Hopf-like bifurcations and multistability in a class of 3D Filippov systems with generalized Liénard’s form

Based on the observable conditions of control systems, a class of 3D Filippov systems with generalized Liénard’s form is proposed. The bifurcation conditions for two types of Hopf-like bifurcations are investigated by considering the stability changes of the sliding region and the invisible two-fold point. The primary objective of this paper is to elucidate the sudden transitions between attractors. Phase portraits, bifurcation diagrams, time series diagrams, Poincaré maps, and basins of attraction are utilized to illustrate the novel and intriguing chaotic behaviors. The simulation results indicate that after undergoing the Hopf-like bifurcation of type I, the proposed system can exhibit multiple types of attractors within remarkably narrow intervals. Even when the pseudo-equilibrium disappears, the multistable phenomena can still emerge by adjusting the parameters.