On the complex bifurcation set for a system with simple dynamics

Mikhail V. Shashkov, Dmitry V. Turaev

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Abstract

Bifurcations of a heteroclinic contour composed of two equilibrium points of saddle-focus type and two heteroclinic orbits are considered. The case is selected where dynamics of the system is simple, i.e., no more than one periodic orbit is born at bifurcations in a small neighborhood of the contour. In spite of the simplicity of dynamic behavior, the structure of the bifurcation set corresponding to multi-round heteroclinic orbits is shown to be rather complicated. The complete bifurcation analysis is done under some conditions of a general position.

Original languageEnglish
Pages (from-to)949-968
Number of pages20
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume6
Issue number5
DOIs
StatePublished - 1 Jan 1996
Externally publishedYes

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