The quasi-periodic behavior in the chaotic movement of the generalized Chau's circuit with periodic excitation

Chaotic circuits can be established conveniently, whichcan be used for chaotic synchronization and chaotic control as well as theimitation of secret communication. The dynamics behavior of chaotic circuitshas been one of the key topics. Up to now, most of the results obtainedfocus on the nonlinear autonomous circuits. However, a lot of nonautonomousfactors such as the electric power source with alternation property mayexist in many real circuits, while few works for such systems can be found.To reveal the dynamics details, it is necessary to investigate the influenceof the nonautonomous terms on the behavior of the dynamics evolution of thecircuits. Based on a fourth-order Chua's circuit, dynamics of the model withperiod-exciting has been explored. Since the coexistence of two symmetricstable equilibrium points in the generalized Chua's circuit, periodicexcitation may lead to two coexisted bifurcation patterns corresponding ofdifferent initial conditions. Chaos can be observed via the break-up of thetorus corresponding quasi-periodic solution, which may evolve fromnon-synchronized state of phase to synchronization. With the variation ofparameters, the chaotic attractor may split into two chaotic attractorssymmetric to each other, which still keep the phase synchronization. Anenlarged chaotic attractor can be observed after the interaction between thetwo symmetric chaotic attractors, which visits the original two chaoticattractors in turn with obvious rhythm. Meanwhile, for every certain timeinterval, the trajectory of the chaos oscillates quasi-periodically forrelatively long time, called as quasi-periodic behavior in chaos. This typeof phenomenon may weaken gradually and finally disappear.