Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation

Abstract

Rank-1 attractors play a vital role in biological systems and the circuit systems. In this paper, we consider a periodically kicked Chua model with two delays in a circuit system. We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations. Then, we derive some explicit formulas about Hopf bifurcation, which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method. Also, we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick, which shows the effect of two delays on the circuit system. Finally, we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system.