Stability and oscillations in a resource-based model of two interacting species with nutrient cycling

In the present study we consider a resource-based model of autotroph–herbivore interaction with nutrient cycling in which the amount of autotroph biomass consumed by the herbivore is assumed to follow a Holling type-II function. We have derived the criteria for existence of a unique feasible steady state of the system. It is shown that there is a threshold value of the external nutrient input at which the system may exhibit Hopf type small amplitude periodic oscillations and above which large amplitude periodic oscillations occur. Finally, we have verified the analytical results through computer simulations.