周期激励下广义蔡氏电路混沌运动中的概周期行为

THE QUASI-PERIODIC BEHAVIOR IN THE CHAOTIC MOVEMENT OF THE GENERALIZED CHAU'S CIRCUIT WITH PERIODIC EXCITATION

由于广义蔡氏电路存在2个对称的稳定平衡点,周期激励可能导致系统出现相应于不同初值的2种共存的分岔模式。概周期解由环面破裂进入混沌,混沌吸引子从相位不同步逐渐演化为同步,并进一步随着参数的变化,产生分裂现象。分裂后的2个相互对称的混沌吸引子仍存在相位同步效应,这2个混沌吸引子再次相互作用后形成扩大了的混沌吸引子,并交替围绕2个子混沌结构来回振荡。同时,在混沌过程中,其轨迹在相当长的一段时间内严格按照概周期行为振荡,即混沌结构中存在局部概周期行为,这种局部概周期行为随参数的变化会逐步减弱,直至消失。

Chaotic circuits can be established conveniently, which can be used for chaotic synchronization and chaotic control as well as the imitation of secret communication. The dynamics behavior of chaotic circuits has been one of the key topics. Up to now, most of the results obtained focus on the nonlinear autonomous circuits. However, a lot of nonautonomous factors such as the electric power source with alternation property may exist in many real circuits, while few works for such systems can be found. To reveal the dynamics details, it is necessary to investigate the influence of the nonautonomous terms on the behavior of the dynamics evolution of the circuits. Based on a fourth-order Chua＇s circuit, dynamics of the model with period-exciting has been explored. Since the coexistence of two symmetric stable equilibrium points in the generalized Chua＇s circuit, periodic excitation may lead to two coexisted bifurcation patterns corresponding of different initial conditions. Chaos can be observed via the break-up of the torus corresponding quasi-periodic solution, which may evolve from non-synchronized state of phase to synchronization. With the variation of parameters, the chaotic attractor may split into two chaotic attractors symmetric to each other, which still keep the phase synchronization. An enlarged chaotic attractor can be observed after the interaction between the two symmetric chaotic attractors, which visits the original two chaotic attractors in turn with obvious rhythm. Meanwhile, for every certain time interval, the trajectory of the chaos oscillates quasi-periodically for relatively long time, called as quasi-periodic behavior in chaos. This type of phenomenon may weaken gradually and finally disappear.