Zero–Hopf bifurcations in Yu–Wang type systems

Abstract

In this paper, we study a three-dimensional system of differential equations which is a generalization of the system introduced by Yu and Wang (Eng Technol Appl Sci Res 3:352-358, 2013), a continuation of the study of chaotic attractors [see Yu and Wang (Eng Tech Appl Sci Res 2:209-215, 2012)]. We show that these systems admit a zero-Hopf non-isolated equilibrium point at the origin and prove the existence of a limit cycle emanating from it. We illustrate our results with some numerical simulations.