On the fold-Hopf bifurcation for continuous piecewise linear differential systems with symmetry

Jaume Llibre, Enrique Ponce, Javier Ros, Francisco Torres

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

In this paper a partial unfolding for an analog to the fold-Hopf bifurcation in three-dimensional symmetric piecewise linear differential systems is obtained. A particular biparametric family of such systems is studied starting from a very degenerate configuration of nonhyperbolic periodic orbits and looking for the possible bifurcation of limit cycles. It is proved that four limit cycles can coexist after perturbation of the original configuration, and other two limit cycles are conjectured. It is shown that the described bifurcation scenario appears for appropriate values of parameters in the celebrated Chua's oscillator. © 2010 American Institute of Physics.
Original languageEnglish
Article number033119
JournalChaos
Volume20
Issue number3
DOIs
Publication statusPublished - 13 Jul 2010

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