Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

Reza Mazrooei-Sebdani, Zohreh Eskandari, Hil Gaétan Ellart Meijer

    Research output: Book/ReportReportOther research output

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    Abstract

    We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages14
    Publication statusPublished - Feb 2017

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.2058
    ISSN (Print)1874-4850

    Keywords

    • EWI-27788
    • IR-104021

    Cite this

    Mazrooei-Sebdani, R., Eskandari, Z., & Meijer, H. G. E. (2017). Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. (Memorandum / Department of Applied Mathematics; No. 2058). Enschede: University of Twente, Department of Applied Mathematics.
    Mazrooei-Sebdani, Reza ; Eskandari, Zohreh ; Meijer, Hil Gaétan Ellart. / Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Enschede : University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; 2058).
    @book{3062ffb8d73341fe8ea29f4b5d109907,
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    abstract = "We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.",
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    publisher = "University of Twente, Department of Applied Mathematics",
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    Mazrooei-Sebdani, R, Eskandari, Z & Meijer, HGE 2017, Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Memorandum / Department of Applied Mathematics, no. 2058, University of Twente, Department of Applied Mathematics, Enschede.

    Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. / Mazrooei-Sebdani, Reza; Eskandari, Zohreh; Meijer, Hil Gaétan Ellart.

    Enschede : University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; No. 2058).

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

    AU - Mazrooei-Sebdani, Reza

    AU - Eskandari, Zohreh

    AU - Meijer, Hil Gaétan Ellart

    PY - 2017/2

    Y1 - 2017/2

    N2 - We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.

    AB - We consider a resonance 1:1 bifurcation with Z3-symmetry in a discrete-time dynamical system. We employ standard normalization and center manifold reduction techniques. With this, we obtain the normal form up to cubic order and also explicit formulas for the critical normal form coefficients. We provide an implementation of our algorithm that can be used in the numerical bifurcation toolbox matcontm. We illustrate our analysis with a Cournot triopoly model from economics.

    KW - EWI-27788

    KW - IR-104021

    M3 - Report

    T3 - Memorandum / Department of Applied Mathematics

    BT - Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Mazrooei-Sebdani R, Eskandari Z, Meijer HGE. Numerical Bifurcation Analysis of Double +1 Multiplier in Z3-Symmetric Maps. Enschede: University of Twente, Department of Applied Mathematics, 2017. 14 p. (Memorandum / Department of Applied Mathematics; 2058).