Permanence for the Discrete Competition Model with Infinite Deviating Arguments

Abstract

Sufficient conditions are obtained for the permanence of the following discrete model of competition:x1k+1=x1(k)exp {r1kK1k+α1k∑s=0+∞J2sx2k-s/1+∑s=0+∞J2sx2k-s-x1k-δ1k};x2(k+1)=x2(k)exp {r2kK2k+α2k∑s=0+∞J1sx1k-s/1+∑s=0+∞J1sx1k-s-x2k-δ2k}, whereri,Ki,αi,Ji, andδi,i=1,2, are nonnegative sequences bounded above and below by positive constants, andKi>αi,i=1,2.