Dynamics of pest control model using natural enemy and refugia plant

In this study, we introduce a pest control model that describes the interaction among pests, natural enemies (predators), and refugia plants, incorporating intraspecific competition within the predator population. Predators interact mutually with refugia plants to maintain their presence in agricultural areas, enhancing their control of the pest population. On the other hand, heightened intraspecific competition for two key resources, nectar and pests, may encourage predators to migrate and exploit new resources. The non-negativity and boundedness of the solutions are shown to ensure that the proposed model is biologically feasible. We perform dynamic analysis to identify all potential equilibrium points and examine their local and global stability characteristics. The model has seven equilibrium points. However, only three of them are conditionally stable. The pest-free equilibrium point is stable under certain conditions, indicating that the pest population may be effectively controlled. Furthermore, we show that our system exhibits a Hopf bifurcation. Finally, we confirm our analytical results through some numerical simulations.