Mario Bernardo, Chris Budd, Alan Richard Champneys, Piotr Kowalczyk

Piecewise-smooth Dynamical Systems (eBook, PDF)

Theory and Applications

• Format: PDF

Produktbeschreibung

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction motivates the ubiquity of such models via examples from mechanics, electronics, control theory and physiology. The key concept is that of 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, illustrated via many examples, both theoretical and experimental. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

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Produktdetails

• Verlag: Springer London
• Seitenzahl: 482
• Erscheinungstermin: 1. Januar 2008
• Englisch
• ISBN-13: 9781846287084
• Artikelnr.: 37342473

Autorenporträt

M. di Bernardo, University of Bristol, UK; University of Naples Federico II, Italy / C.J. Budd, University of Bath, UK / A.R. Champneys, University of Bristol, UK / P. Kowalczyk, University of Bristol, UK; University of Exeter, UK

Inhaltsangabe

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.

Rezensionen

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)