
2015-10-28
The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.
Disks controlling chaos in a 3D dynamical model for elliptical galaxies
Zotos, Euaggelos E
2011-01-01
A 3D dynamical model with a quasi-homogeneous core and a disk component is used for the chaos control in the central parts of elliptical galaxy. Numerical experiments in the 2D system show a very complicated phase plane with a large chaotic sea, considerable sticky layers and a large number of islands, produced by secondary resonances. When the mass of the disk increases, the chaotic regions decrease gradually, and, finally, a new phase plane with only regular orbits appears. This evolution indicates that disks in elliptical galaxies can act as the chaos controllers. Starting from the results obtained in the 2D system, we locate the regions in the phase space of the 3D system, producing regular and chaotic orbits. For this we introduce and use a new dynamical parameter, the S(w) spectrum, which proves to be useful as a fast indicator and allows us to distinguish the regular motion from chaos in the 3D potentials. Other methods for detecting chaos are also discussed.
Nonlinear dynamics in human behavior
Energy Technology Data Exchange (ETDEWEB)
Huys, Raoul [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Jirsa, Viktor K. (eds.) [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Florida Atlantic Univ., Boca Raton, FL (United States). Center for Complex Systems and Brain Sciences
2010-07-01
Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music. (orig.)
Theesar, S Jeeva Sathya; Balasubramaniam, P; Banerjee, Santo
2012-09-01
In Chaos 19, 013102 (2009), the author proposed generalized projective synchronization for time delay systems using nonlinear observer and obtained sufficient condition to ensure projective synchronization for modulated time varying delay. There are concerns with the obtained conditions as the result was applicable only to trivial case of time varying delay τ[over dot](1)(t)=dτ(1)(t)/dt<1. In this paper, we note the drawbacks of the proposed sufficient condition. The new improved sufficient condition for ensuring the projective synchronization of time varying delayed systems is presented. The proposed new criteria have been verified by adopting the Ikeda system.
Nonlinear Approach in Nuclear Dynamics
Gridnev, K. A.; Kartavenko, V. G.; Greiner, W.
2002-11-01
Attention is focused on the various approaches that use the concept of nonlinear dispersive waves (solitons) in nonrelativistic nuclear physics. The problem of dynamical instability and clustering (stable fragments formation) in a breakup of excited nuclear systems are considered from the points of view of the soliton concept. It is shown that the volume (spinodal) instability can be associated with nonlinear terms, and the surface (Rayleigh-Taylor type) instability, with the dispersion terms in the evolution equations. The both instabilities may compensate each other and lead to stable solutions (solitons). A static scission configuration in cold ternary fission is considered in the framework of mean field approach. We suggest to use the inverse mean field method to solve single-particle Schrödinger equation, instead of constrained selfconsistent Hartree-Fock equations. It is shown, that it is possible to simulate one-dimensional three-center system in the approximation of reflectless single-particle potentials. The soliton-like solutions of the Korteweg-de Vries equation are using to describe collective excitations of nuclei observed in inelastic alpha-particle and proton scattering. The analogy between fragmentation into parts of nuclei and buckyballs has led us to the idea of light nuclei as quasi-crystals. We establish that the quasi-crystalline structure can be formed when the distance between the alpha-particles is comparable with the length of the De Broglia wave of the alpha-particle. Applying this model to the scattering of alpha-particles we obtain that the form factor of the clusterized nucleus can be factorized into the formfactor of the cluster and the density of clusters in the nucleus. It gives possibility to study the distribution of clusters in nuclei and to resolve what kind of distribution we are dealing with: a surface or volume one.
Nonlinear Chemical Dynamics and Synchronization
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Tsionas, Mike G.; Michaelides, Panayotis G.
2017-09-01
We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by traditional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014, by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data (;neglected chaos;).
On a New Route to Chaos in Railway Dynamics
DEFF Research Database (Denmark)
True, Hans; Jensen, Carsten Nordstroem
1997-01-01
exist, but only a couple of which are stable. One of them is a chaotic attractor. Cooperrider's bogie model is described in Section 2, and in Section 3 we explain the method of numerical investigation. In Section 4 the results are shown. The main result is that the chaotic attractor is created through...... a period-doubling cascade of the secondary period in an asymptotically stable quasiperiodic oscillation at decreasing speed. Several quasiperiodic windows were found in the chaotic motion. This route to chaos was first described by Franceschini [9], who discovered it in a seven-mode truncation of the plane...... solution is initially unstable, but it gains stability in a saddle-node bifurcation when the branch turns back toward lower speeds. The chaotic attractor disappears abruptly in what is conjectured to be a blue sky catastrophe, when the speed decreases further....
Dynamics and chaos control of asymmetric gyrostat satellites
Aslanov, V. S.; Yudintsev, V. V.
2014-05-01
The motion of a free gyrostat consisting of a platform with a triaxial ellipsoid of inertia and a rotor with a slight asymmetry with respect to the axis of rotation is considered. Dimensionless equations of motion for a system with perturbations caused by the small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations result in a chaotic layer in the separatrix vicinity. Heteroclinic and homoclinic trajectories are written in analytical form for gyrostats with different ratios of their moments of inertia. These trajectories are used to construct a modified Melnikov function, and to produce control that eliminates separatrix chaos. The Poincare sections and Melnikov function are constructed via numerical modeling that demonstrates the effectiveness of control.
Optomechanically induced stochastic resonance and chaos transfer between optical fields
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
Dynamics and vibrations progress in nonlinear analysis
Kachapi, Seyed Habibollah Hashemi
2014-01-01
Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...
Control of Chaotic Regimes in Encryption Algorithm Based on Dynamic Chaos
Sidorenko, V.; Mulyarchik, K. S.
2013-01-01
Chaotic regime of a dynamic system is a necessary condition determining cryptographic security of an encryption algorithm. A chaotic dynamic regime control method is proposed which uses parameters of nonlinear dynamics regime for an analysis of encrypted data.
Synchronized Chaos in Geophysical Fluid Dynamics and in the Predictive Modeling of Natural Systems
Duane, Gregory S.
2008-03-01
The ubiquitous phenomenon of synchronization among regular oscillators in Nature has been shown, in the past two decades, to extend to chaotic systems. Despite sensitive dependence on initial conditions, two chaotic systems will commonly fall into synchronized motion along their strange attractors when only some of the many degrees of freedom of one system are coupled to corresponding variables in the other. In geophysical fluid models, synchronization can mediate scale interactions, so that coupling of degrees of freedom that describe medium-scale components of the flow can result in synchronization, or partial synchronization, at all scales. Chaos synchronization has been used to interpret non-local "teleconnection" patterns in the Earth's climate system and to predict new ones. In the realm of practical meteorology, the fact that two PDE systems, conceived as "truth" and "model", respectively, can be made to synchronize when coupled at only a discrete set of points, explains how observations at a discrete set of weather stations can be sufficient for weather prediction by a synchronously coupled model. Minimizing synchronization error leads to general recipes for assimilation of observed data into a running model that systematize the treatment of nonlinearities in the dynamical equations. Equations can generally be added to adapt parameters as well as states as the model is running, so that the model "learns". The synchronization view of predictive modelling extends to any translationally- any PDE with constant coefficients, the general form of physical theories. The reliance on synchronicity as an organizing principle in Nature, alternative to causality, has philosophical roots in the collaboration of Carl Jung and Wolfgang Pauli, on the one hand, and in traditions outside of European science, on the other.
$\\mathcal{PT}$-Symmetry-Breaking Chaos in Optomechanics
Lü, Xin-You; Ma, Jin-Yong; Wu, Ying
2015-01-01
We demonstrate a $\\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), 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 $\\mathcal{PT}$-symmetry-breaking phase ($\\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\\mathcal{PT}$-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.
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear and nonequilibrium dynamics in geomaterials.
TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A
2004-08-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.
Yin, J. L.; Xing, Q. Q.; Tian, L. X.
2015-03-01
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves
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 flexural waves and chaos behavior in finite-deflection Timoshenko beam
Institute of Scientific and Technical Information of China (English)
Shan-yuan ZHANG; Zhi-fang LIU
2010-01-01
Based on the Timoshenko beam theory,the finite-deflection and the axial inertia are taken into account,and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case,a shock wave solution is given. The small perturbations are further introduced,arising from the damping and the external load to an original Hamilton system,and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
Numata, Ryusuke; Yoshida, Zensho
2003-07-01
Magnetic null points act as scattering centers where particles describe chaotic orbits, and the mixing effect brings about increase of the kinetic entropy. The resultant "chaos-induced resistivity" may explain anomalous diffusion of current in magnetic null regions [Phys. Rev. Lett. 88, 045003 (2002)], which can be much larger than the conventional collisionless resistivity in a high temperature plasma. To study the statistical properties of the system (such as Lyapunov exponents and distribution functions), strong spatial inhomogeneity of the system has been studied to specify the responsible "chaos region."
Nonlinear Dynamic Model Explains The Solar Dynamic
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
Nonlinear dynamics of the left ventricle.
Munteanu, Ligia; Chiroiu, Calin; Chiroiu, Veturia
2002-05-01
The cnoidal method is applied to solve the set of nonlinear dynamic equations of the left ventricle. By using the theta-function representation of the solutions and a genetic algorithm, the ventricular motion can be described as a linear superposition of cnoidal pulses and additional terms, which include nonlinear interactions among them.
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
Rahman, Aminur; Blackmore, Denis
2016-10-01
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark--Sacker (N--S) bifurcations, and even chaos. For example, in [Gilet, PRE 2014], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one-dimensional path model. We prove Gilet's conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.
Abramov, Rafail V
2011-01-01
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the slow climate dynamics with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely pred...
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Department of Economics, University of Calgary, Calgary, Alta., T2N 1N4 (Canada)]. E-mail: Serletis@ucalgary.ca; Shahmoradi, Asghar [Faculty of Economics, University of Tehran, Tehran (Iran, Islamic Republic of)
2007-08-15
This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
Chaos in the Belousov-Zhabotinsky reaction
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...
MEMS linear and nonlinear statics and dynamics
Younis, Mohammad I
2011-01-01
MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
The computational complexity of symbolic dynamics at the edge of order and chaos
Lakdawala, P
1995-01-01
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis for modelling this region is the Universal Turing Machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.
Complex dynamical behavior and chaos control in fractional-order Lorenz-like systems
Institute of Scientific and Technical Information of China (English)
Li Rui-Hong; Chen Wei-Sheng
2013-01-01
In this paper,the complex dynamical behavior of a fractional-order Lorenz-like system with two quadratic terms is investigated.The existence and uniqueness of solutions for this system are proved,and the stabilities of the equilibrium points are analyzed as one of the system parameters changes.The pitchfork bifurcation is discussed for the first time,and the necessary conditions for the commensurate and incommensurate fractional-order systems to remain in chaos are derived.The largest Lyapunov exponents and phase portraits are given to check the existence of chaos.Finally,the sliding mode control law is provided to make the states of the Lorenz-like system asymptotically stable.Numerical simulation results show that the presented approach can effectively guide chaotic trajectories to the unstable equilibrium points.
Impulsive Stabilization of Uncertain Dynamical Systems and Chaos Control
Institute of Scientific and Technical Information of China (English)
LIUBin; YAOJian; FANGJinqing; LIUXinzhi
2004-01-01
In this paper, a general impulsive control problem for uncertain dynamical systems is investigated.By utilizing the method of Lyapunov functions, a set of stability criteria for uncertain impulsive dynamical systems are established. These obtained results are then appliedto derive conditions under which an uncertain dynamical system can be robustly stabilized by an impulsive control law. Finally, we demonstrate our method by controlling the famous Lorenz system with uncertain perturbation.
Chaos concepts, control and constructive use
Bolotin, Yurii; Yanovsky, Vladimir
2017-01-01
This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...
Nonlinear Dynamics of Structures with Material Degradation
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.
Using Lyapunov exponents to predict the onset of chaos in nonlinear oscillators.
Ryabov, Vladimir B
2002-07-01
An analytic technique for predicting the emergence of chaotic instability in nonlinear nonautonomous dissipative oscillators is proposed. The method is based on the Lyapunov-type stability analysis of an arbitrary phase trajectory and the standard procedure of calculating the Lyapunov characteristic exponents. The concept of temporally local Lyapunov exponents is then utilized for specifying the area in the phase space where any trajectory is asymptotically stable, and, therefore, the existence of chaotic attractors is impossible. The procedure of linear coordinate transform optimizing the linear part of the vector field is developed for the purpose of maximizing the stability area in the vicinity of a stable fixed point. By considering the inverse conditions of asymptotic stability, this approach allows formulating a necessary condition for chaotic motion in a broad class of nonlinear oscillatory systems, including many cases of practical interest. The examples of externally excited one- and two-well Duffing oscillators and a planar pendulum demonstrate efficiency of the proposed method, as well as a good agreement of the theoretical predictions with the results of numerical experiments. The comparison of the proposed method with Melnikov's criterion shows a potential advantage of using the former one at high values of dissipation parameter and/or multifrequency type of excitation in dynamical systems.
Theory and application of nonlinear river dynamics
Institute of Scientific and Technical Information of China (English)
Yu-chuan BAI; Zhao-yin WANG
2014-01-01
A theoretical model for river evolution including riverbed formation and meandering pattern formation is presented in this paper. Based on nonlinear mathematic theory, the nonlinear river dynamic theory is set up for river dynamic process. Its core content includes the stability and tropism characteristics of flow motion in river and river selves’ evolution. The stability of river dynamic process depends on the response of river selves to the external disturbance, if the disturbance and the resulting response will eventually attenuate, and the river dynamics process can be restored to new equilibrium state, the river dynamic process is known as stable;otherwise, the river dynamic process is unstable. The river dynamic process tropism refers to that the evolution tendency of river morphology after the disturbance. As an application of this theory, the dynamical stability of the constant curvature river bend is calculated for its coherent vortex disturbance and response. In addition, this paper discusses the nonlinear evolution of the river peristaltic process under a large-scale disturbance, showing the nonlinear tendency of river dynamic processes, such as river filtering and butterfly effect.
Chaos as a Source of Complexity and Diversity in Evolution
Kaneko, K
1993-01-01
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of identical chaotic elements, globally coupled each to other, is briefly reviewed. The clustering is extended to nonlinear dynamics on hypercubic lattices, which enables us to construct a self-organizing genetic algorithm. A mechanism of maintenance of diversity, ``homeochaos", is given in an ecological system with interaction among many species. Homeochaos provides a dynamic stability sustained by high-dimensional weak chaos. A novel mechanism of cell differentiation is presented, based on dynamic clustering. Here, a new concept -- ``open chaos" -- is proposed for the instability in a dynamical system with growing degrees of freedom. It is suggested that studies based on interacting chaotic elements can replace both top-down and bottom-up approaches.
Erçetin, Şefika; Tekin, Ali
2014-01-01
The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.
Nonlinear Dynamics of A Damped Magnetic Oscillator
Kim, S Y
1999-01-01
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. As $A$ is increased, the damped magnetic oscillator, albeit simple looking, exhibits rich dynamical behaviors such as symmetry-breaking pitchfork bifurcations, period-doubling transitions to chaos, symmetry-restoring attractor-merging crises, and saddle-node bifurcations giving rise to new periodic attractors. Besides these familiar behaviors, a cascade of ``resurrections'' (i.e., an infinite sequence of alternating restabilizations and destabilizations) of the stationary points also occurs. It is found that the stationary points restabilize (destabilize) through alternating subcritical (supercritical) period-doubling and pitchfork bifurcations. We also discuss the critical behaviors in the period-doubling cascades.
A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.
Directory of Open Access Journals (Sweden)
William Gilpin
2017-07-01
Full Text Available In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.
Nonlinear dynamics new directions models and applications
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...
Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller
Energy Technology Data Exchange (ETDEWEB)
Laoye, J.A. [Nonlinear and Statistical Physics Research Group, Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye (Nigeria); Vincent, U.E. [Nonlinear and Statistical Physics Research Group, Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye (Nigeria)], E-mail: ue_vincent@yahoo.com; Kareem, S.O. [Nonlinear and Statistical Physics Research Group, Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye (Nigeria)
2009-01-15
This paper examines chaos control of two four-dimensional chaotic systems, namely: the Lorenz-Stenflo (LS) system that models low-frequency short-wavelength gravity waves and a new four-dimensional chaotic system (Qi systems), containing three cross products. The control analysis is based on recursive backstepping design technique and it is shown to be effective for the 4D systems considered. Numerical simulations are also presented.
Differential equations, dynamical systems, and an introduction to chaos
Smale, Stephen; Devaney, Robert L
2003-01-01
Thirty years in the making, this revised text by three of the world''s leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field''s Medal for his work in dynamical systems.* Developed by award-winning researchers and authors* Provides a rigorous yet accessible introduction to differential equations and dynamical systems* Includes bifurcation theory throughout* Contains numerous explorations for students to embark uponNEW IN THIS EDITION* New contemporary material and updated applications* Revisions throughout the text, including simplification...
Dynamic disturbance decoupling for nonlinear systems
Huijberts, H.J.C.; Nijmeijer, H.; Wegen, van der L.L.M.
1992-01-01
In analogy with the dynamic input-output decoupling problem the dynamic disturbance decoupling problem for nonlinear systems is introduced. A local solution of this problem is obtained in the case that the system under consideration is invertible. The solution is given in algebraic as well as in geo
Frozen spatial chaos induced by boundaries
Eguiluz, V M; Piro, O; Balle, S; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Piro, Oreste; Balle, Salvador
1999-01-01
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.
Nonlinear amplitude dynamics in flagellar beating
Oriola, David; Casademunt, Jaume
2016-01-01
The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive crosslinkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatiotemporal dynamics of dynein populations and flagell...
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)
2011-02-28
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)
Neural Network Nonlinear Predictive Control Based on Tent-map Chaos Optimization%基于Tent混沌优化的神经网络预测控制
Institute of Scientific and Technical Information of China (English)
宋莹; 陈增强; 袁著祉
2007-01-01
With the unique ergodicity, irregularity, and special ability to avoid being trapped in local optima, chaos optimization has been a novel global optimization technique and has attracted considerable attention for application in various fields, such as nonlinear programming problems. In this article, a novel neural network nonlinear predictive control (NNPC) strategy based on the new Tent-map chaos optimization algorithm (TCOA) is presented. The feedforward neural network is used as the multi-step predictive model. In addition, the TCOA is applied to perform the nonlinear rolling optimization to enhance the convergence and accuracy in the NNPC. Simulation on a laboratory-scale liquid-level system is given to illustrate the effectiveness of the proposed method.
The transition to chaos conservative classical systems and quantum manifestations
Reichl, Linda E
2004-01-01
This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...
Dynamical Imaging using Spatial Nonlinearity
2014-01-29
Imin )/ (Imax + Imin ) = 0.15 for detection of the bars (from maxima to central dip). For our experimental measurements, the best linear visibility is...Statistical theory for incoherent light propagation in nonlinear media, Physical Review E, 65 (2002) 035602. [52] M.J. Bastiaans, Application of the...1238. [53] M.E. Testorf, B.M. Hennelly, J. Ojeda-Castañeda, Phase-space optics : fundamentals and applications , McGraw-Hill, New York, 2010. [54] K.H
Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper
Directory of Open Access Journals (Sweden)
Hailong Zhang
2015-01-01
Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.
Chaos in a dynamic model of traffic flows in an origin-destination network
Zhang, Xiaoyan; Jarrett, David F.
1998-06-01
In this paper we investigate the dynamic behavior of road traffic flows in an area represented by an origin-destination (O-D) network. Probably the most widely used model for estimating the distribution of O-D flows is the gravity model, [J. de D. Ortuzar and L. G. Willumsen, Modelling Transport (Wiley, New York, 1990)] which originated from an analogy with Newton's gravitational law. The conventional gravity model, however, is static. The investigation in this paper is based on a dynamic version of the gravity model proposed by Dendrinos and Sonis by modifying the conventional gravity model [D. S. Dendrinos and M. Sonis, Chaos and Social-Spatial Dynamics (Springer-Verlag, Berlin, 1990)]. The dynamic model describes the variations of O-D flows over discrete-time periods, such as each day, each week, and so on. It is shown that when the dimension of the system is one or two, the O-D flow pattern either approaches an equilibrium or oscillates. When the dimension is higher, the behavior found in the model includes equilibria, oscillations, periodic doubling, and chaos. Chaotic attractors are characterized by (positive) Liapunov exponents and fractal dimensions.
Nonlinear dynamic vibration absorbers with a saturation
Febbo, M.; Machado, S. P.
2013-03-01
The behavior of a new type of nonlinear dynamic vibration absorber is studied. A distinctive characteristic of the proposed absorber is the impossibility to extend the system to infinity. The mathematical formulation is based on a finite extensibility nonlinear elastic potential to model the saturable nonlinearity. The absorber is attached to a single degree-of-freedom linear/nonlinear oscillator subjected to a periodic external excitation. In order to solve the equations of motion and to analyze the frequency-response curves, the method of averaging is used. The performance of the FENE absorber is evaluated considering a variation of the nonlinearity of the primary system, the damping and the linearized frequency of the absorber and the mass ratio. The numerical results show that the proposed absorber has a very good efficiency when the nonlinearity of the primary system increases. When compared with a cubic nonlinear absorber, for a large nonlinearity of the primary system, the FENE absorber shows a better effectiveness for the whole studied frequency range. A complete absence of quasi-periodic oscillations is also found for an appropriate selection of the parameters of the absorber. Finally, direct integrations of the equations of motion are performed to verify the accuracy of the proposed method.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
Replication of chaos in neural networks, economics and physics
Akhmet, Marat
2016-01-01
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
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. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Multiplexing symbolic dynamics-based chaos communications using synchronization
Blakely, Jonathan N.; Corron, Ned J.
2005-01-01
A novel form of multiplexing information-bearing chaotic waveforms is demonstrated experimentally. This scheme dramatically increases the information carrying capacity of a chaotic communication system. In the transmitter, information is encoded in the chaotic waveforms of two electronic circuits using small perturbations to induce the symbolic dynamics to follow a prescribed symbol sequence. Waveforms from each of the drive oscillators are summed to form a single scalar signal that is transmitted to the receiver. Identical oscillators in the receiver synchronize to their counterparts in the drive system, effectively de-multiplexing the transmitted signal. The transmitted information in each channel is extracted from simple return maps of the receiver oscillators.
Nonlinear dynamics of cell orientation
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
From chaos to order methodologies, perspectives and applications
Chen Guan Rong
1998-01-01
Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include: Fundamentals of nonlinear dynamical systems, essential for understanding and developing chaos control methods.; Parametric variation and paramet
A topological proof of chaos for two nonlinear heterogeneous triopoly game models
Pireddu, Marina
2016-08-01
We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizes its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called "Stretching Along the Paths" technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.
A topological proof of chaos for two nonlinear heterogeneous triopoly game models
Energy Technology Data Exchange (ETDEWEB)
Pireddu, Marina, E-mail: marina.pireddu@unimib.it [Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano (Italy)
2016-08-15
We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizes its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called “Stretching Along the Paths” technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.
Nonlinear dynamics in wurtzite InN diodes under terahertz radiation
Institute of Scientific and Technical Information of China (English)
Feng Wei
2012-01-01
We carry out a theoretical study of nonlinear dynamics in terahertz-driven n+nn+ wurtzite InN diodes by using time-dependent drift diffusion equations.A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect,which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the T1 valley.The appearance of different nonlinear oscillatory modes,including periodic and chaotic states,is attributed to the competition between the self-sustained oscillation and the external driving oscillation.The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods,such as the bifurcation diagram,the Fourier spectrum and the first return map.The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Dynamical Chaos in the Wisdom-Holman Integrator Origins and Solutions
Rauch, K P; Rauch, Kevin P.; Holman, Matthew
1999-01-01
We examine the non-linear stability of the Wisdom-Holman (WH) mapping applied to the integration of perturbed, highly eccentric two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories, unless the step size is chosen small enough to resolve pericenter. The origin of the instability is analyzed analytically using the Stark problem as a fiducial test case. We similarly examine the robustness of several alternative methods: a regularized WH map due to Mikkola (1997); the potential-splitting (PS) approach of Lee et al. (1997); and two types of Stark-based methods. Comparative simulations show the regularized WH map to be stable at high eccentricities, and an enhanced PS algorithm to perform well when close encounters are additionally present. We find Stark-based schemes to be of marginal use in N-body type integrations.
Dynamical systems approach to one-dimensional spatiotemporal chaos: A cyclist's view
Lan, Yueheng
We propose a dynamical systems approach to the study of weak turbulence (spatiotemporal chaos) based on the periodic orbit theory, emphasizing the role of recurrent patterns and coherent structures. After a brief review of the periodic orbit theory and its application to low-dimensional dynamics, we discuss its possible extension to study dynamics of spatially extended systems. The discussion is three-fold. First, we introduce a novel variational scheme for finding periodic orbits in high-dimensional systems. Second, we prove rigorously the existence of periodic structures (modulated amplitude waves) near the first instability of the complex Ginzburg-Landau equation, and check their role in pattern formation. Third, we present the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the shortest periodic orbits, description of the chaotic invariant set in terms of intrinsic coordinates and return maps on the Poincare section.
The Dynamics of Fullerene Structure Formation Order out of Chaos Phenomenon
Selvam, A M
1999-01-01
C60 molecules form spontaneously during vaporization of carbon associated with intense heating and turbulence such as in electrical arcs or flames. Self-organization of fluctuations in the highly turbulent (chaotic) atomized carbon vapor appears to result in the formation of the stable structure of C60 and therefore may be visualized as order out of chaos phenomenon. The geometry of C60, namely, the self-similar quasiperiodic Penrose tiling pattern implies long-range spatiotemporal correlations. Such non-local connections in space and time are ubiquitous to dynamical systems in nature and is recently identified as signatures of self-organized criticality . A cell dynamical system model for turbulent fluid flows developed by the author is summarized and it is shown that the observed quasiperiodic Penrose tiling pattern is a signature of quantum-like mechanics governing flow dynamics.
Abdullaev, Sadrilla
2014-01-01
This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincaré-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statisti...
Nonlinear dynamics in the study of birdsong
Mindlin, Gabriel B.
2017-09-01
Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.
Nonlinear dynamics in particle accelerators
Dilão, Rui
1996-01-01
This book is an introductory course to accelerator physics at the level of graduate students. It has been written for a large audience which includes users of accelerator facilities, accelerator physicists and engineers, and undergraduates aiming to learn the basic principles of construction, operation and applications of accelerators.The new concepts of dynamical systems developed in the last twenty years give the theoretical setting to analyse the stability of particle beams in accelerator. In this book a common language to both accelerator physics and dynamical systems is integrated and dev
Ontology of Earth's nonlinear dynamic complex systems
Babaie, Hassan; Davarpanah, Armita
2017-04-01
As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.
Some Nonlinear Dynamic Inequalities on Time Scales
Indian Academy of Sciences (India)
Wei Nian Li; Weihong Sheng
2007-11-01
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736--751).
Estimating the uncertainty in underresolved nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
Directory of Open Access Journals (Sweden)
Brajendra K Singh
Full Text Available Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons. The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data.We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations.
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Chembo Kouomou, Y; Woafo, P
2003-04-01
We study the spatiotemporal dynamics of a ring of diffusely coupled single-well Duffing oscillators. The transitions from spatiotemporal chaos to cluster and complete synchronization states are particularly investigated, as well as the Hopf bifurcations to instability. It is found that the underlying mechanism of these transitions relies on the motion of the representative points corresponding to the system's nondegenerated spatial transverse Fourier modes in the parametric Strutt diagram. A scaling law is used to demonstrate that the compact interval of the scalar coupling parameter values leading to cluster synchronization broadens in a square-power-like fashion as the number of oscillators is increased. The analytical approach is confirmed by numerical simulations.
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Nonlinear dynamics of a double bilipid membrane.
Sample, C; Golovin, A A
2007-09-01
The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.
Nonlinear adhesion dynamics of confined lipid membranes
To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier
Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.
Superworldvolume dynamics of superbranes from nonlinear realizations
Energy Technology Data Exchange (ETDEWEB)
Bellucci, S. [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, Frascati, RM (Italy); Ivanov, E. [Paris Univ., Paris (France). Lab. de Physique Theorique et des Hautes Energies]|[Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR); Krivonos, S. [Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow (USSR)
2000-07-01
Based on the concept of the partial breaking of global supersymmetry (PBGS), it has been derived the worldvolume superfield equations of motion for N=1, D=4 supermembrane, as well as for the space-time filling D2- and D3-branes, from nonlinear realizations of the corresponding supersymmetries. It has been argued that it is of no need to take care of the relevant automorphism groups when being interested in the dynamical equations. This essentially facilitates computations. As a by-product, it has been obtained a new polynomial representation for the d=3,4 Born-Infeld equations, with merely a cubic nonlinearity.
Nonlinear Dynamics on Interconnected Networks
Arenas, Alex; De Domenico, Manlio
2016-06-01
Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).
Nonlinear dynamics of interacting populations
Bazykin, Alexander D
1998-01-01
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative the
Hamiltonian Chaos Beyond the KAM Theory Dedicated to George M Zaslavsky (1935–2008)
Luo, Albert C J
2011-01-01
“Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935—2008)” covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.
Fractal space-time fluctuations: A signature of quantumlike chaos in dynamical systems
Selvam, A M
2004-01-01
Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal fluctuations exhibit inverse power law form indicating long-range space-time correlations, identified as self-organized criticality. The author has proposed a general systems theory, which predicts the observed self-organized criticality as signatures of quantumlike chaos. The model shows that (1) the fractal fluctuations result from an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. Conventional power spectral analysis of such a logarithmic spiral trajectory will show a continuum of eddies with progressive increase in phase. (2) Power spectral analyses of fractal fluctuations of dynamical systems exhibit the universal inverse power law form of the statistical normal distribution. Such a result indicates that th...
Dynamic video encryption algorithm for H.264/AVC based on a spatiotemporal chaos system.
Xu, Hui; Tong, Xiao-Jun; Zhang, Miao; Wang, Zhu; Li, Ling-Hao
2016-06-01
Video encryption schemes mostly employ the selective encryption method to encrypt parts of important and sensitive video information, aiming to ensure the real-time performance and encryption efficiency. The classic block cipher is not applicable to video encryption due to the high computational overhead. In this paper, we propose the encryption selection control module to encrypt video syntax elements dynamically which is controlled by the chaotic pseudorandom sequence. A novel spatiotemporal chaos system and binarization method is used to generate a key stream for encrypting the chosen syntax elements. The proposed scheme enhances the resistance against attacks through the dynamic encryption process and high-security stream cipher. Experimental results show that the proposed method exhibits high security and high efficiency with little effect on the compression ratio and time cost.
Vesicle Dynamics in a Confined Poiseuille Flow: From Steady-State to Chaos
Aouane, Othmane; Benyoussef, Abdelilah; Wagner, Christian; Misbah, Chaouqi
2014-01-01
Red blood cells (RBCs) are the major component of blood and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: i) the degree of confinement of vesicles within the channel, and ii) the flow strength. Rich and complex dynamics for vesicles are revealed ranging from steady-state shapes (in the form of parachute and slipper) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement, flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.
Energy Technology Data Exchange (ETDEWEB)
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.
A Description of Quantum Chaos
Inoue, K; Ohya, M; Inoue, Kei; Kossakowski, Andrzej; Ohya, Masanori
2004-01-01
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.
A dynamical polynomial chaos approach for long-time evolution of SPDEs
Ozen, H. Cagan; Bal, Guillaume
2017-08-01
We propose a Dynamical generalized Polynomial Chaos (DgPC) method to solve time-dependent stochastic partial differential equations (SPDEs) with white noise forcing. The long-time simulation of SPDE solutions by Polynomial Chaos (PC) methods is notoriously difficult as the dimension of the stochastic variables increases linearly with time. Exploiting the Markovian property of white noise, DgPC [1] implements a restart procedure that allows us to expand solutions at future times in terms of orthogonal polynomials of the measure describing the solution at a given time and the future white noise. The dimension of the representation is kept minimal by application of a Karhunen-Loeve (KL) expansion. Using frequent restarts and low degree polynomials on sparse multi-index sets, the method allows us to perform long time simulations, including the calculation of invariant measures for systems which possess one. We apply the method to the numerical simulation of stochastic Burgers and Navier-Stokes equations with white noise forcing. Our method also allows us to incorporate time-independent random coefficients such as a random viscosity. We propose several numerical simulations and show that the algorithm compares favorably with standard Monte Carlo methods.
Nonlinear Dynamics of Coiling in Viscoelastic Jets
Majmudar, Trushant; Hartt, William; McKinley, Gareth
2010-01-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in great detail; buckling instability in viscous jets leads to regular periodic coiling of the jet that exhibits a non-trivial frequency dependence with the height of the fall. Very few experimental or theoretical studies exist for continuous viscoelastic jets beyond the onset of the first instability. Here, we present a systematic study of the effects of viscoelasticity on the dynamics of free surface continuous jets of surfactant solutions that form worm-like micelles. We observe complex nonlinear spatio-temporal dynamics of the jet and uncover a transition from periodic to doubly-periodic or quasi-periodic to a multi-frequency, possibly chaotic dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the "leaping shampoo effect" or the Kaye effe...
CISM course on exploiting nonlinear behaviour in structural dynamics
Virgin, Lawrence; Exploiting Nonlinear Behavior in Structural Dynamics
2012-01-01
The articles in this volume give an overview and introduction to nonlinear phenomena in structural dynamics. Topics treated are approximate methods for analyzing nonlinear systems (where the level of nonlinearity is assumed to be relatively small), vibration isolation, the mitigation of undesirable torsional vibration in rotating systems utilizing specifically nonlinear features in the dynamics, the vibration of nonlinear structures in which the motion is sufficiently large amplitude and structural systems with control.
Cluster-based control of nonlinear dynamics
Kaiser, Eurika; Spohn, Andreas; Cattafesta, Louis N; Morzynski, Marek
2016-01-01
The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is de...
Nonlinear Dynamics in Double Square Well Potential
Khomeriki, Ramaz; Ruffo, Stefano; Wimberger, Sandro; 10.1007/s11232-007-0096-y
2009-01-01
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.
Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime
Scheel, Mark A.; Thorne, Kip S.
2017-01-01
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.
Time Series Forecasting: A Nonlinear Dynamics Approach
Sello, Stefano
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...
Directory of Open Access Journals (Sweden)
Milovanović Branislav
2007-01-01
Full Text Available Introduction: There are different proofs about association of autonomic nervous system dysfunction, especially nonlinear parameters, with higher mortality after myocardial infarction. Objective The objective of the study was to determine predictive value of Poincare plot as nonlinear parameter and other significant standard risk predictors: ejection fraction of the left ventricle, late potentials, ventricular arrhythmias, and QT interval. Method The study included 1081 patients with mean follow up of 28 months (ranging fom 0-80 months. End-point of the study was cardiovascular mortality. The following diagnostic methods were used during the second week: ECG with commercial software Schiller AT-10: short time spectral analysis of RR variability with analysis of Poincare plot as nonlinear parameter and late potentials; 24-hour ambulatory ECG monitoring: QT interval, RR interval, QT/RR slope, ventricular arrhythmias (Lown >II; echocardiography examinations: systolic disorder (defined as EF<40 %. Results There were 103 (9.52% cardiovascular deaths during the follow-up. In univariate analysis, the following parameters were significantly correlated with mortality: mean RR interval < 800 ms, QT and RR interval space relationship as mean RR interval < 800 ms and QT interval > 350 ms, positive late potentials, systolic dysfunction, Poincare plot as a point, ventricular arrhythmias (Lown > II. In multivariate analysis, the significant risk predictors were: Poincare plot as a point and mean RR interval lower than 800 ms. Conclusion Mean RR interval lower than 800 ms and nonlinear and space presentation of RR interval as a point Poincare plot were multivariate risk predictors.
Predicting vibration signals of automobile engine using chaos theory
Institute of Scientific and Technical Information of China (English)
LIU Chun; ZHANG Laibin; WANG Zhaohui
2004-01-01
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.
Predicting vibration signals of automobile engine using chaos theory
Liu, Chun; Zhang, Laibin; Wang, Zhaohui
2004-01-01
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition) denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method.
Energy enhancement and chaos control in microelectromechanical systems.
Park, Kwangho; Chen, Qingfei; Lai, Ying-Cheng
2008-02-01
For a resonator in an electrostatic microelectromechanical system (MEMS), nonlinear coupling between applied electrostatic force and the mechanical motion of the resonator can lead to chaotic oscillations. Better performance of the device can be achieved when the oscillations are periodic with large amplitude. We investigate the nonlinear dynamics of a system of deformable doubly clamped beam, which is the core in many MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced output energy. Our study suggests that chaos control can lead to energy enhancement and consequently high performance of MEM devices.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Dynamic Associations in Nonlinear Computing Arrays
Huberman, B. A.; Hogg, T.
1985-10-01
We experimentally show that nonlinear parallel arrays can be made to compute with attractors. This leads to fast adaptive behavior in which dynamical associations can be made between different inputs which initially produce sharply distinct outputs. We first define a set of simple local procedures which allow a general computing structure to change its state in time so as to produce classical Pavlovian conditioning. We then examine the dynamics of coalescence and dissociation of attractors with a number of quantitative experiments. We also show how such arrays exhibit generalization and differentiation of inputs in their behavior.
Nonlinear dynamic analysis of sandwich panels
Lush, A. M.
1984-01-01
Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.
Chaos Concepts, Control and Constructive Use
Bolotin, Yurii; Yanovsky, Vladimir
2009-01-01
The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...
Summer study program in geophysical fluid dynamics, Woods Hole Oceanographic Institution: Chaos
Veronis, G.; Hudon, L. M.
1985-11-01
The explosive growth of dynamical system theory stems in large part from the realization that it is applicable to many natural phenomena. Indeed, much of the theoretical development has been sparked by numerical and laboratory experiments which exhibit ordered sequences of behavior that call for a general framework of interpretation. Five lectures exposed us to elementaty examples of bifurcation and chaos, to symmetry breaking, normal forms and temporal and spatial disorder, as well as to pertinent fluid mechanical and astrophysical phenomena. In addition are the development with an elegant summary of different types of intermittency; Seminars on phase instability and turbulence as an extension of the lecture series; and the fascinating correspondence between the frequencies observed in one recent fluid mechanics experiment, and results from number theory relating the Fibonacci series to the golden mean.
Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise
Liu, Feng; Li, Yaguang
A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.
Decrease of cardiac chaos in congestive heart failure
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.
A passive dynamic walking robot that has a deterministic nonlinear gait.
Kurz, Max J; Judkins, Timothy N; Arellano, Chris; Scott-Pandorf, Melissa
2008-01-01
There is a growing body of evidence that the step-to-step variations present in human walking are related to the biomechanics of the locomotive system. However, we still have limited understanding of what biomechanical variables influence the observed nonlinear gait variations. It is necessary to develop reliable models that closely resemble the nonlinear gait dynamics in order to advance our knowledge in this scientific field. Previously, Goswami et al. [1998. A study of the passive gait of a compass-like biped robot: symmetry and chaos. International Journal of Robotic Research 17(12)] and Garcia et al. [1998. The simplest walking model: stability, complexity, and scaling. Journal of Biomechanical Engineering 120(2), 281-288] have demonstrated that passive dynamic walking computer models can exhibit a cascade of bifurcations in their gait pattern that lead to a deterministic nonlinear gait pattern. These computer models suggest that the intrinsic mechanical dynamics may be at least partially responsible for the deterministic nonlinear gait pattern; however, this has not been shown for a physical walking robot. Here we use the largest Laypunov exponent and a surrogation analysis method to confirm and extend Garcia et al.'s and Goswami et al.'s original results to a physical passive dynamic walking robot. Experimental outcomes from our walking robot further support the notion that the deterministic nonlinear step-to-step variations present in gait may be partly governed by the intrinsic mechanical dynamics of the locomotive system. Furthermore the nonlinear analysis techniques used in this investigation offer novel methods for quantifying the nature of the step-to-step variations found in human and robotic gait.
Institute of Scientific and Technical Information of China (English)
Wang Liqin; Cui Li; Zheng Dezhi; Gu Le
2008-01-01
A rotor system supported by roller bearings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar bility caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases.Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.
Predicting Storm Surges: Chaos, Computational Intelligence, Data Assimilation, Ensembles
Siek, M.B.L.A.
2011-01-01
Accurate predictions of storm surge are of importance in many coastal areas. This book focuses on data-driven modelling using methods of nonlinear dynamics and chaos theory for predicting storm surges. A number of new enhancements are presented: phase space dimensionality reduction, incomplete time
Chaos control and taming of turbulence in plasma devices
DEFF Research Database (Denmark)
Klinger, T.; Schröder, C.; Block, D.;
2001-01-01
Chaos and turbulence are often considered as troublesome features of plasma devices. In the general framework of nonlinear dynamical systems, a number of strategies have been developed to achieve active control over complex temporal or spatio-temporal behavior. Many of these techniques apply to p...
Organisational Leadership and Chaos Theory: Let's Be Careful
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…
Nonlinear and stochastic dynamics in the heart
Energy Technology Data Exchange (ETDEWEB)
Qu, Zhilin, E-mail: zqu@mednet.ucla.edu [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Hu, Gang [Department of Physics, Beijing Normal University, Beijing 100875 (China); Garfinkel, Alan [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Integrative Biology and Physiology, University of California, Los Angeles, CA 90095 (United States); Weiss, James N. [Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States); Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095 (United States)
2014-10-10
In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
Nonlinear dynamics analysis of a new autonomous chaotic system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nuchaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
Gradient-based optimization in nonlinear structural dynamics
DEFF Research Database (Denmark)
Dou, Suguang
The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider, fr...
Appropriate Algorithms for Nonlinear Time Series Analysis in Psychology
Scheier, Christian; Tschacher, Wolfgang
Chaos theory has a strong appeal for psychology because it allows for the investigation of the dynamics and nonlinearity of psychological systems. Consequently, chaos-theoretic concepts and methods have recently gained increasing attention among psychologists and positive claims for chaos have been published in nearly every field of psychology. Less attention, however, has been paid to the appropriateness of chaos-theoretic algorithms for psychological time series. An appropriate algorithm can deal with short, noisy data sets and yields `objective' results. In the present paper it is argued that most of the classical nonlinear techniques don't satisfy these constraints and thus are not appropriate for psychological data. A methodological approach is introduced that is based on nonlinear forecasting and the method of surrogate data. In artificial data sets and empirical time series we can show that this methodology reliably assesses nonlinearity and chaos in time series even if they are short and contaminated by noise.
Chaos control of parametric driven Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
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.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
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.
Nonlinear dynamics of neural delayed feedback
Energy Technology Data Exchange (ETDEWEB)
Longtin, A.
1990-01-01
Neural delayed feedback is a property shared by many circuits in the central and peripheral nervous systems. The evolution of the neural activity in these circuits depends on their present state as well as on their past states, due to finite propagation time of neural activity along the feedback loop. These systems are often seen to undergo a change from a quiescent state characterized by low level fluctuations to an oscillatory state. We discuss the problem of analyzing this transition using techniques from nonlinear dynamics and stochastic processes. Our main goal is to characterize the nonlinearities which enable autonomous oscillations to occur and to uncover the properties of the noise sources these circuits interact with. The concepts are illustrated on the human pupil light reflex (PLR) which has been studied both theoretically and experimentally using this approach. 5 refs., 3 figs.
Rossler Nonlinear Dynamical Machine for Cryptography Applications
Pandey, Sunil; Shrivastava, Dr S C
2009-01-01
In many of the cryptography applications like password or IP address encryption schemes, symmetric cryptography is useful. In these relatively simpler applications of cryptography, asymmetric cryptography is difficult to justify on account of the computational and implementation complexities associated with asymmetric cryptography. Symmetric schemes make use of a single shared key known only between the two communicating hosts. This shared key is used both for the encryption as well as the decryption of data. This key has to be small in size besides being a subset of a potentially large keyspace making it convenient for the communicating hosts while at the same time making cryptanalysis difficult for the potential attackers. In the present work, an abstract Rossler nonlinear dynamical machine has been described first. The Rossler system exhibits chaotic dynamics for certain values of system parameters and initial conditions. The chaotic dynamics of the Rossler system with its apparently erratic and irregular ...
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Nonlinear dynamical triggering of slow slip
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Knuth, Matthew W [WISCONSIN; Kaproth, Bryan M [PENN STATE; Carpenter, Brett [PENN STATE; Guyer, Robert A [Los Alamos National Laboratory; Le Bas, Pierre - Yves [Los Alamos National Laboratory; Daub, Eric G [Los Alamos National Laboratory; Marone, Chris [PENN STATE
2010-12-10
Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred
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.
Bifurcation of Periodic Orbits and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
Mei-xiang Cai; Jian-ping Yang
2006-01-01
Duffing equation with fifth nonlinear-restoring force, one external forcing and a phase shift is investigated. The conditions of existences for primary resonance, second-order, third-order subharmonics, morder subharmonics and chaos are given by using second-averaging method, Melnikov methods and bifurcation theory. Numerical simulations including bifurcation diagrams, bifurcation surfaces, phase portraits, not only show the consistence with the theoretical analysis, but also exhibit the new dynamical behaviors. We show the onset of chaos, chaos suddenly disappearing to period orbit, one-band and double-band chaos, period-doubling bifurcations from period 1, 2, and 3 orbits, period-windows (period-2, 3 and 5) in chaotic regions.
Nonlinear dynamics new directions theoretical aspects
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics · Features recent developments on...
Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
Pringle, Chris C T; Kerswell, Rich R
2011-01-01
We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth opt...
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Nonlinear dynamics from lasers to butterflies
Ball, R
2003-01-01
This book is an inspirational introduction to modern research directions and scholarship in nonlinear dynamics, and will also be a valuable reference for researchers in the field. With the scholarly level aimed at the beginning graduate student, the book will have broad appeal to those with an undergraduate background in mathematical or physical sciences.In addition to pedagogical and new material, each chapter reviews the current state of the area and discusses classic and open problems in engaging, surprisingly non-technical ways. The contributors are Brian Davies (bifurcations in maps), Nal
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Nonlinear Dynamic Analysis of MPEG-4 Video Traffic
Institute of Scientific and Technical Information of China (English)
GE Fei; CAO Yang; WANG Yuan-ni
2005-01-01
The main research motive is to analysis and to verify the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/fβ and periodic characteristics. The principal components analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts. So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear behavior and can be characterized by its power spectral density, principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.
The behaviour of PM10 and ozone in Malaysia through non-linear dynamical systems
Sapini, Muhamad Luqman; Rahim, Nurul Zahirah binti Abd; Noorani, Mohd Salmi Md.
2015-10-01
Prediction of ozone (O3) and PM10 is very important as both these air pollutants affect human health, human activities and more. Short-term forecasting of air quality is needed as preventive measures and effective action can be taken. Therefore, if it is detected that the ozone data is of a chaotic dynamical systems, a model using the nonlinear dynamic from chaos theory data can be made and thus forecasts for the short term would be more accurate. This study uses two methods, namely the 0-1 Test and Lyapunov Exponent. In addition, the effect of noise reduction on the analysis of time series data will be seen by using two smoothing methods: Rectangular methods and Triangle methods. At the end of the study, recommendations were made to get better results in the future.
The behaviour of PM10 and ozone in Malaysia through non-linear dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Sapini, Muhamad Luqman [Pusat Pengajian Matematik, Fakulti Sains Komputer & Matematik Universiti Teknologi MARA Kampus Seremban, 70300 Negeri Sembilan (Malaysia); Rahim, Nurul Zahirah binti Abd [Pengajian Matematik, Fakulti Sains Komputer & Matematik Universiti Teknologi MARA Kampus Jasin, 77000 Melaka (Malaysia); Noorani, Mohd Salmi Md. [Pusat Pengajian Sains Matematik, Fakulti Sains & Teknologi Universiti Kebangsaan Malaysia, 43650 Selangor (Malaysia)
2015-10-22
Prediction of ozone (O3) and PM10 is very important as both these air pollutants affect human health, human activities and more. Short-term forecasting of air quality is needed as preventive measures and effective action can be taken. Therefore, if it is detected that the ozone data is of a chaotic dynamical systems, a model using the nonlinear dynamic from chaos theory data can be made and thus forecasts for the short term would be more accurate. This study uses two methods, namely the 0-1 Test and Lyapunov Exponent. In addition, the effect of noise reduction on the analysis of time series data will be seen by using two smoothing methods: Rectangular methods and Triangle methods. At the end of the study, recommendations were made to get better results in the future.
Nonlinear Dynamics of Electrostatically Actuated MEMS Arches
Al Hennawi, Qais M.
2015-05-01
In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using a multi- mode Galarkin Reduced Order Model (ROM). We investigate the static response of the arch experimentally where we show several jumps due to the snap-through instability. Experimentally, a case study of in-plane silicon micromachined arch is studied and its mechanical behavior is measured using optical techniques. We develop an algorithm to extract various parameters that are needed to model the arch, such as the induced axial force, the modulus of elasticity, and the initially induced initial rise. After that, we excite the arch by a DC electrostatic force superimposed to an AC harmonic load. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Then, we excite the arch by an electric load of two AC frequency components, where we report a combination resonance of the summed type. Agreement is reported among the theoretical and experimental work.
Nonlinear dynamical characteristics of bed load motion
Institute of Scientific and Technical Information of China (English)
BAI; Yuchuan; XU; Haijue; XU; Dong
2006-01-01
Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dynamics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear system of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D'Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper presents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.
Desai, A.; Witteveen, J.A.S.; Sarkar, S.
2013-01-01
The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, su
CHAOS-BASED ADVANCED ENCRYPTION STANDARD
Abdulwahed, Naif B.
2013-05-01
This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed
Spirals, chaos, and new mechanisms of wave propagation.
Chen, P S; Garfinkel, A; Weiss, J N; Karagueuzian, H S
1997-02-01
The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.
Institute of Scientific and Technical Information of China (English)
方锦清; 罗晓曙; 陈关荣; 翁甲强
2001-01-01
Beam halo-chaos is essentially a complex spatiotemporal chaotic motion in a periodic-focusing channel of a highpower linear proton accelerator. The controllability condition for beam halo-chaos is analysed qualitatively. A special nonlinear control method, i.e. the wavelet-based function feedback, is proposed for controlling beam halochaos. Particle-in-cell simulations are used to explore the nature of halo-chaos formation, which has shown that the beam hMo-chaos is suppressed effectively after using nonlinear control for the proton beam with an initial full Gaussian distribution. The halo intensity factor Hav is reduced from 14%o to zero, and the other statistical physical quantities of beam halo-chaos are more than doubly reduced. The potential applications of such nonlinear control in experiments are briefly pointed out.
Sparse Identification of Nonlinear Dynamics (SINDy)
Brunton, Steven; Proctor, Joshua; Kutz, Nathan
2016-11-01
This work develops a general new framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The so-called sparse identification of nonlinear dynamics (SINDy) method results in models that are parsimonious, balancing model complexity with descriptive ability while avoiding over fitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including the chaotic Lorenz system, to the canonical fluid vortex shedding behind an circular cylinder at Re=100. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in the characterization and control of fluid dynamics.
Nonlinear Dynamic Characteristics of the Railway Vehicle
Uyulan, Çağlar; Gokasan, Metin
2017-06-01
The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests
Başar, Erol; Güntekin, Bahar
2007-04-01
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Synchronization of Nonlinear Oscillators Over Networks with Dynamic Links
De Persis, Claudio
2015-01-01
In this paper we investigate the problem of synchronization of homogeneous nonlinear oscillators coupled by dynamic links. The output of the nonlinear oscillators is the input to the dynamic links, while the output of these dynamics links is the quantity available to the distributed controllers at t
Neuromechanical tuning of nonlinear postural control dynamics
Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.
2009-06-01
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.
Bubble and Drop Nonlinear Dynamics (BDND)
Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.
1998-01-01
Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.
Time Series Forecasting A Nonlinear Dynamics Approach
Sello, S
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...
Quasiperiodicity and suppression of multistability in nonlinear dynamical systems
Lai, Ying-Cheng; Grebogi, Celso
2017-06-01
It has been known that noise can suppress multistability by dynamically connecting coexisting attractors in the system which are otherwise in separate basins of attraction. The purpose of this mini-review is to argue that quasiperiodic driving can play a similar role in suppressing multistability. A concrete physical example is provided where quasiperiodic driving was demonstrated to eliminate multistability completely to generate robust chaos in a semiconductor superlattice system.
Nonlinear dynamics of the wake of an oscillating cylinder
Olinger, D. J.; Sreenivasan, K. R.
1988-02-01
The wake of an oscillating cylinder at low Reynolds numbers is a nonlinear system in which a limit cycle due to natural vortex shedding is modulated, generating in phase space a flow on a torus. It is experimentally shown that the system displays Arnol'd tongues for rational frequency ratios, and approximates the devil's staircase along the critical line. The 'singularity spectrum' as well as spectral peaks at various Fibonacci sequences accompanying quasi-periodic transition to chaos shows that the system belongs to the same universality class as the sine circle map.
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Directory of Open Access Journals (Sweden)
Shaohua Luo
2016-09-01
Full Text Available This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.
Luo, Shaohua; Hou, Zhiwei; Zhang, Tao
2016-09-01
This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the "explosion of complexity" of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.
Measurement induced chaos with entangled states
Kiss, T; Tóth, L D; Gábris, A; Jex, I; Alber, G
2011-01-01
Quantum control, in a broad sense, may include measurement of quantum systems and, as a feed back operation, selection from an ensemble conditioned on the measurements. The resulting dynamics can be nonlinear and, if applied iteratively, can lead to true chaos in a quantum system. We consider the dynamics of an ensemble of two qubit systems subjected to measurement and conditional selection. We prove that the iterative dynamics leads to true chaos in the entanglement of the qubits. A class of special initial states exhibits high sensitivity to the initial conditions. In the parameter space of the special initial states we identify two types of islands: one converging to a separable state, while the other being asymptotically completely entangled. The islands form a fractal like structure. Adding noise to the initial state introduces a further stable asymptotic cycle.
Directory of Open Access Journals (Sweden)
Yu. P. Machekhin
2015-01-01
Full Text Available The article considers the issue of measurement of dynamic variables of open nonlinear dynamical systems. Most of real physical and biological systems in the surrounding world are the nonlinear dynamic systems. The spatial, temporal and spatio-temporal structures are formed in such systems because of dissipation. The collective effects that associated with the processes of self-organization and evolution are possible there too. The objective of this research is a compilation of the Shannon entropy measurement equations for case of nonlinear dynamical systems. It’s proposed to use the interval mathematics methods for this. It is shown that the measurement and measurement results analysis for variables with complex dynamics, as a rule, cannot be described by classical metrological approaches, that metrological documents, for example GUM, contain. The reason of this situation is the mismatch between the classical mathematical and physical approaches on the one hand and processes that occur in real dynamic systems on the other hand. For measurement of nonlinear dynamical systems variables the special measurement model and measurement results analysis model are created. They are based on Open systems theory, Dynamical chaos theory and Information theory. It’s proposed to use the fractal, entropic and temporal scales as tools for evaluation of a systems state. As a result of research the Shannon entropy measurement equations, based on interval representations of measurement results. are created, like for an individual dynamic variable as for nonlinear dynamic system. It is shown that the measurement equations, based on interval mathematics methods, contains the exact solutions and allows take into account full uncertainty. The new results will complement the measurement model and the measurement results analysis model for case of nonlinear dynamic systems.
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-lie; ZHANG Guo-yin; YAO Ai-hong
2010-01-01
This paper presents an algorithm that combines the chaos optimization algorithm with the maximum entropy(COA-ME)by using entropy model based on chaos algorithm,in which the maximum entropy is used as the second method of searching the excellent solution.The search direction is improved by chaos optimization algorithm and realizes the selective acceptance of wrong solution.The experimental result shows that the presented algorithm can be used in the partitioning of hardware/software of reconfigurable system.It effectively reduces the local extremum problem,and search speed as well as performance of partitioning is improved.
Consensus tracking for multiagent systems with nonlinear dynamics.
Dong, Runsha
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
2012 Symposium on Chaos, Complexity and Leadership
Erçetin, Şefika
2014-01-01
These proceedings from the 2012 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.
Prediction based chaos control via a new neural network
Energy Technology Data Exchange (ETDEWEB)
Shen Liqun [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: liqunshen@gmail.com; Wang Mao [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China); Liu Wanyu [School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001 (China); Sun Guanghui [Space Control and Inertia Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China)
2008-11-17
In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network.
Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control
Energy Technology Data Exchange (ETDEWEB)
Behzad, Mehdi [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: m_behzad@sharif.edu; Salarieh, Hassan [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-06-15
This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of extended Kalman filter and the sliding mode control, a synchronizing control law is proposed. As a case study, the presented algorithm is applied to the Lur'e-Genesio chaotic systems as the drive-response dynamic systems. Simulation results show the good performance of the algorithm in synchronizing the chaotic systems in presence of noisy environment.
Harnessing quantum transport by transient chaos.
Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M
2013-03-01
Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
Kahraman, A.; Singh, R.
1991-02-01
Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.
Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach
Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep
2009-12-01
In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction σ of predators cooperates in prey's hunting, while the rest of the population 1-σ hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K ,C0) and (K ,σ) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity Kc decreases at increasing σ, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.
Nonlinear Dynamics and Optimization of Spur Gears
Pellicano, Francesco; Bonori, Giorgio; Faggioni, Marcello; Scagliarini, Giorgio
In the present study a single degree of freedom oscillator with clearance type non-linearity is considered. Such oscillator represents the simplest model able to analyze a single teeth gear pair, neglecting: bearings and shafts stiffness and multi mesh interactions. One of the test cases considered in the present work represents an actual gear pair that is part of a gear box of an agricultural vehicle; such gear pair gave rise to noise problems. The main gear pair characteristics (mesh stiffness and inertia) are evaluated after an accurate geometrical modelling. The meshing stiffness of the gear pair is piecewise linear and time varying (in particular periodic); it is evaluated numerically using nonlinear finite element analysis (with contact mechanics) for different positions along one mesh cycle, then it is expanded in Fourier series. A direct numerical integration approach and a smoothing technique have been considered to obtain the dynamic scenario. Bifurcation diagrams of Poincaré maps are plotted according to some sample case study from literature. Optimization procedures are proposed, in order to find optimal involute modifications that reduce gears vibration.
On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics
DEFF Research Database (Denmark)
True, Hans
1999-01-01
We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed....
Dynamics of the Drosophila circadian clock: theoretical anti-jitter network and controlled chaos.
Directory of Open Access Journals (Sweden)
Hassan M Fathallah-Shaykh
Full Text Available BACKGROUND: Electronic clocks exhibit undesirable jitter or time variations in periodic signals. The circadian clocks of humans, some animals, and plants consist of oscillating molecular networks with peak-to-peak time of approximately 24 hours. Clockwork orange (CWO is a transcriptional repressor of Drosophila direct target genes. METHODOLOGY/PRINCIPAL FINDINGS: Theory and data from a model of the Drosophila circadian clock support the idea that CWO controls anti-jitter negative circuits that stabilize peak-to-peak time in light-dark cycles (LD. The orbit is confined to chaotic attractors in both LD and dark cycles and is almost periodic in LD; furthermore, CWO diminishes the Euclidean dimension of the chaotic attractor in LD. Light resets the clock each day by restricting each molecular peak to the proximity of a prescribed time. CONCLUSIONS/SIGNIFICANCE: The theoretical results suggest that chaos plays a central role in the dynamics of the Drosophila circadian clock and that a single molecule, CWO, may sense jitter and repress it by its negative loops.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Nonlinear dynamics of electron-positron clusters
Manfredi, Giovanni; Haas, Fernando; 10.1088/1367-2630/14/7/075012
2012-01-01
Electron-positron clusters are studied using a quantum hydrodynamic model that includes Coulomb and exchange interactions. A variational Lagrangian method is used to determine their stationary and dynamical properties. The cluster static features are validated against existing Hartree-Fock calculations. In the linear response regime, we investigate both dipole and monopole (breathing) modes. The dipole mode is reminiscent of the surface plasmon mode usually observed in metal clusters. The nonlinear regime is explored by means of numerical simulations. We show that, by exciting the cluster with a chirped laser pulse with slowly varying frequency (autoresonance), it is possible to efficiently separate the electron and positron populations on a timescale of a few tens of femtoseconds.
Chua's Nonlinear Dynamics Perspective of Cellular Automata
Pazienza, Giovanni E.
2013-01-01
Chua's `Nonlinear Dynamics Perspective of Cellular Automata' represents a genuine breakthrough in this area and it has had a major impact on the recent scientific literature. His results have been accurately described in a series of fourteen papers appeared over the course of eight years but there is no compendious introduction to his work. Therefore, here for the first time, we present Chua's main ideas as well as a few unpublished results that have not been included in his previous papers. This overview illustrates the essence of Chua's work by using a clear terminology and a consistent notation, and it is aimed at those who want to approach this subject through a concise but thorough exposition.
Surfactant and nonlinear drop dynamics in microgravity
Jankovsky, Joseph Charles
2000-11-01
Large amplitude drop dynamics in microgravity were conducted during the second United States Microgravity Laboratory mission carried onboard the Space Shuttle Columbia (20 October-5 November 1995). Centimeter- sized drops were statically deformed by acoustic radiation pressure and released to oscillate freely about a spherical equilibrium. Initial aspect ratios of up to 2.0 were achieved. Experiments using pure water and varying aqueous concentrations of Triton-X 100 and bovine serum albumin (BSA) were performed. The axisymmetric drop shape oscillations were fit using the degenerate spherical shape modes. The frequency and decay values of the fundamental quadrupole and fourth order shape mode were analyzed. Several large amplitude nonlinear oscillation dynamics were observed. Shape entrainment of the higher modes by the fundamental quadrupole mode occurred. Amplitude- dependent effects were observed. The nonlinear frequency shift, where the oscillation frequency is found to decrease with larger amplitudes, was largely unaffected by the presence of surfactants. The percentage of time spent in the prolate shape over one oscillation cycle was found to increase with oscillation amplitude. This prolate shape bias was also unaffected by the addition of surfactants. These amplitude-dependent effects indicate that the nonlinearities are a function of the bulk properties and not the surface properties. BSA was found to greatly enhance the surface viscoelastic properties by increasing the total damping of the oscillation, while Triton had only a small influence on damping. The surface concentration of BSA was found to be diffusion-controlled over the time of the experiments, while the Triton diffusion rate was very rapid. Using the experimental frequency and decay values, the suface viscoelastic properties of surface dilatational viscosity ( ks ) and surface shear viscosity ( ms ) were found for varying surfactant concentrations using the transcendental equation of Lu
XXIII International Conference on Nonlinear Dynamics of Electronic Systems
Stoop, Ruedi; Stramaglia, Sebastiano
2017-01-01
This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Using Nonlinear Dynamics for Environmental Management of the Vadose Zone and Groundwater
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris
2003-03-27
The need to improve characterization and prediction methods for flow and transport in partially saturated and saturated heterogeneous soils and fractured rock has long been recognized. Such improvement would be specifically welcomed in the fields of environmental management, containment and remediation of contaminated sites. Until recently, flow and transport processes in heterogeneous soils and fractured rock (with oscillating irregularities) were assumed to be random and were analyzed using conventional stochastic and deterministic methods. In this presentation, I will present the results of laboratory and field investigations of flow and transport in unsaturated soils and fractured rock, applying the methods of nonlinear dynamics and deterministic chaos. I will discuss using these methods for the development of improved characterization and prediction methods as well as for the development of remediation technologies for contaminated soils and groundwater.
The control of high-dimensional chaos in time-delay systems to an arbitrary goal dynamics.
Bunner, M. J.
1999-03-01
We present the control of high-dimensional chaos, with possibly a large number of positive Lyapunov exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control force. In the case of an unknown system, a formula to compute a model-based control force is derived. We give an example by demonstrating the control of the Mackey-Glass system toward a fixed point and a Rossler dynamics. (c) 1999 American Institute of Physics.
Spatiotemporal Chaos in Distributed Systems: Theory and Practice
Pavlos, George P.; Iliopoulos, A. C.; Tsoutsouras, V. G.; Karakatsanis, L. P.; Pavlos, E. G.
This paper presents theoretical and experimental results concerning the hypothesis of spatiotemporal chaos in distributed physical systems far from equilibrium. Modern tools of nonlinear time series analysis, such as the correlation dimension and the maximum Lyapunov exponent, were applied to various time series, corresponding to different physical systems such as space plasmas (solar flares, magnetic-electric field components) lithosphere-faults system (earthquakes) brain and cardiac dynamics during or without epileptic episodes. Futhermore, the method of surrogate data was used for the exclusion of 'pseudo chaos' caused by the nonlinear distortion of a purely stochastic process. The results of the nonlinear analysis presented in this study constitute experimental evidence for significant phenomena indicated by the theory of nonequilibrium dynamics such as nonequilibrium phase transition, chaotic synchronization, chaotic intermittency, directed percolation, defect turbulence, spinodal nucleation and clustering.
Interactions between nonlinear spur gear dynamics and surface wear
Ding, Huali; Kahraman, Ahmet
2007-11-01
In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear.
NONLINEAR RESPONSES OF A FLUID-CONVEYING PIPE EMBEDDED IN NONLINEAR ELASTIC FOUNDATIONS
Institute of Scientific and Technical Information of China (English)
Qin Qian; Lin Wang; Qiao Ni
2008-01-01
The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method diseretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.
Nonlinear Dynamic Study on Geomagnetic Polarity Reversal and Cretaceous Normal Superchron
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is generally acknowledged that geomagnetic polarity has reversed many times in geological history and an abnormal geologic phenomenon is the Cretaceous normal superchron. However, the causes have been unknown up to now. The nonlinear theory has been applied to analyze the phenomenon in geomagnetic polarity reversal and the Cretaceous normal superchron. The Cretaceous normal superchron implies that interaction of the Earth's core-mantle and liquid movement in the outer core may be the lowest energy state and the system of Earth magnetic field maintains a sort of temporal or spatial order structure by exchanging substance and energy in the outside continuously.During 121-83 Ma, there was no impact of a celestial body that would result in a geomagnetic polarity reversal, which may be a cause for occurrence of the Cretaceous normal superchron. The randomness of geomagnetic polarity reversal has the self-reversion characteristic of chaos and the chaos theory gives a simple and clear explanation for the dynamic cause of the geomagnetic polarity reversal.
Chaos Control in Mechanical Systems
Directory of Open Access Journals (Sweden)
Marcelo A. Savi
2006-01-01
Full Text Available Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.
Pattern control and suppression of spatiotemporal chaos using geometrical resonance
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J.A. E-mail: jorge@pion.ivic.ve; Bellorin, A.; Reyes, L.I.; Vasquez, C.; Guerrero, L.E
2004-11-01
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schroedinger, phi (cursive,open) Greek{sup 4}, and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743].
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
Noise tolerant spatiotemporal chaos computing
Energy Technology Data Exchange (ETDEWEB)
Kia, Behnam; Kia, Sarvenaz; Ditto, William L. [Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822 (United States); Lindner, John F. [Physics Department, The College of Wooster, Wooster, Ohio 44691 (United States); Sinha, Sudeshna [Indian Institute of Science Education and Research (IISER), Mohali, Punjab 140306 (India)
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.
Exploiting chaos for applications
Energy Technology Data Exchange (ETDEWEB)
Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)
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.
Ventilatory chaos is impaired in carotid atherosclerosis.
Directory of Open Access Journals (Sweden)
Laurence Mangin
Full Text Available Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%, 23 with moderate stenosis (<70%, and 25 controls. Chaos was characterized by the noise titration method, the correlation dimension and the largest Lyapunov exponent. Baroreflex sensitivity was estimated in the frequency domain. In the control group, 92% of the time series exhibit nonlinear deterministic chaos with positive noise limit, whereas only 68% had a positive noise limit value in the stenoses groups. Ventilatory chaos was impaired in the groups with carotid stenoses, with significant parallel decrease in the noise limit value, correlation dimension and largest Lyapunov exponent, as compared to controls. In multiple regression models, the percentage of carotid stenosis was the best in predicting the correlation dimension (p<0.001, adjusted R(2: 0.35 and largest Lyapunov exponent (p<0.001, adjusted R(2: 0.6. Baroreflex sensitivity also predicted the correlation dimension values (p = 0.05, and the LLE (p = 0.08. Plaque removal after carotid surgery reversed the loss of ventilatory complexity. To conclude, ventilatory chaos is impaired in carotid atherosclerosis. These findings depend on the severity of the stenosis, its localization, plaque surface and morphology features, and is independently associated with baroreflex sensitivity reduction. These findings should help to understand the determinants of ventilatory complexity and breathing control in pathological conditions.
Light dynamics in nonlinear trimers ans twisted multicore fibers
Castro-Castro, Claudia; Srinivasan, Gowri; Aceves, Alejandro B; Kevrekidis, Panayotis G
2016-01-01
Novel photonic structures such as multi-core fibers and graphene based arrays present unique opportunities to manipulate and control the propagation of light. Here we discuss nonlinear dynamics for structures with a few (2 to 6) elements for which linear and nonlinear properties can be tuned. Specifically we show how nonlinearity, coupling, and parity-time PT symmetric gain/loss relate to existence, stability and in general, dynamical properties of nonlinear optical modes. The main emphasis of our presentation will be on systems with few degrees of freedom, most notably couplers, trimers and generalizations thereof to systems with 6 nodes.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Bifurcations and Chaos in Duffing Equation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The Duffing equation with even-odd asymmetrical nonlinear-restoring force and one external forcing is investigated. The conditions of existence of primary resonance, second-order, third-order subharmonics, m-order subharmonics and chaos are given by using the second-averaging method, the Melnikov method and bifurcation theory. Numerical simulations including bifurcation diagram, bifurcation surfaces and phase portraits show the consistence with the theoretical analysis. The numerical results also exhibit new dynamical behaviors including onset of chaos, chaos suddenly disappearing to periodic orbit, cascades of inverse period-doubling bifurcations, period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, symmetry-breaking of periodic orbits, interleaving occurrence of chaotic behaviors and period-one orbit, a great abundance of periodic windows in transient chaotic regions with interior crises and boundary crisis and varied chaotic attractors. Our results show that many dynamical behaviors are strictly departure from the behaviors of the Duffing equation with odd-nonlinear restoring force.
Deterministic polarization chaos from a laser diode
Virte, Martin; Thienpont, Hugo; Sciamanna, Marc
2014-01-01
Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.
Bifurcation and chaos in the simple passive dynamic walking model with upper body.
Li, Qingdu; Guo, Jianli; Yang, Xiao-Song
2014-09-01
We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.
Bifurcation and chaos in the simple passive dynamic walking model with upper body
Energy Technology Data Exchange (ETDEWEB)
Li, Qingdu; Guo, Jianli [Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2014-09-01
We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.
A Study of Nonlinear Dynamics in Equity Market Index: Evidence from Turkey
Directory of Open Access Journals (Sweden)
Riza Emekter
2016-01-01
Full Text Available The dynamics of Istanbul Stock Exchange (ISE 100 index is explored in this study for the past 25 years. The main motivation of this paper is to find out the source and nature of any dependence in the ISE index. There is dependence in the log returns of the ISE. This dependence is not a linear dependence since no ARIMA models remove the dependence. Moreover, the dependence cannot be explained by nonlinear autoregressive process (GARCH and important relevant macroeconomics variables. The persistence in the return dependence is not short term (3-months or less in nature. Nonlinearity in the ISE index is caused by non-Gaussian innovations and it is not likely to be caused by chaos. Duration dependence test suggests that there is no evidence of a rational bubble in the log returns. There is some evidence of a structural break in the Turkish equity market around May 2000. However, the results do not change significantly when the same analyses are applied on the pre-and post- May 2000 periods. These results suggest that ISE 100 index is relatively efficient. Although there is dependence, the predictable component of the index is nonlinear, non-chaotic, and bubble-free. The predictable component is uncorrelated with any macro factors and cannot be explained by conditional autoregressive variance.
Chaos control using sliding-mode theory
Energy Technology Data Exchange (ETDEWEB)
Nazzal, Jamal M. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)]. E-mail: jnazzal@ammanu.edu.jo; Natsheh, Ammar N. [Faculty of Engineering, Al-Ahliyya Amman University, Post Code 19328 Amman (Jordan)
2007-07-15
Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller.
Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.
Gritli, Hassène; Khraief, Nahla; Belghith, Safya
2012-11-01
This paper presents a study of the passive dynamic walking of a compass-gait biped robot as it goes down an inclined plane. This biped robot is a two-degrees-of-freedom mechanical system modeled by an impulsive hybrid nonlinear dynamics with unilateral constraints. It is well-known to possess periodic as well as chaotic gaits and to possess only one stable gait for a given set of parameters. The main contribution of this paper is the finding of a window in the parameters space of the compass-gait model where there is multistability. Using constraints of a grazing bifurcation on the basis of a shooting method and the Davidchack-Lai scheme, we show that, depending on initial conditions, new passive walking patterns can be observed besides those already known. Through bifurcation diagrams and Floquet multipliers, we show that a pair of stable and unstable period-three gait patterns is generated through a cyclic-fold bifurcation. We show also that the stable period-three orbit generates a route to chaos.
Chaos theory applied to the caloric response of the vestibular system.
Aasen, T
1993-12-01
Developments in the field of nonlinear dynamics has given us a new conceptual framework for understanding the mechanisms involved in the regulation of complex nonlinear systems. This concept, called "chaos" or "deterministic chaos," has been applied to EKG, EEG, and other physiological signals, but not yet to the ENG signal. The underlying geometrical structure in chaotic dynamics is fractal (noninteger dimension), and calculating the fractal dimension of the electronystagmographic recording from caloric testing gave a dimension ranging from 3.3 to 7.7. This result demonstrates that the multidimensional vestibular system, with its numerous neurological pathways, can somehow reduce the degrees of freedom and give rise to an irregular dynamic low-dimensional behavior, which is associated with deterministic chaos.
Srivastava, Nilabh; Haque, Imtiaz
2009-03-01
Over the past two decades, extensive research has been conducted on developing vehicle transmissions that meet the goals of reduced exhaust emissions and increased vehicle efficiency. A continuously variable transmission is an emerging automotive transmission technology that offers a continuum of gear ratios between desired limits. A chain CVT is a friction-limited drive whose dynamic performance and torque capacity rely significantly on the friction characteristic of the contact patch between the chain and the pulley. Although a CVT helps to maximize the vehicle fuel economy, its complete potential has not been accomplished in a mass-production vehicle. The present research focuses on developing models to analyze friction-induced nonlinear dynamics of a chain CVT drive and identify possible mechanisms that cause degradation of the overall dynamic performance by inducing chaos and self-sustained vibrations in the system. Two different mathematical models of friction, which characterize different operating or loading conditions, are embedded into a detailed planar multibody model of chain CVT in order to capture the various friction-induced effects in the system. Tools such as stick-slip oscillator dynamics, Lyapunov exponents, phase-space reconstruction, and recurrence plotting are incorporated to characterize the nonlinear dynamics of such a friction-limited system. The mathematical models, the computational scheme, and the results corresponding to different loading scenarios are discussed. The results discuss the influence of friction characteristics on the nonlinear dynamics and torque transmitting capacity of a chain CVT drive.
Nonlinear dynamical model of an automotive dual mass flywheel
Directory of Open Access Journals (Sweden)
Lei Chen
2015-06-01
Full Text Available The hysteresis, stick–slip, and rotational speed-dependent characteristics in a basic dual mass flywheel are obtained from a static and a dynamic experiments. Based on the experimental results, a nonlinear model of the transferred torque in this dual mass flywheel is developed, with the overlying form of nonlinear elastic torque and frictional torque. The nonlinearities of stiffness are investigated, deriving a nonlinear model to describe the rotational speed-dependent stiffness. In addition, Bouc–Wen model is used to model the hysteretic frictional torque. Thus, the nonlinear 2-degree-of-freedom system of this dual mass flywheel is set up. Then, the Levenberg–Marquardt method is adopted for the parameter estimation of the frictional torque. Finally, taking the nonlinear stiffness in this model into account, the parameters of Bouc–Wen model are estimated based on the dynamic test data.
Chaos in classical string dynamics in $\\hat{\\gamma}$ deformed $AdS_5 \\times T^{1,1}$
Panigrahi, Kamal L
2016-01-01
We consider a circular string in $\\hat{\\gamma}$ deformed $AdS_5 \\times T^{1,1}$ which is localized in the center of $AdS_5$ and winds around the two circles of deformed $T^{1,1}$. We observe chaos in the phase space of the circular string implying non-integrability of string dynamics. The chaotic behaviour in phase space is controlled by energy as well as the deforming parameter $\\hat{\\gamma}$. We further show that the point like object exhibits non-chaotic behaviour. Finally we calculate the Lyapunov exponent for both extended and point like object in support of our first result.
Chaos Synchronization Using Adaptive Dynamic Neural Network Controller with Variable Learning Rates
Directory of Open Access Journals (Sweden)
Chih-Hong Kao
2011-01-01
Full Text Available This paper addresses the synchronization of chaotic gyros with unknown parameters and external disturbance via an adaptive dynamic neural network control (ADNNC system. The proposed ADNNC system is composed of a neural controller and a smooth compensator. The neural controller uses a dynamic RBF (DRBF network to online approximate an ideal controller. The DRBF network can create new hidden neurons online if the input data falls outside the hidden layer and prune the insignificant hidden neurons online if the hidden neuron is inappropriate. The smooth compensator is designed to compensate for the approximation error between the neural controller and the ideal controller. Moreover, the variable learning rates of the parameter adaptation laws are derived based on a discrete-type Lyapunov function to speed up the convergence rate of the tracking error. Finally, the simulation results which verified the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized using the proposed ADNNC scheme.
Transistor-based metamaterials with dynamically tunable nonlinear susceptibility
Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.
2016-08-01
We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
The numerical dynamic for highly nonlinear partial differential equations
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
Nonlinear switching dynamics in a photonic-crystal nanocavity
DEFF Research Database (Denmark)
Yu, Yi; Palushani, Evarist; Heuck, Mikkel;
2014-01-01
the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms......We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...
Kong, Xiangxi; Sun, Wei; Wang, Bo; Wen, Bangchun
2015-06-01
The dynamic behaviors and stability of the linear guide considering contact actions are studied by multi-term incremental harmonic balance method (IHBM). Based on fully considering the parameters of the linear guide, a static model is developed and the contact stiffness is calculated according to Hertz contact theory. A generalized time-varying and piecewise-nonlinear dynamic model of the linear guide is formulated to perform an accurate investigation on its dynamic behaviors and stability. The numerical simulation is used to confirm the feasibility of the approach. The effects of excitation force and mean load on the system are analyzed in low-order nonlinearity. Multi-term IHBM and numerical simulation are employed to the effect of high-order nonlinearity and show the transition to chaos. Additionally, the effects of preload, initial contact angle, the number and diameter of balls are discussed.
Nonlinear dynamics of zigzag molecular chains (in Russian)
DEFF Research Database (Denmark)
Savin, A. V.; Manevitsch, L. I.; Christiansen, Peter Leth;
1999-01-01
Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry-dependent...
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Transitions from phase-locked dynamics to chaos in a piecewise-linear map
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Mosekilde, Erik; De, S.
2008-01-01
place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic...
Structure of the channeling electrons wave functions under dynamical chaos conditions
Shul'ga, N F; Tarnovsky, A I; Isupov, A Yu
2015-01-01
The stationary wave functions of fast electrons axially channeling in the silicon crystal near [110] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.
Pettersson, Mass Per; Nordström, Jan
2015-01-01
This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dime...
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Maier, Rodrigo; Tonini, Eduardo Valentino
2015-01-01
We examine the dynamics of a Bianchi IX model on a 4-dim brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. Einstein's equations on the brane reduces to a 6-dim Hamiltonian dynamical system with additional terms that implement nonsingular bounces in the model. The phase space of the model has two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, and two asymptotic de Sitter critical points, one acting as an attractor to late-time dynamics. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders $R \\times S^3$, where $R$ is a saddle direction and $S^3$ is the center manifold of unstable periodic orbits (the nonlinear extension of the center-center sector). By a proper canonical transformation we separate the degrees of freedom of the dynamics into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom connected ...
Tuning quantum measurements to control chaos
Eastman, Jessica K.; Hope, Joseph J.; Carvalho, André R. R.
2017-01-01
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes. PMID:28317933
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
Quantum chaos in QCD and hadrons
Markum, H; Pullirsch, R; Sengl, B; Wagenbrunn, R F; Markum, Harald; Plessas, Willibald; Pullirsch, Rainer; Sengl, Bianka; Wagenbrunn, Robert F.
2005-01-01
This article is the written version of a talk delivered at the Workshop on Nonlinear Dynamics and Fundamental Interactions in Tashkent and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. In accordance to the title, the presentation is twofold and begins with research results on quantum chromodynamics and the quark-gluon plasma. We conclude with recent research work on the spectroscopy of baryons. Within the framework of a relativistic constituent quark model we investigate the excitation spectra of the nucleon and the delta with regard to a possible chaotic behavior for the cases when a hyperfine interaction of either Goldstone-boson-exchange or one-gluon-exchange type is added to the confinement interaction. Agreement with predictions from the experimental hadron spectrum is established.
Directory of Open Access Journals (Sweden)
Richard Ottermanns
Full Text Available In this study we present evidence that anthropogenic stressors can reduce the resilience of age-structured populations. Enhancement of disturbance in a model-based Daphnia population lead to a repression of chaotic population dynamics at the same time increasing the degree of synchrony between the population's age classes. Based on the theory of chaos-mediated survival an increased risk of extinction was revealed for this population exposed to high concentrations of a chemical stressor. The Lyapunov coefficient was supposed to be a useful indicator to detect disturbance thresholds leading to alterations in population dynamics. One possible explanation could be a discrete change in attractor orientation due to external disturbance. The statistical analysis of Lyapunov coefficient distribution is proposed as a methodology to test for significant non-linear effects of general disturbance on populations. Although many new questions arose, this study forms a theoretical basis for a dynamical definition of population recovery.
Siegel, H; Siegel, Helge; Belomestnyi, Dennis
2006-01-01
The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points representing the freeflow (non-congested) and the congested state regime. These traffic states have different statistical properties, with respect to waiting time distribution, velocity distribution and autocorrelation. Logdifferences of velocity records reveal non-normal, obviously leptocurtic distribution. Further, linear and nonlinear phase-plane based analysis methods yield no evidence for any determinism or deterministic chaos to be involved in traffic dynamics on shorter than diurnal time scales. Several Hurst-exponent estimators indicate long-range dependence for the free flow state. Finally, our results are not in accordance to the typical heuristic fingerprints of self-organized criticality. We suggest the more simplistic assumption of a non-critical phase transition between...
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS
Institute of Scientific and Technical Information of China (English)
朱位秋; 蔡国强
2002-01-01
This paper provides an overview of significant advances in nonlinearstochastic dynamics during the past two decades, including random response, stochas-tic stability, stochastic bifurcation, first passage problem and nonlinear stochasticcontrol. Topics for future research are also suggested.
Unified Nonlinear Flight Dynamics and Aeroelastic Simulator Tool Project
National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes a R&D effort to develop a Unified Nonlinear Flight Dynamics and Aeroelastic Simulator (UNFDAS) Tool that will combine...
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
Cartwright, J H E; Piro, O; Cartwright, Julyan H. E.; Gonzalez, Diego L.; Piro, Oreste
1999-01-01
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Global Optimal Trajectory in Chaos and NP-Hardness
Latorre, Vittorio; Gao, David Yang
This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Controlling the dynamical behavior of nonlinear fiber ring resonators with balanced loss and gain
Deka, Jyoti P; Sarma, Amarendra K
2015-01-01
We show the possibility of controlling the dynamical behavior of a single fiber ring (SFR) resonator system with the fiber being an amplified (gain) channel and the ring being attenuated (loss) nonlinear dielectric medium. The system considered here is a simple alteration in the basic building block of the parity time (PT) symmetric synthetic coupler structures reported in A. Regensburger et al., Nature 488, 167 (2012). We find that this result in a dynamically controllable algorithm for the chaotic dynamics inherent in the system. We have also shown the dependence of the period doubling point upon the input amplitude, emphasizing on the dynamical aspects of our system. Moreover, the fact that the resonator essentially plays the role of a damped harmonic oscillator has been elucidated with the non-zero intensity inside the resonator due to constant influx of input light. This study may be a step forward to further investigations in regard to the inter-connectivity between the PT symmetry and chaos along with ...
A NOVEL APPROACH TO GENERATE FRACTAL IMAGES USING CHAOS THEORY
Directory of Open Access Journals (Sweden)
K. Thamizhchelvy
2014-08-01
Full Text Available We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS technique. The chaos theory is an unpredictable behavior arises in the dynamical system. Chaos in turns explains the nonlinearity and randomness. Chaotic behavior depends upon the initial condition called as “seed” or “key”. Pseudo Random Number Generator (PRNG fixes the initial condition from the difference equations. The system uses the PRNG value and it generates the fractals, also it is hard to break. We apply the rules to generate the fractals. The different types of fractals are generated for the same data, because of the great sensitivity to the initial condition. It can be used as a digital signature in online applications such as e-Banking and online shopping.
When chaos meets hyperchaos: 4D Rössler model
Energy Technology Data Exchange (ETDEWEB)
Barrio, Roberto, E-mail: rbarrio@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Angeles Martínez, M., E-mail: gelimc@unizar.es [Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Serrano, Sergio, E-mail: sserrano@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Wilczak, Daniel, E-mail: wilczak@ii.uj.edu.pl [Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków (Poland)
2015-10-09
Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite “noisy”. We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques. - Highlights: • The coexistence of chaos and hyperchaos in the 4D Rössler system is proved via Computer-Assisted Proofs techniques. • A global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. • The long transient behaviors make difficult in numerical simulations to distinguish chaos from hyperchaos in some situations.