The dynamical behavior of a piecewise-linear electric circuit with periodical excitation

Since the chaotic phenomenon in Chua's circuit was reported, the complicateddynamics in nonlinear circuits has been one of the key topics to attract alot of researchers. Based on Chua's circuits, many modified models have beenestablished, which exhibit rich nonlinear behaviors, such as intermittencyand chaos crisis. Because of the piecewise-linear function between thecurrent and the voltage introduced, non-smooth bifurcation may occur at thesingular positions. Up to now, most of the obtained results focus on thedynamics of autonomous vector fields. However, many real electric circuitsare non-autonomous, in which the time-dependent terms may come from thealternating current or the controllers. Therefore, it is very important toexplore the evolution of the dynamics of such types of systems.Based on the bifurcation prosperities of a fourth-order autonomouspiecewise-linear electric circuit, complicated dynamics of the oscillatorwith periodic excitation for two different excitation amplitudes has beeninvestigated in details. Two coexisted bifurcation forms for weak excitationare presented. Different chaotic attractors can be observed via sequences ofassociated bifurcations, which may interact with each other to form anenlarged chaotic attractor. While for the relatively strong excitation, theperiodic orbit circling around the original two equilibrium points does notsplit into two parts, resulting in the disappearance of the coexistedphenomenon. Because of the different scale between the natural frequency andthe excitation frequency, fast-slow effect was obviously found on thebehaviors of both the weak and strong excitation, such as periodicsolutions, quasi-periodic movements, and even for chaotic oscillation.Furthermore, the mechanism of fast-slow effect has been discussed from theview point of bifurcation.