Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems 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 with Mathematics 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.
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems 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 with Computers categories.
Technical problems often lead to differential equations withpiecewise-smooth right-hand sides. Problems in mechanicalengineering, for instance, violate the requirements of smoothness ifthey involve collisions, finite clearances, or stickOCoslipphenomena."
Piecewise Smooth Dynamical Systems
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Author : Mario Bernardo
language : en
Publisher: Springer
Release Date : 2008-01-15
Piecewise Smooth Dynamical Systems written by Mario Bernardo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-15 with Mathematics categories.
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Piecewise Smooth Dynamical Systems
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Author : Mario Bernardo
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-01
Piecewise Smooth Dynamical Systems written by Mario Bernardo 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 2008-01-01 with Mathematics categories.
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures
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Author : Viktor Avrutin
language : en
Publisher: World Scientific
Release Date : 2019-05-28
Continuous And Discontinuous Piecewise Smooth One Dimensional Maps Invariant Sets And Bifurcation Structures written by Viktor Avrutin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-28 with Mathematics categories.
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
Bifurcations In Piecewise Smooth Continuous Systems
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Author : David John Warwick Simpson
language : en
Publisher: World Scientific
Release Date : 2010
Bifurcations In Piecewise Smooth Continuous Systems written by David John Warwick Simpson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Science categories.
Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. NeimarkSacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems Series A
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher:
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems Series A written by Zhanybai T. Zhusubaliyev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Bifurcation theory categories.
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.
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.
Elements Of Applied Bifurcation Theory
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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-29
Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov 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 2004-06-29 with Mathematics categories.
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.