Zero-Hopf Bifurcation in the Rössler’s Second System

Abstract

This paper is devoted to study the zero-Hopf bifurcation of the Rössler's second system. We characterize the parameters for which a zero-Hopf equilibrium point takes place at each point. We prove that there are three oneparameter families exhibiting such equilibria. The averaging theory of the first order is also applied to prove the existence of one periodic orbit bifurcating from the zero-Hopf equilibrium at the origin. Here, to visualize this, FireFlies software is used.