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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    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{\circledR} 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{\circledR} software MatContM This book is an ideal reference volume for professionals searching for results for a particular bifurcation",
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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).