Abstract
Recently, pest control has become a very interesting research topic because it is closely associated with agricultural and economic loss. Empirical evidence shows that pest insects are responsible for lower crop production and many other adverse effects on the farming sector. There are several biological, physical and chemical control mechanisms. However, the biological control of pest populations by using natural enemies is one of the most important ecosystem services adopted in agriculture around the world. In the present study, we consider an ecological model consisting of prey (pest) and its natural enemy as the predator. Different system equilibria are obtained, their stability is analyzed, and Hopf bifurcation of the system around the interior equilibrium is discussed. The sufficient permanence criteria of the system are also derived. Moreover, we perform bifurcation analysis to explore the existence of limit cycle. We also investigate the stability property of the positive periodic solution when the interior equilibrium loses its stability. Our analytical results are further verified through numerical simulations. Our findings suggest that, in the absence of a super predator, pest and natural enemy show stable coexistence. However, in the presence of super predator, if the natural enemy is killed at a lower rate, both pest and natural enemy coexist. Finally, above a threshold value, the natural enemy is eradicated from the system and pest outbreak occurs.