Dynamics of the Stage Structured Population Model, Predator Accompanied by Michaelis Menten Holling Type Functional Responseand Delay and Prey Taking Refuge

Abstract

The current work considers predator prey system, prey taking refuge, predator reckoned with time delay and Michaelis Menten Holling type II response function undergoing two stages: juvenile and mature. From the characteristic equation, we derive conditions for the local stability of the system at the equilibrium points. Also, at the coexistence equilibrium point, the system is analyzed for the occurrence of Hopf bifurcation. Lyapunov function provides sufficient conditions for the global stability of the system. Numerical simulations are given to support the theory.