具有多分界面的非线性电路中的非光滑分岔

本文分析了具有多分界面的非线性电路在不同时间尺度下的快慢动力学行为. 在一定的参数条件下,系统的周期解为簇发解,表现出明显的快慢效应. 根据状态变量变化的快慢,把全系统划分为快子系统和慢子系统两组. 根据快慢分析法将慢变量看作快子系统的控制参数,分析了快子系统的平衡点在向量场不同区域内的稳定性. 非光滑系统的分岔与向量场的分界面密切相关,对于具有快慢效应的两时间尺度非光滑系统,快子系统的分岔则取决于分界面两侧平衡点的性质. 通过在临界面引入广义Jacobi矩阵,讨论了快子系统非光滑分岔的类型,即多次穿越分关键词：非线性电路多分界面非光滑分岔快慢效应

Non-smooth bifurcation in nonlinear electrical circuits with multiple switching boundaries

The fast-slow dynamics of a nonlinear electrical circuit with multiple switching boundaries is investigated in this paper. For suitable parameters, periodic bursting phenomenon can be observed. The full system can be divided into slow and fast subsystems because of the difference between variational speeds of state variables. According to the slow-fast analysis, the slow variable, which modulates the behavior of the system, can be treated as a quasi-static bifurcation parameter for the fast subsystem to analyze the stabilities of equilibrium points in different areas of vector field. The bifurcation is dependent on the switching boundary in the vector field. In particular, for the two-time scale non-smooth system with fast-slow effect, the bifurcation of fast subsystem is determined by the characteristics of equilibrium points on both sides of the switching boundary. Furthermore, the generalized Jacobian matrix at the non-smooth boundary is introduced to explore the type of non-smooth bifurcation (i.e., multiple crossing bifurcation) in the fast subsystem, which can also be used to explain the mechanism for symmetric bursting phenomenon of the full system.