Nonlinear Dynamics And Chaos

Advertisement



  nonlinear dynamics and chaos: Nonlinear Dynamics and Chaos Steven H. Strogatz, 2018-05-04 This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Chaos J. M. T. Thompson, H. B. Stewart, 2002-02-15 Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos. Expands on the bestselling, highly regarded first edition A new chapter which will cover the new research in the area since first edition Glossary of terms and a bibliography have been added All figures and illustrations will be 'modernised' Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics Highly illustrated Excellent introductory text, can be used for an advanced undergraduate/graduate course text
  nonlinear dynamics and chaos: Applications of Chaos and Nonlinear Dynamics in Engineering - Santo Banerjee, Mala Mitra, Lamberto Rondoni, 2011-09-10 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 ‘recipe book’ full of tried and tested, successful engineering applications
  nonlinear dynamics and chaos: Nonlinear Dynamics, Chaos, and Instability William A. Brock, David Arthur Hsieh, Blake Dean LeBaron, 1991 Brock, Hsieh, and LeBaron show how the principles of chaos theory can be applied to such areas of economics and finance as the changing structure of stock returns and nonlinearity in foreign exchange.
  nonlinear dynamics and chaos: Chaos and Integrability in Nonlinear Dynamics Michael Tabor, 1989-01-18 Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations, and soliton dynamics.
  nonlinear dynamics and chaos: Nonlinear Dynamics Muthusamy Lakshmanan, Shanmuganathan Rajaseekar, 2012-12-06 Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.
  nonlinear dynamics and chaos: Introduction to Applied Nonlinear Dynamical Systems and Chaos Stephen Wiggins, 2003-10-01 This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: Will serve as one of the most eminent introductions to the geometric theory of dynamical systems. --Monatshefte für Mathematik
  nonlinear dynamics and chaos: Nonlinear Dynamics And Chaos Nicholas B. Tufillaro, Tyler Abbott, Jeremiah Reilly, 1992-05-20 This essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Chaos Steven H. Strogatz, 2007
  nonlinear dynamics and chaos: Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities Marian Wiercigroch, Bram de Kraker, 2000 Annotation Consisting primarily of contributions written by engineers from Europe, Asia, and the US, this volume provides a general methodology for describing, solving, and analyzing discontinuous systems. The focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction, or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials, and dynamics of metal cutting. Of likely interest to new and experienced researchers working in the field of applied mathematics and physics, mechanical and civil engineering, and manufacturing. Lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR.
  nonlinear dynamics and chaos: The Illustrated Dictionary of Nonlinear Dynamics and Chaos Tomasz Kapitaniak, Steven R. Bishop, 1999-03-03 The study of nonlinear dynamics is one of the most active fields in modern science. It reaches across the whole range of scientific study, and is applied in fields as diverse as physics, engineering, biology, economics and medicine. However, the mathematical language used to describe nonlinear dynamics, and the proliferation of new terminology, can make the use of nonlinear dynamics a daunting task to the non-specialist. In addition,the simultaneous growth in the use of nonlinear dynamics across different fields, and the cross-fertilization of ideas from different disciplines, mean that names and methods used and developed in one field may be altered when 're-discovered' in a different context, making understanding the literature a difficult and time-consuming task. The Illustrated Dictionary of Nonlinear Dynamics and Chaos addresses these problems. It presents, in an alphabetical format, the key terms, theorems and equations which arise in the study of nonlinear dynamics. New mathematical ideas are described and explained with examples and, where appropriate, illustrations are included to aid clarification and understanding. For some entries, the descriptions are self-contained, but should more detail be required, references are included for further reading. Where alternative terms are used for a single concept, an entry is placed under the name in most common usage, with cross-references given under other names. The Illustrated Dictionary of Nonlinear Dynamics and Chaos is an invaluable reference source for all those who use nonlinear dynamics in their research, whether they are newcomers to the field who need help to understand the literature, or more experienced researchers who need a concise and handy reference.
  nonlinear dynamics and chaos: Chaos and Complexity Theory for Management: Nonlinear Dynamics Banerjee, Santo, 2012-11-30 Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.
  nonlinear dynamics and chaos: Chaos and Nonlinear Dynamics Robert C. Hilborn, 1994 Mathematics of Computing -- Miscellaneous.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Quantum Chaos Sandro Wimberger, 2016-09-03 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.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Chaos in Semiconductors K Aoki, 2000-12-07 The field of nonlinear dynamics and low-dimensional chaos has developed rapidly over the past twenty years. The principal advances have been in theoretical aspects but more recent applications in a wide variety of the sciences have been made. Nonlinear Dynamics and Chaos in Semiconductors is the first book to concentrate on specific physical and experimental situations in semiconductors as well as examine how to use chaos theory to explain semiconductor phenomena. Written by a well-respected researcher of chaos in semiconductors, Nonlinear Dynamics and Chaos in Semiconductors provides a rich and detailed account of progress in research on nonlinear effects in semiconductor physics. Discussing both theory and experiment, the author shows how this powerful combination has lead to real progress with difficult nonlinear problems in this technologically important field. Nonlinear carrier dynamics, caused by low-temperature impact ionization avalanche of impurities in extrinsic semiconductors, and the emergence of intractable chaos are treated in detail. The book explores impact ionization models, linear stability analysis, bifurcation theory, fractal dimensions, and various analytical methods in chaos theory. It also describes spatial and spatiotemporal evolution of the current density filament formed by the impact ionization avalanche.
  nonlinear dynamics and chaos: Chaos, Catastrophe, and Human Affairs Stephen J. Guastello, 2013-05-13 Whether talking about steering a wheelbarrow over rugged terrain or plotting the course of international relations, human performance systems involve change. Sometimes changes are subtle or evolutionary, sometimes they are catastrophic or revolutionary, and sometimes the changes are from periods of relative calm to periods of vibrant oscillations to periods of chaos. As a general rule, more complex systems are likely to produce more complex forms of change. Although social scientists have long acknowledged that change occurs and have considered ways to effect desirable change, the dynamical processes of change have been poorly understood in the past. This volume combines recent advances in mathematics and experimental design with the best available social science theories to produce a new, integrated, and compact theory of work, organizations, and social evolution. The domains of application extend from human decision-making processes to personnel selection and work motivation, work performance under conditions of stress, accident and health risk analysis, the development of social institutions and economic systems, creativity and innovation, organizational development and group dynamics, and political revolutions and war. Relative to other literature on nonlinear dynamical systems theory (NDS), this book is unique in that it integrates new developments in NDS with substantive psychological theory. It builds on many recent developments in organizational theory to show that nonlinear dynamics were often implicit in those works all along. The result is an entirely new way of viewing social events, understanding change processes, and asking questions about social systems. This book also contains much new empirical work and explains the newly developed methods for testing these new hypotheses.
  nonlinear dynamics and chaos: Methods of Qualitative Theory in Nonlinear Dynamics Leonid P. Shilnikov, 1998 Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
  nonlinear dynamics and chaos: Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors Eckehard Schöll, 2001-02-22 This book brings together concepts from semiconductor physics, nonlinear-dynamics and chaos to examine semiconductor transport phenomena.
  nonlinear dynamics and chaos: Dynamics with Chaos and Fractals Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily, 2020-01-01 The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.
  nonlinear dynamics and chaos: Nonlinear Wave Dynamics J. Engelbrecht, 2013-04-17 At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Chaos Steven H. Strogatz, 2014-07-29 This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.
  nonlinear dynamics and chaos: Differential Equations, Dynamical Systems, and an Introduction to Chaos Morris W. Hirsch, Stephen Smale, Robert L. Devaney, 2003-12-06 Differential Equations, Dynamical Systems, and an Introduction to Chaos, Second Edition, provides a rigorous yet accessible introduction to differential equations and dynamical systems. The original text by three of the world's leading mathematicians has become the standard textbook for graduate courses in this area. Thirty years in the making, this Second Edition brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The book explores the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It presents the simplification of many theorem hypotheses and includes bifurcation theory throughout. It contains many new figures and illustrations; a simplified treatment of linear algebra; detailed discussions of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor; and increased coverage of discrete dynamical systems. This book will be particularly useful to advanced students and practitioners in higher mathematics. - 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 upon NEW IN THIS EDITION - New contemporary material and updated applications - Revisions throughout the text, including simplification of many theorem hypotheses - Many new figures and illustrations - Simplified treatment of linear algebra - Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor - Increased coverage of discrete dynamical systems
  nonlinear dynamics and chaos: Understanding Nonlinear Dynamics Daniel Kaplan, Leon Glass, 2012-12-06 Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.
  nonlinear dynamics and chaos: Nonlinear Dynamics and Statistics Alistair I. Mees, 2012-12-06 All models are lies. The Earth orbits the sun in an ellipse with the sun at one focus is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to understand (that is, tell useful lies about) dynamical systems directly from observa tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description.
  nonlinear dynamics and chaos: Applications of Nonlinear Dynamics Visarath In, Patrick Longhini, Antonio Palacios, 2009-02-11 The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.
  nonlinear dynamics and chaos: Complex Nonlinearity Vladimir G. Ivancevic, Tijana T. Ivancevic, 2008-05-31 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 the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
  nonlinear dynamics and chaos: Introduction to Experimental Nonlinear Dynamics Lawrence N. Virgin, 2000-03-28 Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. Largely because of this extensive reach, nonlinear dynamics and chaos have become very active fields of study and research. This book uses an extended case study - an experiment in mechanical vibration - to introduce and explore the subject of nonlinear behavior and chaos. Beginning with a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Experimental mechanical vibration is the unifying theme as the narrative evolves from a local, linear, largely analytical foundation toward the rich and often unpredictable world of nonlinearity. Advanced undergraduate and graduate students, as well as practising engineers, will find this book a lively, accessible introduction to the complex world of nonlinear dynamics.
  nonlinear dynamics and chaos: Nonlinear Waves, Solitons and Chaos Eryk Infeld, George Rowlands, 2000-07-13 This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.
  nonlinear dynamics and chaos: Nonlinear Dynamics in Equilibrium Models John Stachurski, Alain Venditti, Makoto Yano, 2012-01-25 Optimal growth theory studies the problem of efficient resource allocation over time, a fundamental concern of economic research. Since the 1970s, the techniques of nonlinear dynamical systems have become a vital tool in optimal growth theory, illuminating dynamics and demonstrating the possibility of endogenous economic fluctuations. Kazuo Nishimura's seminal contributions on business cycles, chaotic equilibria and indeterminacy have been central to this development, transforming our understanding of economic growth, cycles, and the relationship between them. The subjects of Kazuo's analysis remain of fundamental importance to modern economic theory. This book collects his major contributions in a single volume. Kazuo Nishimura has been recognized for his contributions to economic theory on many occasions, being elected fellow of the Econometric Society and serving as an editor of several major journals. Chapter “Introduction” is available open access under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License via link.springer.com.
  nonlinear dynamics and chaos: Chaos Kathleen T. Alligood, Tim D. Sauer, James A. Yorke, 2006-04-06 Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.
  nonlinear dynamics and chaos: A Survey of Nonlinear Dynamics Richard Lee Ingraham, 1992 This book is intended to give a survey of the whole field of nonlinear dynamics (or ?chaos theory?) in compressed form. It covers quite a range of topics besides the standard ones, for example, pde dynamics and Galerkin approximations, critical phenomena and renormalization group approach to critical exponents. The many meanings or measures of ?chaos? in the literature are summarized. A precise definition of chaos based on a carefully limited sensitive dependence is offered. An application to quantum chaos is made. The treatment does not emphasize mathematical rigor but insists that the crucial concepts and theorems be mathematically well-defined. Thus topology plays a basic role. This alone makes this book unique among short surveys, where the inquisitive reader must usually be satisfied with colorful similes, analogies, and hand-waving arguments.Richard Ingraham graduated with B.S. summa cum laude in mathematics from Harvard college and with M.A. and Ph.D in Physics from Harvard Graduate School. He was granted the Sheldon Prize Traveling Fellowship by Harvard College and was a member of the Institute for Advanced Study at Princeton for two years.
  nonlinear dynamics and chaos: Dynamics and Chaos in Manufacturing Processes Francis C. Moon, 1997-11-19 This book examines the dynamics, chaos and complexity in manufacturing processes. Part I explores the direct application of nonlinear dynamics and chaos theory to machining, grinding, and rolling processes. Part II examines promising new concepts in nonlinear dynamics that may have direct uses in manufacturing processes which include: impact, friction, and fracture dynamics to control methods that harness the theory of chaotic dynamics.
  nonlinear dynamics and chaos: Nonlinear Dynamics In Circuits Louis M Pecora, T Carroll, 1995-11-16 This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.
  nonlinear dynamics and chaos: Nonlinear Dynamics in Physiology Mark Shelhamer, 2007 This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from physiologists to bioengineer.Initial chapters present background material on dynamic systems, statistics, and linear system analysis. Each computational technique is demonstrated with examples drawn from physiology, and several chapters present case studies from oculomotor control, neuroscience, cardiology, psychology, and epidemiology. Throughout the text, historical notes give a sense of the development of the field and provide a perspective on how the techniques were developed and where they might lead. The overall approach is based largely on the analysis of trajectories in the state space, with emphasis on time-delay reconstruction of state-space trajectories. The goal of the book is to enable readers to apply these methods to their own research.
  nonlinear dynamics and chaos: Chaos in Dynamical Systems Edward Ott, 2002-08-22 Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.
  nonlinear dynamics and chaos: Nonlinear Dynamics George Datseris, Ulrich Parlitz, 2022-03-14 This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.
  nonlinear dynamics and chaos: Recent Trends In Chaotic, Nonlinear And Complex Dynamics Jan Awrejcewicz, Rajasekar Shanmuganathan, Minvydas Ragulskis, 2021-07-26 In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.
  nonlinear dynamics and chaos: Chaos, Complexity and Leadership 2020 Şefika Şule Erçetin, Şuay Nilhan Açıkalın, Emir Vajzović, 2021-07-30 This book analyzes a range of new developments in various fields concerning the concepts of chaos and complexity theory. The proceedings of the 7th International Symposium on Chaos, Complexity and Leadership feature newly developed concepts involving various research methodologies for identifying chaos and complexity in different fields of the sciences and leadership. In addition, it explores chaotic and complex systems from all fields of knowledge in order to stake a claim of prevalence of compatibility between knowledge fields. Particular emphasis is placed on exploring non-linearity in order to open a discussion on new approaches to and perspectives on chaos, complexity and leadership. Readers will find coverage of important events that have recently taken place in our world, regardless of whether they were social, political, economic or scientific in nature. The book explores diverse aspects of and issues related to the effects of chaos and complexity in the world; discusses the application of nonlinear dynamics in order to arrive at transformational policies; and offers projections of tomorrow’s world using an interdisciplinary approach. Though primarily intended for readers with an interest in nonlinear science, thanks to its focus on the application of chaos and complexity to other disciplines, the book appeals to a broad readership.
  nonlinear dynamics and chaos: Digital Communications Using Chaos and Nonlinear Dynamics Lawrence E. Larson, Lev S. Tsimring, 2006-07-20 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 participated in US Army sponsored Multi-University Research Initiative on Digital Communication using Nonlinear Dynamics. It will be useful for active researchers and advanced graduate students interested in this exciting new field.
Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …

Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …

Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …

Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …

Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …

Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...

Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …

Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …

Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …

Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …

Home | Nonlinear Dynamics - Springer
Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The journal covers nonlinear dynamics …

Methods in Nonlinear Analysis - SpringerLink
Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials …

Nonlinear Acoustics - SpringerLink
Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous …

Home | Journal of Nonlinear Science - Springer
The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. It features papers …

Nonlinear Systems: Analysis, Stability, and Control | SpringerLink
Coupled with this set of analytic advances has been the vast increase in computational power available for both the simulation and visualization of nonlinear systems as well as for the …

Articles | Nonlinear Dynamics - Springer
4 days ago · Nonlinear Dynamics is a hybrid journal publishing original content at the forefront of nonlinear dynamic research across diverse systems and scales. The ...

Nonlinear Dynamics: A Concise Introduction Interlaced with Code ...
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at …

Data-driven nonlinear and stochastic dynamics with control
Dec 16, 2024 · The analysis is developed with reference to a nonlinear beam where the two boundary conditions have nonlinearities and masses, with the goal of identifying the uncertain …

Lectures on Nonlinear Dynamics - SpringerLink
This book presents a compilation of lectures delivered at the São Paulo School of Advanced Sciences on Nonlinear Dynamics, categorized into four groups: parametric resonance, …

Aims and scope | Nonlinear Dynamics - Springer
Nonlinear Dynamics provides a forum for the rapid publication of original research in the field of nonlinear dynamics. The scope of the journal encompasses all nonlinear dynamic phenomena …