Bifurcations at infinity in a model for 1: 4 resonance

B Krauskopf

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6 Citations (Scopus)

Abstract

The equation (z) over dot = e(i alpha)z + e(i phi)z\z\(2) + bz(-3) models a map near a Hopf bifurcation with 1:4 resonance. It is a conjecture by V. I. Arnol'd that this equation contains all versal unfoldings of Z(4)-equivariant planar vector fields. We study its bifurcations at infinity and show that the singularities of codimension two unfold versally in a neighborhood. We give an unfolding of the codimension-three singularity for b = 1, phi = 3 pi/2 and alpha = 0 in the system parameters and use numerical methods to study global phenomena to complete the description of the behavior near co. Our results are evidence in support of the conjecture.

Original languageEnglish
Pages (from-to)899-931
Number of pages33
JournalErgodic Theory and Dynamical Systems
Volume17
Publication statusPublished - Aug-1997

Keywords

  • LOCAL BIFURCATIONS

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