Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 931798, 7 pages
doi:10.1155/2010/931798

Permanence of a discrete model of mutualism with infinite deviating arguments

Abstract

We propose a discrete model of mutualism with infinite deviating arguments, that is x1(n+1)=x1(n)exp{r1(n)[(K1(n)+α1(n)∑s=0∞J2(s)x2(n−s))/(1+∑s=0∞J2(s)x2(n−s))−x1(n−σ1(n))]},x2(n+1)=x2(n)exp{r2(n)[(K2(n)+α2(n)∑s=0∞J1(s)x1(n−s))/(1+∑s=0∞J1(s)x1(n−s))−x2(n−σ2(n))]}. By some Lemmas, sufficient conditions are obtained for the permanence of the system.