Global stability analysis and optimal taxation control for a harvested prey predator system with prey refuge

In this paper, we investigate a prey predator model system with selective harvest effort on predator, where prey refuge is considered and taxation is utilized as a control instrument to protect the population from overexploitation. Conditions which influence positiveness and boundedness of solutions of model system are studied. Local stability analysis around all equilibria of model system are discussed due to variation of prey refuge and taxation. Furthermore, global stability of model system around the positive equilibrium is investigated based on Bendixson criterion. By using Pontryagin´s maximum principle, an optimal taxation control is derived to ensure the sustainable development of biological resource and prosperous commercial harvesting.