Details

Subject(s)

• Differentiable dynamical systems [Browse]
• Bifurcation theory [Browse]

Related name

Di Bernardo, M. (Mario) [Browse]

Series

• Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 163. [More in this series]
• Applied mathematical sciences ; 163

Subseries of

Applied Mathematical Sciences

Summary note

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.

Notes

Description based upon print version of record.

Bibliographic references

Includes bibliographical references (p. [459]-473) and index.

Language note

English

Contents

• 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.

Show 5 more Contents items

ISBN

• 1-281-17910-8
• 9786611179106
• 1-84628-708-1

OCLC

605678314

Doi

10.1007/978-1-84628-708-4

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