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Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations
Author: Jacob Palis Júnior
Publisher: Cambridge University Press
Published: 1995-01-05
Total Pages: 248
ISBN-13: 9780521475723
DOWNLOAD EBOOK →A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
Stability, Instability and Chaos
Author: Paul Glendinning
Publisher: Cambridge University Press
Published: 1994-11-25
Total Pages: 408
ISBN-13: 9780521425667
DOWNLOAD EBOOK →An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Global Bifurcations and Chaos
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
Published: 2013-11-27
Total Pages: 505
ISBN-13: 1461210429
DOWNLOAD EBOOK →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.
Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations
Homoclinic Bifurcations and Chaos in a Two-degree-of-freedom Magneto-mechanical Nonlinear System
Elements of Differentiable Dynamics and Bifurcation Theory
Author: David Ruelle
Publisher: Elsevier
Published: 2014-05-10
Total Pages: 196
ISBN-13: 1483272184
DOWNLOAD EBOOK →Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
Bifurcation and Chaos in Engineering
Author: Yushu Chen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 465
ISBN-13: 1447115759
DOWNLOAD EBOOK →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.
Chaos, Bifurcations and Fractals Around Us
Author: Wanda Szemplinska-Stupnicka
Publisher: World Scientific
Published: 2003-11-11
Total Pages: 116
ISBN-13: 981448363X
DOWNLOAD EBOOK →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
Robust Chaos and Its Applications
Author: Elhadj Zeraoulia
Publisher: World Scientific
Published: 2012
Total Pages: 473
ISBN-13: 9814374075
DOWNLOAD EBOOK →Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.
