Resumen de Analysis of Degenerate Fold–Hopf Bifurcation in a Three-Dimensional Differential System

Gheorghe Tigan

• In this work we study degenerate fold–Hopf bifurcation of codimension three in a differential system of the form x˙=-x-y-z,y˙=x+ay+bxy,z˙=bx-cz.We prove that the classical theory of the fold–Hopf bifurcation cannot be applied for studying the system’s behavior. However, using tools from averaging theory we prove the existence of periodic orbits generated by this bifurcation.