Numerical Bifurcation Analysis of Maps: From Theory to Software

Research output: Book/ReportBookAcademic

Abstract

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
Original languageEnglish
Place of PublicationCambridge, UK
PublisherCambridge University Press
Number of pages420
ISBN (Print)9781108499675
Publication statusPublished - Mar 2019

Publication series

NameCambridge Monographs on Applied and Computational Mathematics
PublisherCambridge University Press
Volume34

Fingerprint

Bifurcation Analysis
Numerical Analysis
Bifurcation
Software
Discrete-time Dynamical Systems
MATLAB
Chaos Theory
Homoclinic
Invariant Manifolds
Dynamical Model
Ecology
Systems Theory
Lyapunov Exponent
Control Parameter
Two Parameters
Fixed point
Numerical Methods
Economics
Engineering
Cycle

Cite this

Kouznetsov, I. A., & Meijer, H. G. E. (2019). Numerical Bifurcation Analysis of Maps: From Theory to Software. (Cambridge Monographs on Applied and Computational Mathematics; Vol. 34). Cambridge, UK: Cambridge University Press.
Kouznetsov, Iouri Aleksandrovitsj ; Meijer, Hil Gaétan Ellart. / Numerical Bifurcation Analysis of Maps : From Theory to Software. Cambridge, UK : Cambridge University Press, 2019. 420 p. (Cambridge Monographs on Applied and Computational Mathematics).
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Kouznetsov, IA & Meijer, HGE 2019, Numerical Bifurcation Analysis of Maps: From Theory to Software. Cambridge Monographs on Applied and Computational Mathematics, vol. 34, Cambridge University Press, Cambridge, UK.

Numerical Bifurcation Analysis of Maps : From Theory to Software. / Kouznetsov, Iouri Aleksandrovitsj; Meijer, Hil Gaétan Ellart.

Cambridge, UK : Cambridge University Press, 2019. 420 p. (Cambridge Monographs on Applied and Computational Mathematics; Vol. 34).

Research output: Book/ReportBookAcademic

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Kouznetsov IA, Meijer HGE. Numerical Bifurcation Analysis of Maps: From Theory to Software. Cambridge, UK: Cambridge University Press, 2019. 420 p. (Cambridge Monographs on Applied and Computational Mathematics).