Dynamical Behavior of a Stage Structured Prey–Predator Model with Two Delays and Monod–Haldane Functional Response

Abstract

In this paper, a new stage structured prey–predator model with Monod–Haldane functional response is proposed and the stages for predator have been considered. The proposed mathematical model consists of three nonlinear delay differential equations to describe the interaction among prey, immature predator and mature predator populations. Two time delays viz. feedback delay and gestation delay have been used as the bifurcation parameter. A rigorous mathematical analysis has been carried out by considering all possible cases for both the delays. Conditions for local stability and Hopf bifurcation have been investigated in all cases. Furthermore, by using normal form method, Riesz representing theory and central manifold theorem, formulae are derived for the direction of Hopf bifurcation and stability of bifurcating periodic solutions. Global stability analysis is carried out and the numerical simulation to validate the theory is also executed at the end.