参数激励下分段线性两尺度系统的分岔

Bifurcation of Piecewise Linear System with Two Time Scales in Parametric Excitation

对参数激励下分段线性系统进行了稳定性及分岔分析。以蔡氏电路系统为模型,在电阻中引入周期变化的部分,使得周期激励频率与系统固有频率之间存在量级差异,构造了两时间尺度非光滑动力系统。将该非自治系统化为广义自治系统,研究广义平衡点的稳定性,给出其失稳的分岔条件。在非光滑面处引用广义Jacobian矩阵进行非光滑分岔分析,得到了相应的分岔条件。

The stability and bifurcation of piecewise linear systems in parametric excitation were investigated.Based on the Chua 's circuit system model,periodic change part was introduced into the resistance. There existed order gap between the natural frequency and the exited frequency. A non-smooth dynamical system of two time scales was constructed. Firstly,non-autonomous system was transformed to the autonomous system,then,the stability of the generalized equilibrium point was studied and the corresponding bifurcation condition of losing stability was given. By using the generalized Jacobian matrix to non-smooth bifurcation analysis in the non-smooth surface,the corresponding bifurcation conditions of non-smooth surfaces were given.