The Filippov Approach for Predator-Prey System Involving Mixed Type of Functional Responses

Abstract

In this paper, a Filippov type model is proposed for the predator-prey system. The smooth subsystems of the proposed model admit regular and virtual equilibrium points and their dynamics is explored. The tangent points, boundary equilibrium and pseudo-equilibrium are obtained on discontinuity boundary. Equation of sliding motion is obtained using the Filippov’s convex method and sliding mode dynamics is discussed. It has been shown that the Filippov system admits pseudo-equilibrium, only if virtual equilibrium of two subsystems coexist. The value of threshold parameter is computed for which tangent point and boundary equilibrium collide. The two parameter bifurcation diagram is drawn to show the existence of regular and virtual equilibrium points in different regions. The existence of boundary equilibrium bifurcation is investigated through numerical simulation, as value of threshold parameter varies.