Dynamic behaviors of a non-selective harvesting May cooperative system incorporating partial closure for the populations

Abstract

A cooperative system of May type incorporating partial closure for the populations and non-selective harvesting is proposed and studied in this paper. The locally stability property of the equilibria are determined by analyzing the Jacobian matrix of the system about the equilibria. By using the comparison theorem of the differential equation, sufficient conditions which ensure the global attractivity of the boundary equilibria are obtained. By using the iterative method, we are able to show that the conditions which ensure the existence of the unique positive equilibrium is enough to ensure its global attractivity. Our study shows that the intrinsic growth rate and the fraction of the stocks for the harvesting plays crucial role on the dynamic behaviors of the system. Numeric simulations are carried out to show the feasibility of our results.