Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system

Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium points of the modified Chua circuit system. By using the averaging theory, we consider zero-Hopf bifurcation of the modified Chua system. Moreover, the existence of periodic solutions in the modified Chua system is derived from the classical Hopf bifurcation theorem.