Advances in Difference Equations
Volume 2009 (2009), Article ID 976865, 19 pages
doi:10.1155/2009/976865

Almost periodic solutions of prey-predator discrete models with delay

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.