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 chainmodel with Michaelis-Menten type ratio-dependent functional responses. Boundednessof the time-delayed system is established. A simple criterion for deterministic extinctionis derived. It has been shown that the time-delay may introduce instability in the systemthrough Hopf bifurcation. Computer simulations are carried out to explain the analyticalfindings. It is discussed how these ideas illuminate some of the observed properties ofreal populations in the field, and explores practical implications.