Asymptotically periodic solutions of Volterra system of difference equations

A Volterra system of difference equations of the form xs(n+1)=as(n)+bs(n)xs(n)+∑p=1r∑i=0nKsp(n,i)xp(i) where n∈Nn∈N, as,bs,xs:N→Ras,bs,xs:N→R and Ksp:N×N→RKsp:N×N→R, s=1,2,…,rs=1,2,…,r is studied. Sufficient conditions for the existence of asymptotically periodic solutions of this system are derived.