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Piecewise-smooth Dynamical Systems

Theory and Applications

  • Mario di Bernardo Laurea
  • Alan R. Champneys
  • Christopher J. Budd
  • Piotr Kowalczyk

Part of the Applied Mathematical Sciences book series (AMS, volume 163)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 1-45
  3. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 47-119
  4. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 121-170
  5. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 171-217
  6. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 219-252
  7. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 253-305
  8. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 307-353
  9. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 355-408
  10. Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, Piotr Kowalczyk
    Pages 409-458
  11. Back Matter
    Pages 359-481

About this book

Introduction

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.

Keywords

Bifurcation Dynamical Systems Piecewise-Smooth Standard calculus differential equation electronics

Editors and affiliations

  • Mario di Bernardo Laurea
    • 1
    • 2
  • Alan R. Champneys
    • 3
  • Christopher J. Budd
    • 4
  • Piotr Kowalczyk
    • 5
    • 6
  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK
  2. 2.Department of Systems and Computer ScienceUniversity of Naples Federico IINaplesItaly
  3. 3.Department of Engineering MathematicsUniversity of BristolBristolUK
  4. 4.Department of Mathematical SciencesUniversity of BathBathUK
  5. 5.School of Engineering Computer Science and MathematicsUniversity of ExeterExeterUK
  6. 6.Department of Engineering MathematicsUniversity of BristolBristolUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84628-708-4
  • Copyright Information Springer-Verlag London Limited 2008
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84628-039-9
  • Online ISBN 978-1-84628-708-4
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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