DYNAMICAL ANALYSIS OF A SINGLE-SPECIES POPULATION MODEL WITH MIGRATIONS AND HARVEST BETWEEN PATCHES

A single-species population model with migrations and harvest between the protected patch and the unprotected patch is formulated and investigated in this paper. We study the local stability and the global stability of the equilibria. The research points out, under some suitable conditions, the singlespecies population model admits a unique positive equilibrium, which is globally asymptotically stable. We also derive that the trivial solution is globally asymptotically stable when the harvesting rate exceeds the threshold. Further, we discuss the practical effects of the protection zones and the harvest. The main results indicate that the protective zones indeed eliminate the extinction of the species under some cases, and the theoretical threshold of harvest to the practical management of the endangered species is provided as well. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.