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

Permanence of a Discrete Model of Mutualism with Infinite Deviating Arguments

Xuepeng Li and Wensheng Yang

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China

Received 15 July 2009; Accepted 13 January 2010

Academic Editor: Binggen Zhang

Copyright © 2010 Xuepeng Li and Wensheng Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.