Management and analysis of predator-prey fishery model

Abstract

In this article, we study a predator-prey like fishery model where predator's functional response is ratio-dependent and prey population is harvested continuously following Michaelis-Menten type harvesting rate. Mathematical results like positive invariance, boundedness, stability of the system have been studied. The dynamics of the zero equilibria have been investigated using blow-up technique. The optimal policy of exploitation in equilibrium case is derived by using Pontryagin's maximal principle. It is observed that a proper harvesting strategy and the knowledge about the biological characteristics of interacting species should be used in tackling overexploitation or extinction of the species. Our simulation results indicate that the system may exhibit bistability depending on the initial prey density over the predator.