Optimal harvesting and stability for a prey–predator model

Abstract

This paper describes a fish prey–predator model with a new functional response. The dynamics of the system is discussed mainly from the point of view of permanence and stability. We obtain conditions that affect the persistence of the system. Local asymptotic stability of various equilibrium solutions is explored to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. We then examine possibilities of the existence of bionomic equilibrium. Lastly, the optimal harvesting policy is obtained by using the Pontryagin’s maximum principle. The objective is to maximize the monetary social benefit as well as conservation of the ecosystem.