A stochastic model for autotroph–herbivore system with nutrient reclycing

The concept of a food web has been a central organising theme in ecology ever since its classical development. Studies of nutrient–autotroph–herbivore system require special attention in this context. In this paper, we have proposed and analysed a nutrient–autotroph–herbivore system with instantaneous nutrient recycling. We have observed that if the external nutrient input exceeds certain threshold determined by the other parameters of the system, then the system is locally as well as globally asymptotically stable around the positive interior equilibrium. Moreover, to observe the effect of environmental stochasticity on such system, the deterministic model has been modified by allowing random fluctuations around the positive interior equilibrium. The stochastic stability properties of the model have been investigated both analytically and numerically suggesting that the deterministic model is robust with respect to stochastic perturbations. Suitable thresholds of the intensity of the stochasticity have been obtained to control the system under the influence of environmental stress.