Zero-Hopf bifurcation in the Chua’s circuit

Abstract

An equilibrium point of a differential system in R 3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. First, we prove that the Chua’s circuit can have three zero-Hopf equilibria varying its three parameters. Later, we show that from the zero-Hopf equilibrium point localized at the origin of coordinates can bifurcate one periodic orbit. Moreover, we provide an analytic estimation of the expression of this periodic orbit and we have determined the kind of the stability of the periodic orbit in function of the parameters of the perturbation. The tool used for proving these results is the averaging theory of second order.