Abstract: The dynamics of a piecewise-linear electric circuit with order gap between the natural frequency and the excitation frequency is investigated. Based on the bifurcation theory, the prosperities of the autonomous system have been discussed. After turning to the non-autonomous case, the periodic excitation may cause the disappearance of the equilibria and the system may oscillate periodically according to the frequency of the excitation. Different types of slow-fast effect can be observed in the numerical simulations. The mechanism of these phenomena has been analyzed from the view point of bifurcation, and the conclusion agrees well with the numerical results.

Key words: nonautonomous electric circuit, excitation frequency, slow-fast effect, bifurcation, dynamics

摘要： 基于四阶分段线性电路的分岔探讨了系统在周期激励下的复杂动力学行为。从理论上分析了与该非自治电路相应的自治系统平衡点的稳定性及其演化条件。进而引入周期激励，自治条件下的所有平衡态将被扭扩为相应的转化形式，当外激励频率与其固有频率相比存在量级上的差异时，系统存在明显的快慢效应。通过数值计算得出了非自治系统动力学行为演化的过程和特点，由分岔的角度分析了系统快慢效应产生的机制。仿真结果与理论分析基本符合，在一定程度上证明了分析方法的有效性。

关键词: 非自治电路系统, 激励频率, 快慢效应, 分岔, 动力学行为