Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results.

A bioeconomic model of nonselective harvesting of two competing fish species

This paper deals with the combined bioeconomic harvesting of two competing fish species, each of which obeys the Gompertz law of growth. The catch-rate functions are chosen so as to reflect saturation effects with respect to stock abundance as well as harvesting effort. The stability of the dynamical system is discussed and the existence of a bionomic equilibrium is examined. The optimal harvest policy is studied with the help of Pontryagin's maimum principle. The results are illustrated with the help of a numerical example.