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

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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

Keywords

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

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