Dynamics of predator prey model using Gompertz function with impulsive biological control and unilaterally impulsive diffusion

Abstract

This paper lays down a prey-predator model with a novel attempt of assuming Gompertz growth function as a primary growth function. The model consists of two regions which are joined by diffusion of predator populations. The Gompertz growth function monitors the population of pests and one of the predators. The model assumes the release of biological control(natural enemies) impulsively to suppress the biological pest. The reason of incorporating natural enemy impulsively is due to the fact that they are applied only when pest population becomes uncontrollable. The analysis includes boundedness of the system, global stability of pest-extinction case fllowed by the permanence of the system. Finally, the analytical results are validated numerically.