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Author: Proctor, Sherrie L.,

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Bifurcations and chaos in piecewise-smooth dynamical systems /

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 va...

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Bibliographic Details
Main Authors: Zhusubaliyev, Zhanybai T
Corporate Authors: World Scientific Firm
Group Author: Mosekilde, Erik
Published: World Scientific Pub. Co.,
Publisher Address: Singapore ; River Edge, N.J. :
Publication Dates: 2003.
Literature type: eBook
Language: English
Series: World Scientific series on nonlinear science. Series A ; v. 44
Subjects:
Bifurcation theory
Chaotic behavior in systems
Differentiable dynamical systems
Electronic books
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/5313#t=toc
Summary: 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
Carrier Form: 1 online resource (xii,363pages) : illustrations.
Bibliography: Includes bibliographical references and index.
ISBN: 9789812564436 (electronic bk.)
CLC: O177.91
Contents: 1. On the dynamics of nonlinear systems. 1.1. Unpredictability and chaos. 1.2. Oscillations and chaos in engineering systems. 1.3. Simple one-dimensional maps. 1.4. Border-collision bifurcations. 1.5. The sewing approach -- 2. Basic concepts and methods. 2.1. Bifurcation analysis for the H non map. 2.2. Division of the parameter plane. 2.3. Further analysis of the H non map. 2.4. Piecewise-smooth two-dimensional maps. 2.5. Some remaining problems -- 3. Relay control systems. 3.1. Bifurcations and chaos in relay systems. 3.2. Modeling relay systems with hysteresis. 3.3. Algorithms for determi

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