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探讨了具有分段线性特性的广义BVP电路系统随参数变化的复杂动力学演化过程.其非光滑分界面将相空间划分成不同的区域,分析了各区域中平衡点的稳定性,得到其相应的简单分岔和Hopf分岔的临界条件.给出了不同分界面处广义Jacobian矩阵特征值随辅助参数变化的分布情况,讨论了分界面处系统可能存在的分岔行为,指出当广义特征值穿越虚轴时可能引起Hopf分岔,导致系统由周期振荡转变为概周期振荡,而当出现零特征值时则导致系统的振荡在不同平衡点之间转换.针对系统的两种典型振荡行为,结合数值模拟验证了理论分析的结果.
The complex dynamical evolution process of generalized BVP system with piecewise linear characteristic is discussed. The non-smooth interface divides the phase space into different regions and analyzes the stability of the equilibrium points in each region. Correspondingly, And the critical conditions of Hopf bifurcation.The distributions of the eigenvalues of the generalized Jacobian matrices with respect to the auxiliary parameters at different interfaces are given.The possible bifurcation behavior of the system at the interface is discussed and it is pointed out that when the generalized eigenvalue The Hopf bifurcation may occur when the system crosses the imaginary axis, leading to the system transition from periodic oscillation to almost periodic oscillation, while when there is zero eigenvalue, the oscillation of the system will be switched between different equilibrium points. For two typical oscillation behaviors of the system, The results of theoretical analysis are verified by numerical simulation.