Yuri A. Kuznetsov

Numerical Bifurcation Analysis of Maps (eBook, PDF)

From Theory to Software

• Format: PDF

Produktbeschreibung

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(R) 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 16. Mai 2019
• Englisch
• ISBN-13: 9781108695145
• Artikelnr.: 56550907

Autorenporträt

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).

Inhaltsangabe

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
References
Index.