Sliding bursting dynamics and bifurcation mechanisms in a nonsmooth coupled Duffing and van der Pol system with fast-slow effect

This paper aims to explore the sliding bursting dynamics of a four-dimensional Filippov system with an external excitation. Five novel sliding bursting patterns can be observed in this system with specific parameter values. Their generation mechanisms are investigated utilizing the fast-slow analysis method. Our investigation reveals that the Hopf-like boundary equilibrium bifurcations can induce transitions between spiking and quiescent states, resulting in bursting oscillations within the system. The spiking oscillations may appear as a combination of oscillations with different amplitudes and diverse sliding structures, caused by the sliding bifurcations, fold bifurcation of nonsmooth limit cycles and period-doubling bifurcation. Additionally, the system exhibits the coexistence of multiple attractors, where the structure of the attraction basin and the inertia of movement together can affect the spiking oscillations, leading to the trajectory transitions between different attractors. Our findings enhance the understanding of the generation mechanisms behind the bursting dynamics in high-dimensional Filippov systems.