Copyright © 2009 Tomomi Itokazu and Yoshihiro Hamaya. 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

The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1(n+1)=x1(n)exp⁡{b1(n)−a1(n)x1(n)−c2(n)∑s=−∞nK2(n−s)x2(s)}, x2(n+1)=x2(n)exp⁡{−b2(n)−a2(n)x2(n)+c1(n)∑s=−∞nK1(n−s)x1(s)} and a competitive system xi(n+1)=xi(n)exp⁡{bi(n)−aiixi(n)−∑j=1,j≠il∑s=−∞nKij(n−s)xj(s)}, by using certain stability properties, which are referred to as (K,ρ)-weakly uniformly asymptotic stable in hull and (K,ρ)-totally stable.