多分界面下四维蔡氏电路的张弛簇发及其机制研究

在经典蔡氏电路的基础上,引入反馈元件,建立了包含多个分界面的四维广义蔡氏电路.在适当的参数条件下,状态变量之间会存在量级上的差距,从而构成了包含两个时间尺度的快慢耦合系统.分析了快子系统的平衡点及其性质,进而利用微分包含理论,探讨了不同的非光滑分界面上的奇异性.给出了系统在两组参数条件下的不同周期簇发行为,应用快慢分析法探讨了系统轨迹在经过多个分界面时的特殊簇发现象,揭示了多吸引子共存时不同的簇发行为的形成机理以及非光滑分岔对簇发行为的影响.

Relaxation bursting and the mechanism of four-dimensional Chua's circuit with multiple interfaces

Based on the classical Chua's circuit, a four-dimensional Generalized Chua's circuit with multiple interfaces is established by introducing feedback elements. For the appropriate condition, there exists a difference in order of magnitude between the variables of state and a fast-slow coupled system, thereby forming a fast- and slow-coupled system at time scale. Analyzing the equilibrium points and the characteristics of the fast subsystems, and combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored. Two types of periodic bursting phenomena for different conditions are presented. Fast-slow analysis is employed to explore the special cluster phenomenon while the system trajectory passes across multiple interfaces. The coexisting different bursting mechanisms for the case with multiple attractors are explored in detail, while the influence of non-smooth bifurcations on bursting behavior is revealed.