Analysing a prey predator model for stability with prey refuge-stage structure on predator

Abstract

This paper analyses a model of prey predator with Michaelis Menten- Holling type functional response with inclusion of a constant proportion of prey refuge and predator stage structure. The analysed model consists of three nonlinear ordinary differential equations which describe the interaction between the prey and juvenile & adult predators. The system is studied for its local stability by determining the equilibrium points and obtaining the conditions for its local stability. Suitable Lyapunov function has been constructed to obtain the global asymptotic stability of the system.