Dynamics analysis in a non-smooth Lü system with two time scales

To explore the bursting behaviours in a dynamic system with non-smooth factor, this paper takes Lü system as an example, introduces a non-smooth term and a periodic external excitation, ensures that there exists an order gap between the natural frequency and the exited frequency, then a non-smooth dynamic system with two time scales is established. Through the stability analysis of the equilibrium point, the conditions of fold bifurcation and Hopf bifurcation are given. The numerical simulations show the bursting oscillations of the system under different parameter values and the dynamic behaviours of the trajectory at the non-smooth interface. In addition, combining with numerical calculation and related bifurcation theory, the bifurcation types of the system at the interface are determined. Finally, the mechanism of oscillations is revealed by the superposition of bifurcation curves and transformed phase portraits.