DYNAMICS IN A COMPETITIVE LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH MULTIPLE DELAYS

Abstract

In this paper, we investigate a discrete competitive Lotka-Volterra predator-prey model with multiple delays.  For general non-autonomous case, sufficient conditions which ensure the permanence and the global stability of the system are derived by applying the differential inequality theory.  For periodic case, sufficient conditions which guarantee the existence of an unique globally stable positive periodic solution are established.  Some numerical simulations which illustrate our theoretical findings are carried out.