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Applied Mathematical Sciences

Piecewise-smooth Dynamical Systems

Theory and Applications

Authors: Bernardo, M., Budd, C., Champneys, A.R., Kowalczyk, P.

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  • A comprehensive 'tool-kit' providing a complete reference to Bifurcation theory for piecewise smooth dynamical systems
  • Introduces the main ideas through examples, adds detail in subsequent chapters and finishes with more applications showing how the theory matches physical experiments
  • Develops the theory in a systematic, logical manner
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eBook 83,29 €
price for Spain (gross)
  • ISBN 978-1-84628-708-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-1-84628-039-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-84996-548-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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 2009 i)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-1-84628-708-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-1-84628-039-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,99 €
price for Spain (gross)
  • ISBN 978-1-84996-548-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Piecewise-smooth Dynamical Systems
Book Subtitle
Theory and Applications
Authors
Series Title
Applied Mathematical Sciences
Series Volume
163
Copyright
2008
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84628-708-4
DOI
10.1007/978-1-84628-708-4
Hardcover ISBN
978-1-84628-039-9
Softcover ISBN
978-1-84996-548-4
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XXII, 482
Topics