Bifurcation And Chaos

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Bifurcation And Chaos In Nonsmooth Mechanical Systems

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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 2003

Bifurcation And Chaos In Nonsmooth Mechanical Systems written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.

This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Bifurcations And Chaos In Piecewise Smooth Dynamical Systems Applications To Power Converters Relay And Pulse Width Modulated Control Systems And Human Decision Making Behavior

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Author : Zhanybai T Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003-06-25

Bifurcations And Chaos In Piecewise Smooth Dynamical Systems Applications To Power Converters Relay And Pulse Width Modulated Control Systems And Human Decision Making Behavior written by Zhanybai T Zhusubaliyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-25 with Science categories.

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Bifurcation And Chaos In Complex Systems

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Author :
language : en
Publisher: Elsevier
Release Date : 2006-06-30

Bifurcation And Chaos In Complex Systems written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-30 with Science categories.

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.· New Views for Difficult Problems· Novel Ideas and Concepts · Hilbert's 16th Problem· Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems· Stochastic and Fuzzy Nonlinear Dynamical Systems· Fuzzy Bifurcation· Parametrical, Nonlinear Systems· Mode Interactions in nonlinear dynamical systems

Bifurcation And Chaos In Simple Dynamical Systems

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Author : Jan Awrejcewicz
language : en
Publisher: World Scientific
Release Date : 1989

Bifurcation And Chaos In Simple Dynamical Systems written by Jan Awrejcewicz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.

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.

Chaos Bifurcations And Fractals Around Us A Brief Introduction

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Author : Wanda Szemplinska-stupnicka
language : en
Publisher: World Scientific
Release Date : 2003-11-11

Chaos Bifurcations And Fractals Around Us A Brief Introduction written by Wanda Szemplinska-stupnicka and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-11 with Technology & Engineering categories.

During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.

The Lorenz Equations

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Author : Colin Sparrow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Lorenz Equations written by Colin Sparrow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.

Differential Equations Bifurcations And Chaos In Economics

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Author : Wei-bin Zhang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-07-18

Differential Equations Bifurcations And Chaos In Economics written by Wei-bin Zhang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Business & Economics categories.

Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.

Bifurcation And Chaos

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Author : Jan Awrejcewicz
language : en
Publisher: Springer
Release Date : 1995

Bifurcation And Chaos written by Jan Awrejcewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.

Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is self-contained and includes an elementary introduction, an exposition of the present state of the art, and details of recent theoretical, computational and experimental results. Included among the practical systems analysed are: hysteretic circuits, Josephson circuits, magnetic systems, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This book contains important information and ideas for all mathematicians, physicists and engineers whose work in R & D or academia involves the practical consequences of chaotic dynamics.

Bifurcation And Chaos In Engineering

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Author : Yushu Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Bifurcation And Chaos In Engineering written by Yushu Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.