A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays

In this paper we consider the permanence of the following Lotka-Volterra di screte competition system with delays k(1), k(2), l(1), and l(2): x(n + 1) = x(n)exp(r(1)[1 - x(n - k(2)) - mu (2)y(n - k(2))]}, y(n + 1) = y(n)exp{r( 2)[l - mu (2)x(n - l(1)) - y(n - l(2))]}. We show the system is permanent f or all nonnegative integers k(1), k(2), l(1) and l(2), if and only if mu (1 ) < 1 and <mu>(2) < 1 hold. <(c)> 2001 Academic Press.