The Effects of Time Delay on Stage Structured Model with Michaelis-Mentens-Type Harvesting

Abstract

This research work investigate the effect of time delay on the stage structured model with Michaelis-Mentens-type harvesting. The study proved the existence of all potential equilibria of the system. However, the analysis was concentrated on coexistence equilibrium E∗ to establish its stability at τ = 0. For τ > 0, the stability switch and associated Hopf bifurcation were proved. This characteristics were not found in the previous work. Numerical simulations were done using Matlab to confirm the dynamics of the analytic solution.