Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Degenerate with respect to parameters fold-Hopf bifurcations

Pages: 2115 - 2140, Volume 37, Issue 4, April 2017      doi:10.3934/dcds.2017091

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Gheorghe Tigan - Department of Mathematics, Politehnica University of Timisoara, Pta Victoriei, No. 2, 300006, Timisoara, Timis, Romania (email)

Abstract: In this work we study degenerate with respect to parameters fold-Hopf bifurcations in three-dimensional differential systems. Such degeneracies arise when the transformations between parameters leading to a normal form are not regular at some points in the parametric space. We obtain new generic results for the dynamics of the systems in such a degenerate framework. The bifurcation diagrams we obtained show that in a degenerate context the dynamics may be completely different than in a non-degenerate framework.

Keywords:  Dynamical systems, normal forms, fold-Hopf bifurcations, degenerate bifurcations, bifurcation diagrams.
Mathematics Subject Classification:  Primary: 37G05, 37G10; Secondary: 37G15.

Received: May 2016;      Revised: November 2016;      Available Online: December 2016.