快慢耦合振子的张驰簇发及其非光滑分岔机制

通过引入适当的参数值, 得到了两时间尺度下的快慢耦合振子, 分析了耦合系统及子系统的平衡点及其性质, 进而利用微分包含理论, 探讨了非光滑分界面上的奇异性, 指出在适当的参数条件下, 系统轨迹在穿越分界面时会产生由Hopf分岔和Fold分岔组合的非常规分岔. 给出了不同参数条件下的周期簇发行为, 分析了簇发过程的振荡特性, 指出激发态的频率取决于快子系统在非光滑分界面上的Hopf分岔频率, 而慢子系统的固有频率影响了簇发行为的振荡周期, 并进一步揭示了由非光滑分岔引起的不同周期簇发的分岔机制.

RELAXATION BURSTING OF A FAST-SLOW COUPLED OSCILLATOR AS WELL AS THE MECHANISM OF NON-SMOOTH BIFURCATION

By introducing suitable values of the parameters,a fast-slow coupled oscillator has been obtained. Under the analysis of the equilibrium points as well as the characteristics of the coupled system and the subsystems, combining the theory of Clarke differential inclusions,the singularities on the non-smooth boundaries are explored,which reveals that the non-conventional bifurcation composed of Hopf bifurcation and Fold bifurcation may occur when the trajectory passes across the boundary for suitable parameters.Different types of bursting phenomena associated with the corresponding parameters conditions have been obtained,the oscillating characteristics of which is discussed in details.It is pointed out that the frequency of the spiking in bursters may depend on the frequency related to Hopf bifurcation of the fast subsystem on the non-smooth boundary, while the natural frequency of the slow subsystem may influence the oscillating period of the bursters.The bifurcation mechanism of the different periodic bursters caused by the non-smooth bifurcation are presented in the end.