Overview
- A comprehensive 'tool-kit' that provides a complete reference to bifurcation theory for piecewise-smooth dynamical systems
- The informal introduction serves as a primer for the non-specialist and introduces all the main ideas with real-world examples
- The inclusion of a comprehensive bibliography and many open questions will serve as a stimulus for future research
- Includes supplementary material: sn.pub/extras
Part of the book series: Applied Mathematical Sciences (AMS, volume 163)
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Table of contents (9 chapters)
Keywords
About this book
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.
Reviews
From the reviews:
"This book is undoubtedly a strong contribution to the field of bifurcation and chaos analysis and more generally to the field of nonsmooth dynamical systems analysis. The authors have made a remarkable effort in mixing intricate technical developments with numerous examples, numerical results, and experimental results."
IEEE Control Systems Magazine
"PSDS presents a valuable compendium of information about the bifurcations of different types of piecewise-smooth systems, but it stops short of completely specifying the mathematical context within which the bifurcation phenomena it discusses are generic. That leaves lots of interesting work to do in studying piecewise-smooth dynamical systems. PSDS is an excellent starting point where one can find extensive analysis of diverse examples."
SIAM Book Reviews
"This book treats dynamical systems that have a piecewise smooth right-hand-side. … Graphical sketches are abundant, supporting the presentation of the essential ideas behind arguments and techniques. Overall, the level of presentation makes the book useful as a source of theoretical background knowledge for researchers and postgraduate students in engineering and applied mathematics. It is also suitable as a reference for undergraduate projects or advanced undergraduate reading groups." (Jan Sieber, Zentralblatt MATH, Vol. 1146, 2008)
"The book … providing motivation by showing a variety of applications and new phenomena. … This book offers a very good survey of the rapidly developing area of the dynamics of non-smooth systems … . the authors succeed in building up a systematic framework which is based on relevant applications. … This is a book rich in content and an excellent introduction to this new area. The book is configured as a compiled introduction for graduate students and researchers interested in this area." (Tassilo Küpper, Mathematical Reviews, Issue 2009i)
Editors and Affiliations
Bibliographic Information
Book Title: Piecewise-smooth Dynamical Systems
Book Subtitle: Theory and Applications
Editors: Mario di Bernardo Laurea, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-1-84628-708-4
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2008
Hardcover ISBN: 978-1-84628-039-9Published: 15 January 2008
Softcover ISBN: 978-1-84996-548-4Published: 19 October 2010
eBook ISBN: 978-1-84628-708-4Published: 01 January 2008
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: XXII, 482
Topics: Analysis, Dynamical Systems and Ergodic Theory, Control, Robotics, Mechatronics, Vibration, Dynamical Systems, Control, Electrical Engineering, Applications of Mathematics