Conservation of a fishery through optimal taxation: a dynamic reaction model

The present paper deals with the problem of selective harvesting in a ratio-dependent predator-prey fishery in which both the predator and prey obey the logistic law of growth. To protect fish population from over exploitation a control instrument tax is imposed. The existence of its steady states and their stability are studied. The problem of optimal taxation policy is then solved by using Pontryagin's maximal principle. Finally some numerical examples are taken to illustrate the results.