Analytic study of two limit cycles bifurcating from a zero–Hopf equilibrium

Abstract

In this paper, we provide sufficient conditions for the existence of two limit cycles bifurcating from the unique zero–Hopf equilibrium of the differential system (Formula presented.) where a, b, and c are real arbitrary parameters. Our study uses the averaging theory. This differential system has been studied previously for some authors, because it can exhibit chaotic motion when it has no equilibrium points.