Chaos In Nonlinear Oscillators

Author : Muthusamy Lakshmanan,K. Murali
Publisher : World Scientific
Page : 346 pages
File Size : 55,9 Mb
Release : 1996
Category : Science
ISBN : 9810221436

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Chaos in Nonlinear Oscillators by Muthusamy Lakshmanan,K. Murali Pdf

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.

Author : Tomasz Kapitaniak
Publisher : World Scientific
Page : 672 pages
File Size : 44,6 Mb
Release : 1992
Category : Science
ISBN : 9810206534

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Chaotic Oscillators by Tomasz Kapitaniak Pdf

This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 628 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642556883

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author : H. D. I. Abarbanel,M. I. Rabinovich,Mikhael M. Sushchik
Publisher : World Scientific Publishing Company Incorporated
Page : 158 pages
File Size : 48,5 Mb
Release : 1993
Category : Science
ISBN : 981021409X

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Introduction to Nonlinear Dynamics for Physicists by H. D. I. Abarbanel,M. I. Rabinovich,Mikhael 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.

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 45,6 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 : Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura
Publisher : Springer
Page : 300 pages
File Size : 50,5 Mb
Release : 2010-05-17
Category : Science
ISBN : 9783642046292

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Nonlinear Dynamics and Chaos: Advances and Perspectives by Marco Thiel,Jürgen Kurths,M. Carmen Romano,György Károlyi,Alessandro Moura Pdf

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

Author : Tomasz Kapitaniak
Publisher : Manchester University Press
Page : 240 pages
File Size : 47,9 Mb
Release : 1991
Category : Health & Fitness
ISBN : 0719033640

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Chaotic Oscillations in Mechanical Systems by Tomasz Kapitaniak Pdf

Author : Livija Cveticanin
Publisher : Springer
Page : 317 pages
File Size : 52,5 Mb
Release : 2017-05-29
Category : Technology & Engineering
ISBN : 9783319588261

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Strong Nonlinear Oscillators by Livija Cveticanin Pdf

This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Author : Jan Awrejcewicz
Publisher : World Scientific
Page : 266 pages
File Size : 43,5 Mb
Release : 1991
Category : Technology & Engineering
ISBN : 9810205791

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Bifurcation and Chaos in Coupled Oscillators by Jan Awrejcewicz Pdf

This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book. The nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Three different mechanical, and one biomechanical, examples are used to demonstrate a general systematical approach to the study of dissipative dynamical systems. Many original examples of special chaotic behavior are discussed and illustrated.

Author : Awrejcewicz Jan
Publisher : World Scientific
Page : 136 pages
File Size : 55,6 Mb
Release : 1989-10-01
Category : Science
ISBN : 9789814520058

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Bifurcation And Chaos In Simple Dynamical Systems by Awrejcewicz Jan Pdf

This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge.

Author : Luo Albert C J
Publisher : World Scientific
Page : 252 pages
File Size : 52,5 Mb
Release : 2017-12-15
Category : Science
ISBN : 9789813231696

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Resonance And Bifurcation To Chaos In Pendulum by Luo Albert C J Pdf

A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum. Contents: Resonance and Hamiltonian ChaosHamiltonian Chaos in PendulumParametric Chaos in PendulumNonlinear Discrete SystemsPeriodic Flows in Continuous SystemsPeriodic Motions to Chaos in Pendulum Readership: Researchers and academics in the field of mathematics. Keywords: Mathematics;Resonance: Bifurcation;Chaos in Pendulum;Nonlinear Science, Chaos & Dynamical SystemsReview:0

Author : Jes£s Manuel Gonz lez-Miranda
Publisher : World Scientific
Page : 225 pages
File Size : 55,5 Mb
Release : 2004
Category : Science
ISBN : 9781860944888

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Synchronization and Control of Chaos by Jes£s Manuel Gonz lez-Miranda Pdf

- A broad and systematic account of research on dynamics of coupled and driven chaotic oscillators

Author : Livija Cveticanin
Publisher : Springer
Page : 239 pages
File Size : 55,5 Mb
Release : 2014-05-22
Category : Science
ISBN : 9783319052724

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Strongly Nonlinear Oscillators by Livija Cveticanin Pdf

This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.

Author : John H. Lowenstein
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 53,7 Mb
Release : 2013-07-30
Category : Science
ISBN : 9783642281549

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Pseudochaotic Kicked Oscillators by John H. Lowenstein Pdf

"Pseudochaotic Kicked Oscillators: Renormalization, Symbolic Dynamics, and Transport" presents recent developments in pseudochaos, which is concerned with complex branching behaviors of dynamical systems at the interface between orderly and chaotic motion. Pseudochaos is characterized by the trapping of orbits in the vicinity of self-similar hierarchies of islands of stability, producing phase-space displacements which increase asymptotically as a power of time. This monograph is a thorough, self-contained investigation of a simple one-dimensional model (a kicked harmonic oscillator) which exhibits pseudochaos in its purest form. It is intended for graduate students and researchers in physics and applied mathematics, as well as specialists in nonlinear dynamics. Dr. John H. Lowenstein is a Professor Emeritus in the Department of Physics at New York University, USA.

Author : A. V. Gaponov-Grekhov,M. I. Rabinovich
Publisher : Unknown
Page : 216 pages
File Size : 55,8 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