Analysis of Degenerate Fold-Hopf Bifurcation in a Three-Dimensional Differential System.

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.<graphic></graphic>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. [ABSTRACT FROM AUTHOR]