Numerical bifurcation analysis of double +1 multiplier in ℤ3-symmetric maps

Reza Mazrooei-Sebdani* (Corresponding Author), Zohreh Eskandari, Hil G.E. Meijer

*Corresponding author for this work

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    Abstract

    We consider a resonance 1:1 bifurcation with (Formula presented.)-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 languageEnglish
    Pages (from-to)1402-1413
    JournalJournal of difference equations and applications
    Volume24
    Issue number9
    DOIs
    Publication statusPublished - 2 Sep 2018

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    Keywords

    • UT-Hybrid-D
    • Bifurcation
    • Z3-symmetry
    • Numerical continuation
    • Critical Normal Form
    • Resonance 1:1

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