Asymptotically periodic solutions of Volterra system of difference equations

Abstract

A Volterra system of difference equations of the form x s ( n + 1 ) = a s ( n ) + b s ( n ) x s ( n ) + ∑ p = 1 r ∑ i = 0 n K s p ( n , i ) x p ( i ) where n ∈ N , a s , b s , x s : N → R and K s p : N × N → R , s = 1 , 2 , … , r is studied. Sufficient conditions for the existence of asymptotically periodic solutions of this system are derived.