Effect of time delay in an autotroph-herbivore system with nutrient cycling

In the present study we consider a mathematical model of a non-interactive type autotroph-herbivore system in which the amount of autotroph biomass consumed by the herbivore is assumed to follow a Holling type II functional response. We have also incorporated discrete time delays in the numerical response term to represent a delay due to gestation, and in the recycling term which represents the time required for bacterial decomposition. We have derived conditions for global asymptotic stability of the model in the absence of delays. Conditions for delay-induced asymptotic stability of the steady state are also derived. The length of the delay preserving stability has been estimated and interpreted ecologically.