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Yuri A. Kuznetsov, Hil G. E. Meijer - Numerical Bifurcation Analysis of Maps, Inbunden

Inbunden, Engelska, 2019

Numerical Bifurcation Analysis of Maps

From Theory to Software

Av Yuri A. Kuznetsov, Hil G. E. Meijer

Del 34 i serien Cambridge Monographs on Applied and Computational Mathematics

2312 kr

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Beskrivning
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.
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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 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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'The topic of this book is the study of local and global bifurcations (qualitative changes in dynamics) of discrete-time maps as parameters are varied … This book could be used as reference to known results on bifurcations of maps, or as a guide to the software MatcontM. It is clearly written and contains many high-quality figures.' Carlo Laing, zbMATH

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