Nonlinear Dynamics And Chaotic Phenomena An Introduction

Author : B.K Shivamoggi
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 51,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401724425

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Nonlinear Dynamics and Chaotic Phenomena by B.K Shivamoggi Pdf

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Author : Bhimsen K. Shivamoggi
Publisher : Springer
Page : 375 pages
File Size : 49,7 Mb
Release : 2014-05-14
Category : Technology & Engineering
ISBN : 9789400770942

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Nonlinear Dynamics and Chaotic Phenomena: An Introduction by Bhimsen K. Shivamoggi Pdf

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 emphasis on some aspects of fluid dynamics and plasma physics reflecting the author’s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on. This book has grown out of the author’s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum. This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering. This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises.

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 51,9 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

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.

Author : Gregory L. Baker,Jerry P. Gollub
Publisher : Cambridge University Press
Page : 282 pages
File Size : 48,9 Mb
Release : 1996
Category : Science
ISBN : 0521471060

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Chaotic Dynamics by Gregory L. Baker,Jerry P. Gollub Pdf

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.

Author : Joseph L. McCauley
Publisher : Unknown
Page : 72 pages
File Size : 42,8 Mb
Release : 1988
Category : Chaotic behavior in systems
ISBN : UVA:X001969445

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An Introduction to Nonlinear Dynamics and Chaos Theory by Joseph L. McCauley Pdf

Author : Robert C. Hilborn
Publisher : Unknown
Page : 676 pages
File Size : 44,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0198507232

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Chaos and Nonlinear Dynamics by Robert C. Hilborn Pdf

This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.

Author : Lui Lam
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 54,8 Mb
Release : 2003-11-14
Category : Science
ISBN : 038740614X

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Introduction to Nonlinear Physics by Lui Lam Pdf

This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.

Author : Kathleen T. Alligood,Tim D. Sauer,James A. Yorke
Publisher : Springer Science & Business Media
Page : 603 pages
File Size : 52,9 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387224923

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Chaos by Kathleen T. Alligood,Tim D. Sauer,James A. Yorke Pdf

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.

Author : George Datseris,Ulrich Parlitz
Publisher : Springer Nature
Page : 243 pages
File Size : 51,8 Mb
Release : 2022-03-13
Category : Science
ISBN : 9783030910327

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Nonlinear Dynamics by George Datseris,Ulrich Parlitz Pdf

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.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 860 pages
File Size : 50,8 Mb
Release : 2003-10-01
Category : Mathematics
ISBN : 9780387001777

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Introduction to Applied Nonlinear Dynamical Systems and Chaos by Stephen Wiggins Pdf

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

Author : Sandro Wimberger
Publisher : Springer Nature
Page : 270 pages
File Size : 50,8 Mb
Release : 2023-01-01
Category : Science
ISBN : 9783031012495

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

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. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : H D I Abarbanel,M I Rabinovich,M M Sushchik
Publisher : World Scientific
Page : 168 pages
File Size : 48,5 Mb
Release : 1993-06-23
Category : Science
ISBN : 9789814504126

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Introduction to Nonlinear Dynamics for Physicists by H D I Abarbanel,M I Rabinovich,M M Sushchik Pdf

This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon. Contents:IntroductionNonlinear Oscillator without DissipationEquilibrium States of a Nonlinear Oscillator with DissipationOscillations in Systems with Nonlinear Dissipation-GeneratorsThe Van der Pol GeneratorThe Poincaré MapSlow and Fast Motions in Systems with One Degree of FreedomForced Nonlinear Oscillators: Linear and Nonlinear ResonancesForced Generator: SynchronizationCompetition of ModesPoincaré Indices and Bifurcations of Equilibrium StatesResonance Interactions between OscillatorsSolitonsSteady Propagation of Shock WavesFormation of Shock WavesSolitons. Shock Waves. Wave Interaction. The Spectral ApproachWeak Turbulence. Random Phase ApproximationRegular Patterns in Dissipative MediaDeterministic Chaos. Qualitative DescriptionDescription of a Circuit with Chaos. Chaos in MapsBifurcations of Periodic Motions. Period DoublingControlled Nonlinear Oscillator. IntermittencyScenarios of the Onset of Chaos. Chaos through Quasi-PeriodicityCharacteristics of Chaos. Experimental Observation of ChaosMultidimensional Chaos. Discrete Ginzburg-Landau ModelProblems to Accompany the Lectures Readership: Physicists. keywords: “These lecture notes briefly introduce the reader to new ideas, so would be a useful addition to a library or a source of ideas for lectures or projects; a good student may also find this text useful as a quick introduction to many new ideas.” Contemporary Physics “Introduction to Nonlinear Dynamics for Physicists … is a compact and fairly terse high-level set of 24 lectures.” New Scientist

Author : Jan Awrejcewicz,Rajasekar Shanmuganathan,Minvydas Ragulskis
Publisher : World Scientific
Page : 561 pages
File Size : 52,8 Mb
Release : 2021-07-26
Category : Science
ISBN : 9789811221910

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Recent Trends In Chaotic, Nonlinear And Complex Dynamics by Jan Awrejcewicz,Rajasekar Shanmuganathan,Minvydas Ragulskis Pdf

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.

Author : Francis C. Moon
Publisher : John Wiley & Sons
Page : 528 pages
File Size : 41,5 Mb
Release : 2008-11-20
Category : Science
ISBN : 9783527617517

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Chaotic and Fractal Dynamics by Francis C. Moon Pdf

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Author : H Nagashima
Publisher : CRC Press
Page : 176 pages
File Size : 48,6 Mb
Release : 2019-06-06
Category : Mathematics
ISBN : 9780429525650

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Introduction to Chaos by H Nagashima Pdf

This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations. It is helpful for postgraduate students and researchers in mathematics, physics and other areas of science.