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Numerical Bifurcation Analysis of Maps
From Theory to Software

$140.00 (C)

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: May 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781108499675

$ 140.00 (C)

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About the Authors
  • This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

    • Provides state-of-the-art analysis of bifurcations of discrete-time dynamical systems
    • Theory is connected with practical applications, as well as step-by-step tutorials on how to analyze particular bifurcations using the free MATLAB® software MatContM
    • This book is an ideal reference volume for professionals searching for results for a particular bifurcation
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    Product details

    • Date Published: May 2019
    • format: Hardback
    • isbn: 9781108499675
    • length: 420 pages
    • dimensions: 235 x 157 x 23 mm
    • weight: 0.82kg
    • contains: 22 b/w illus. 136 colour illus. 16 tables
    • availability: In stock
  • Table of Contents

    Part I. Theory:
    1. Analytical methods
    2. One-parameter bifurcations of maps
    3. Two-parameter local bifurcations of maps
    4. Center-manifold reduction for local bifurcations
    Part II. Software:
    5. Numerical methods and algorithms
    6. Features and functionality of MatContM
    7. MatContM tutorials
    Part III. Applications:
    8. Examples

  • Authors

    Yuri A. Kuznetsov, Universiteit Utrecht, The Netherlands
    Yuri A. Kuznetsov is Associate Professor at Utrecht University and Professor of Numerical Bifurcation Methods at the University of Twente. He has made significant contributions to the theory of codimension two bifurcations of smooth ODEs and iterated maps. His recent work has focussed on efficient numerical continuation and normal form analysis of maps, ODEs and DDEs, and on applications of these methods in ecology, economics, engineering, and neuroscience. He is also the author of the widely-used text and reference Elements of Applied Bifurcation Theory, 3rd edition (2010).

    Hil G. E. Meijer, University of Twente, Enschede, The Netherlands
    Hil G. E. Meijer is Assistant Professor at the University of Twente, Enschede, The Netherlands. He has extensive experience in numerical bifurcation theory and interdisciplinary applications such as modeling Parkinson's disease and epilepsy. He is a co-supervisor of the MatCont software project and has given numerous workshops on its use.

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