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This paper studies a particular type of planar Filippov system that consists of two discontinuity boundaries separating the phase plane into three disjoint regions with different dynamics. This type of system has wide applications in various subjects. As an illustration, a plant disease model and an avian-only model are presented, and their bifurcation scenarios are investigated. By means of the regularization approach, the blowing up method, and the singular perturbation theory, we provide a different way to analyze the dynamics of this type of Filippov system. In particular, the boundary equilibrium bifurcations of such systems are studied. As a consequence, the nonsmooth fold bifurcation becomes a saddle-node bifurcation, while the persistence bifurcation disappears after regularization. [ABSTRACT FROM AUTHOR]

Filippov systems have found applications in various fields. This paper mainly studies five Lotka–Volterra models of Filippov type, including a competitive system with linear interaction between two species, a competitive system with Holling type II or type III functional response and a symbiosis system with Holling type II or type III functional response. We investigate the stability of all equilibria and the boundary equilibrium bifurcations of these systems, either a persistence bifurcation or a nonsmooth fold bifurcation. We present the numerical simulation results for each case. Consequently, based on both theory and simulation, we analyze the ecological aspects under the intervention of harvesting at different prescribed thresholds. [ABSTRACT FROM AUTHOR]