Study On The Complex Dynamic Behavior Of Some Filippov Systems

In this paper,we firstly investigate the dry friction self-excited oscillator.When the coefficient of maximum static friction is larger than that of sliding friction,the system is rewritten by modified Filippov theory,then the sliding region is obtained theoretically and verified by the numerical simulation.Furthermore,if the coefficient of maximum static friction exceeds that of sliding friction,we discover the coexistence of multiple attractors,such as period-1 orbit and equilibrium point,period-2 orbit and equilibrium point.But it is not true if they are equal.This shows that the friction coefficient has a great influence on the dynamic behaviors of the system.Simultaneously,some sliding bifurcations,such as crossing-sliding bifurcation,switching-sliding bifurcation and grazing-sliding bifurcation,are also found.Secondly,we research a certain Filippov system,obtain the switching layer system of a non-smooth system on switching layer,analyse the stability of its equilibrium points,and numerically find complicated dynamics of the switching layer system,which mainly include hidden periodic attractor,hidden chaotic attractor and the coexistence of multiple attractors.This means that they are hidden in non-smooth systems.