Nonlinear Oscillations And Waves In Dynamical Systems

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Nonlinear Oscillations and Waves in Dynamical Systems

Polina S. Landa
Nonlinear Oscillations and Waves in Dynamical Systems Book PDF

Author : Polina S. Landa
Publisher : Springer
Page : 544 pages
File Size : 54,9 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 9401587647

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Nonlinear Oscillations and Waves in Dynamical Systems by Polina S. Landa Pdf

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Nonlinear Oscillations and Waves in Dynamical Systems

P.S Landa
Nonlinear Oscillations and Waves in Dynamical Systems Book PDF

Author : P.S Landa
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 49,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401587631

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Nonlinear Oscillations and Waves in Dynamical Systems by P.S Landa Pdf

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Oscillations and Waves

M.I Rabinovich,D.I. Trubetskov
Oscillations and Waves Book PDF

Author : M.I Rabinovich,D.I. Trubetskov
Publisher : Springer Science & Business Media
Page : 586 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400910331

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Oscillations and Waves by M.I Rabinovich,D.I. Trubetskov Pdf

'Et mai - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Dynamical Systems and Nonlinear Waves in Plasmas

Santo Banerjee,Asit Saha
Dynamical Systems and Nonlinear Waves in Plasmas Book PDF

Author : Santo Banerjee,Asit Saha
Publisher : CRC Press
Page : 218 pages
File Size : 44,9 Mb
Release : 2021-09-10
Category : Science
ISBN : 9781000404753

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Dynamical Systems and Nonlinear Waves in Plasmas by Santo Banerjee,Asit Saha Pdf

Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Nonlinear Oscillations

Ali H. Nayfeh,Dean T. Mook
Nonlinear Oscillations Book PDF

Author : Ali H. Nayfeh,Dean T. Mook
Publisher : John Wiley & Sons
Page : 720 pages
File Size : 45,5 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783527617593

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Nonlinear Oscillations by Ali H. Nayfeh,Dean T. Mook Pdf

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.

Introduction to Nonlinear Oscillations

Vladimir I. Nekorkin
Introduction to Nonlinear Oscillations Book PDF

Author : Vladimir I. Nekorkin
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 40,6 Mb
Release : 2016-05-02
Category : Science
ISBN : 9783527685431

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Introduction to Nonlinear Oscillations by Vladimir I. Nekorkin Pdf

A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.

Nonlinearities in Action

A. V. Gaponov-Grekhov,M. I. Rabinovich
Nonlinearities in Action Book PDF

Author : A. V. Gaponov-Grekhov,M. I. Rabinovich
Publisher : Unknown
Page : 216 pages
File Size : 43,5 Mb
Release : 1992
Category : Chaotic behavior in systems
ISBN : UCSD:31822015233554

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Nonlinearities in Action by A. V. Gaponov-Grekhov,M. I. Rabinovich Pdf

Introduction to Nonlinear Dynamics for Physicists

H D I Abarbanel,M I Rabinovich,M M Sushchik
Introduction to Nonlinear Dynamics for Physicists Book PDF

Author : H D I Abarbanel,M I Rabinovich,M M Sushchik
Publisher : World Scientific
Page : 168 pages
File Size : 41,6 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

Nonlinear Oscillations of Hamiltonian PDEs

Massimiliano Berti
Nonlinear Oscillations of Hamiltonian PDEs Book PDF

Author : Massimiliano Berti
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 52,5 Mb
Release : 2007-10-01
Category : Mathematics
ISBN : 9780817646806

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Nonlinear Oscillations of Hamiltonian PDEs by Massimiliano Berti Pdf

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

Nonlinear Oscillations in Physical Systems

Chihiro Hayashi
Nonlinear Oscillations in Physical Systems Book PDF

Author : Chihiro Hayashi
Publisher : Princeton University Press
Page : 405 pages
File Size : 45,8 Mb
Release : 2014-07-14
Category : Science
ISBN : 9781400852871

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Nonlinear Oscillations in Physical Systems by Chihiro Hayashi Pdf

This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Oscillations in Planar Dynamic Systems

Ronald E Mickens
Oscillations in Planar Dynamic Systems Book PDF

Author : Ronald E Mickens
Publisher : World Scientific
Page : 340 pages
File Size : 53,8 Mb
Release : 1996-01-11
Category : Mathematics
ISBN : 9789814500333

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Oscillations in Planar Dynamic Systems by Ronald E Mickens Pdf

This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples. Contents:Oscillatory SystemsLindstedt-Poincaré Perturbation MethodMethod of Krylov–Bogoliubov–MitropolskyHarmonic BalanceMulti-Time ExpansionsGeneral Second-Order SystemsAppendices Readership: Applied mathematicians. keywords:Nonlinear Oscillations;Perturbation Methods;Multi-Time Expansions;Harmonic Balance;Stability;Qualitative Theory of Differential Equations;Periodic Functions;Lindstedt-Poincare Method;Averaging Method “This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems … a clear presentation of necessary background materials and by the working out of many examples.” Lavoisier-Technique et Documentation