Stability and oscillations of an autotroph-herbivore model with time delay

In the present study a mathematical model of a non-interactive type of auto troph-herbivore system with discrete time delay due to gestation is propose d. The amount of autotroph biomass consumed by the herbivore is assumed to follow a Holling type-II function. We have derived the conditions for asymp totic stability and switching to instability of the steady state. The lengt h of the delay preserving the stability has also been derived. Finally, the conditions for instability and bifurcation results have been derived for t he linearized model. Phase portraits of the original nonlinear model have b een simulated and the results have been interpreted ecologically.