A Filippov Pest-Natural Enemy-Predator Model Describing the Effect of Predators

In this article, a novel attempt has been made to develop a Filippov mathematical system focusing on the pest-natural enemy-predator model. The pest population is predated by natural enemy and the natural enemy gets consumed by predators. The growth rate of the pest population follows the Smith model. The non-smooth dynamical behavior of the system is analyzed, which involves sliding and crossing segments and their domains followed by the existence and stability of pseudo-equilibrium, tangent points and regular points. The co-existence of regular equilibria and a pseudo-equilibrium is also shown. Several kinds of bifurcations, like boundary node/focus bifurcations and sliding crossing bifurcation, are investigated using theoretical and numerical techniques. Finally, analytical results are verified by numerical simulations. The observations from our study show a significant role of control strategy in the Filippov system in changing its dynamics.