Effect of time-delay on a ratio-dependent food chain model

Abstract

This paper aims to study the effect of time-delay on a tritrophic food chain model with Michaelis-Menten type ratio-dependent functional responses. Boundedness of the time-delayed system is established. A simple criterion for deterministic extinction is derived. It has been shown that the time-delay may introduce instability in the system through Hopf bifurcation. Computer simulations are carried out to explain the analytical findings. It is discussed how these ideas illuminate some of the observed properties of real populations in the field, and explores practical implications.