Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity

Abstract

We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin's maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.