Asymptotically periodic solutions of Volterra system of difference equations

A Volterra system of difference equations of the form xs.n C 1/ D as.n/ C bs.n/xs.n/ C Xr pD1 Xn iD0 Ksp.n; i/xp.i/ where n 2 N, as; bs; xs: N ! R and Ksp: N N ! R, s D 1; 2; : : : ; r is studied. Sufficient conditions for the existence of asymptotically periodic solutions of this system are derived.