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
Tomomi Itokazu
and Yoshihiro Hamaya
Department of Information Science, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
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.