The influence of partial closure for the populations to a harvesting Lotka-Volterra commensalism model

The aim of this paper is to investigate the dynamic behaviors of a harvesting Lotka-Volterra commensalism model incorporating partial closure for the populations. By analyzing the characteristic equation of the variational matrix, sufficient conditions which ensure the local stability of the equilibria are obtained; By applying the differential inequality theory and the Dulac criterion, sufficient conditions which ensure the globally asymptotical stability of the equilibria are obtained; Our study shows that depending on the fraction of the stock available for harvesting, the system maybe extinction, partial survival or two species coexist in a stable state. The dynamic behaviors of the system becomes complicated compared with the non-harvesting system. Numeric simulations are carried out to show the feasibility of the main results.