Bifurcation And Chaos In Engineering

Author : Yushu Chen,Andrew Y.T. Leung
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447115755

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Bifurcation and Chaos in Engineering by Yushu Chen,Andrew Y.T. Leung Pdf

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.

Author : Zhanybai T. Zhusubaliyev,Erik Mosekilde
Publisher : World Scientific
Page : 377 pages
File Size : 50,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812384201

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Bifurcations and Chaos in Piecewise-smooth Dynamical Systems by Zhanybai T. Zhusubaliyev,Erik Mosekilde Pdf

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.

Author : Wei-Bin Zhang
Publisher : Elsevier
Page : 459 pages
File Size : 53,9 Mb
Release : 2006-01-05
Category : Mathematics
ISBN : 9780080462462

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Discrete Dynamical Systems, Bifurcations and Chaos in Economics by Wei-Bin Zhang Pdf

This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics. A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics Mathematical definitions and theorems are introduced in a systematic and easily accessible way Examples are from almost all fields of economics; technically proceeding from basic to advanced topics Lively illustrations with numerous figures Numerous simulation to see paths of economic dynamics Comprehensive treatment of the subject with a comprehensive and easily accessible approach

Author : Jan Awrejcewicz
Publisher : Springer
Page : 296 pages
File Size : 46,6 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034417280

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Bifurcation and Chaos by Jan Awrejcewicz Pdf

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.

Author : Jan Awrejcewicz,Vadim Anatolevich Krys'ko
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 46,5 Mb
Release : 2009-11-11
Category : Technology & Engineering
ISBN : 9783540776765

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Chaos in Structural Mechanics by Jan Awrejcewicz,Vadim Anatolevich Krys'ko Pdf

This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.

Author : Anonim
Publisher : Elsevier
Page : 400 pages
File Size : 51,5 Mb
Release : 2006-06-30
Category : Science
ISBN : 0080462669

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Bifurcation and Chaos in Complex Systems by Anonim Pdf

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

Author : Jan Awrejcewicz
Publisher : Unknown
Page : 292 pages
File Size : 45,5 Mb
Release : 1994-12-14
Category : Electronic
ISBN : 3642793304

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Bifurcation and Chaos by Jan Awrejcewicz Pdf

Author : Saber N. Elaydi
Publisher : CRC Press
Page : 440 pages
File Size : 40,5 Mb
Release : 2007-11-09
Category : Mathematics
ISBN : 9781420011043

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Discrete Chaos by Saber N. Elaydi Pdf

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determi

Author : Jan Awrejcewicz,Claude-Henri Lamarque
Publisher : World Scientific
Page : 564 pages
File Size : 49,7 Mb
Release : 2003
Category : Science
ISBN : 9789812384591

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Bifurcation and Chaos in Nonsmooth Mechanical Systems by Jan Awrejcewicz,Claude-Henri Lamarque Pdf

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.

Author : Guanrong Chen
Publisher : CRC Press
Page : 670 pages
File Size : 53,9 Mb
Release : 1999-09-28
Category : Technology & Engineering
ISBN : 0849305799

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Controlling Chaos and Bifurcations in Engineering Systems by Guanrong Chen Pdf

Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.

Author : Tomasz Kapitaniak
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642571435

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Chaos for Engineers by Tomasz Kapitaniak Pdf

A desription of the new mathematical ideas in nonlinear dynamics in such a way that engineers can apply them to real physical systems.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 46,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461210429

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Global Bifurcations and Chaos by Stephen Wiggins Pdf

Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques whereby these mechanisms can be detected in specific systems. These techniques can be viewed as generalizations of Melnikov's method to multi-degree of freedom systems subject to slowly varying parameters and quasiperiodic excitations. A unique feature of the book is that each theorem is illustrated with drawings that enable the reader to build visual pictures of global dynamcis of the systems being described. This approach leads to an enhanced intuitive understanding of the theory.

Author : Jan Awrejcewicz,Peter Hagedorn
Publisher : BoD – Books on Demand
Page : 360 pages
File Size : 48,9 Mb
Release : 2012-10-24
Category : Mathematics
ISBN : 9789535108160

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Nonlinearity, Bifurcation and Chaos by Jan Awrejcewicz,Peter Hagedorn Pdf

Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.

Author : Wanda Szemplinska-Stupnicka
Publisher : World Scientific
Page : 116 pages
File Size : 47,7 Mb
Release : 2003-11-11
Category : Technology & Engineering
ISBN : 9789814483636

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Chaos, Bifurcations and Fractals Around Us by Wanda Szemplinska-Stupnicka Pdf

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. Contents:Ueda's “Strange Attractors”PendulumVibrating System with Two Minima of Potential Energy Readership: Undergraduates, graduate students, academics and researchers in engineering. Keywords:Nonlinear Dynamics;Chaotic Vibrations;Nonlinear Resonance;Local and Global Bifurcations;Fractal Basins of Attraction;Transient Chaos;Persistent Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 48,6 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.