Degenerate with respect to parameters fold-Hopf bifurcations

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.