A two-species predator-prey model in an environment enriched by a biotic resource

Abstract

Classical population growth models assume that the environmental carrying capacity is a fixed parameter, which is not often realistic. We propose a modified predator-prey model where the carrying capacity of the environment is dependent on the availability of a biotic resource. In this model both populations are able to consume the resource, thus altering the environment. Stability, bifurcation and numerical analyses are presented to illustrate the system’s dynamical behaviour. Bistability occurs in certain parameter regions. This could describe the transition from a beneficial environment to a detrimental one. We examine special cases of the system and show that both permanence and extinction are possible.