Complex bursting oscillations induced by bistable structure in a four-dimensional Filippov-type laser system

The main purpose of this paper is to investigate the complicated dynamical behaviours as well as the mechanism of a Filippov-type system. By introducing a non-smooth term and a periodic external excitation to a four-dimensional laser system, a new Filippov-type system with two scales can be obtained. When an order gap exists between the exciting frequency and the natural one, the whole excitation term can be considered as a slow-varying parameter. For smooth subsystems, the equilibrium branches along with bifurcations, such as fold bifurcation (FB) and Hopf bifurcation (HB) are derived. Boundary equilibrium bifurcation and non-smooth bifurcations, according to differential inclusion theory, are also explored by introducing an auxiliary parameter to the system. Several types of sliding movements, such as grazing-sliding and multisliding, can be observed with slow variation. In addition, due to the coexistence of stable attractors in the vector field, the symmetry breaking phenomenon of bursting attractors appears, the mechanism of which can be revealed by overlapping the transformed phase portrait and bifurcation curves.