Modeling the dynamics of plant-insect-natural enemy with gestation delay for top predator

Abstract

In this study a non-linear mathematical model is formulated to study and analyze an ecological system consisting of plants, insects preying on plants and insects natural enemy as predator. We analyze the dynamics of the system in a systematic manner. Here we have assumed that plants grow logistically, insect population depends on plants and predator population also depends on insects. Gestation delay for predators is taken into account. Positivity and boundedness of the system is established. The existence and stability of different equilibria are discussed. The existence of Hopf-bifurcation of the system is analyzed. Then we extended our proposed model to stochastic model and simulation results for both stochastic and deterministic models are compared.