Influence of prey reserve capacity on predator–prey dynamics

In this article the dynamics of a predator and prey population has been modelled when a reserve is created to protect a certain number of prey population from predation. This investigation is essential to derive some guiding principles to conserve the prey population and also to understand the behaviour and dependence of predator population on the reserve capacity. The present study concerns analysis of a fairly general model and hence some of the existing results based on specific explicit models, like Lotka–Volterra model and Rosenzweig–MacArthur model, can be derived from this work. In this study, conditions have been derived for coexistence of predator and prey, and extinction of predators. Results are obtained for global stability of required equilibrium of the model. Also, a method is suggested to compute reserve capacity in order to drive the ecosystem state to a required level. The key results developed in this article have been illustrated using numerical simulation. These results can be interpreted in different contexts like resource conservation, pest management, bio-economics of a renewable resource, etc.