A Necessary and Sufficient Condition for Permanence of a Lotka–Volterra Discrete System with Delays Original Research Article

In this paper we consider the permanence of the following Lotka–Volterra discrete competition system with delays k1, k2, l1, and l2: x(n + 1) = x(n)exp{r1[1 − x(n − k1) − μ1y(n − k2)]}, y(n + 1) = y(n)exp{r2[1 − μ2x(n − l1) − y(n − l2)]}. We show the system is permanent for all nonnegative integers k1, k2, l1, and l2, if and only if μ1 < 1 and μ2 < 1 hold.