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＜電子ブック＞
Piecewise-smooth Dynamical Systems : Theory and Applications / by Mario Bernardo, Chris Budd, Alan Richard Champneys, Piotr Kowalczyk
(Applied Mathematical Sciences. ISSN:2196968X ; 163)

版	1st ed. 2008.
出版者	(London : Springer London : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	XXII, 482 p : online resource
著者標目	*Bernardo, Mario author Budd, Chris author Champneys, Alan Richard author Kowalczyk, Piotr author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Dynamical systems LCSH:Control engineering LCSH:Robotics LCSH:Automation LCSH:Multibody systems LCSH:Vibration LCSH:Mechanics, Applied LCSH:Electrical engineering LCSH:Mathematics FREE:Analysis FREE:Dynamical Systems FREE:Control, Robotics, Automation FREE:Multibody Systems and Mechanical Vibrations FREE:Electrical and Electronic Engineering FREE:Applications of Mathematics
一般注記	Qualitative theory of non-smooth dynamical systems -- Border-collision in piecewise-linear continuous maps -- Bifurcations in general piecewise-smooth maps -- Boundary equilibrium bifurcations in flows -- Limit cycle bifurcations in impacting systems -- Limit cycle bifurcations in piecewise-smooth flows -- Sliding bifurcations in Filippov systems -- Further applications and extensions Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems. The primary purpose of this book is to present a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify complex behavior via bifurcation theory in a systematic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes diverse phenomena such as grazing, border-collision, sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoretical and experimental. Aimed at a wide audience of applied mathematicians, engineers and scientists at the early postgraduate level, the book assumes only the standard background of basic calculus and linear algebra for most of the presentation and will be an indispensable resource for students and researchers. The inclusion of a comprehensive bibliography and many open questions will also serve as a stimulus for future research HTTP:URL=https://doi.org/10.1007/978-1-84628-708-4

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