A memristive non-smooth dynamical system with coexistence of bimodule periodic oscillation

In order to explore the bursting oscillations and the formation mechanism of memristive non-smooth systems, a third-order memristor model and an external periodic excitation are introduced into a non-smooth dynamical system, and a novel 4D memristive non-smooth system with two-timescale is established. The system is divided into two different subsystems by a non-smooth interface, which can be used to simulate the scenario where a memristor encounters a non-smooth circuit in practical application circuits. Three different bursting patterns and bifurcation mechanisms are analyzed with the time series, the corresponding phase portraits, the equilibrium bifurcation diagrams, and the transformed phase portraits. It is pointed that not only the stability of the equilibrium trajectory but also the non-smooth interface may influence the bursting phenomenon, resulting in the sudden jumping of the trajectory and non-smooth bifurcation at the non-smooth interface. In particular, the coexistence of bimodule periodic oscillations at the non-smooth interface can be observed in this system. Finally, the correctness of the theoretical analysis is well verified by the numerical simulation and Multisim circuit simulation. This paper is of great significance for the future analysis and engineering application of the memristor in non-smooth circuits.