| Dewey Class |
515.39 |
| 515.48 |
| Title |
Piecewise-smooth Dynamical Systems ([Ebook]) : Theory and Applications / edited by Mario di Bernardo Laurea, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk. |
| Author |
Di Bernardo, Mario
See Also: author |
| Added Personal Name |
Champneys, Alan R. |
| Budd, Christopher J. |
| Kowalczyk, Piotr |
| Laurea, Mario di Bernardo |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
London : Springer , 2008. |
| Physical Details |
: online resource. |
| Series |
Applied mathematical sciences 0066-5452 ; ; 163 |
| ISBN |
9781846287084 |
| 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.: |
| Contents note |
Introduction -- Qualitative theory of nonsmooth 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 -- References -- Index. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
http://dx.doi.org/10.1007/978-1-84628-708-4 |
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