Permanence for the Discrete Competition Model with Infinite Deviating Arguments

Abstract EN

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}, where ri,Ki,αi, Ji, and δi, i=1,2, are nonnegative sequences bounded above and below by positive constants, and Ki>αi, i=1,2.