Trichotomy of a system of two difference equations

In this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations xn+1 = A+ k i=1 aixn−pi m j=1 bj yn−qj , yn+1 = B + k i=1 ciyn−pi m j=1 dj xn−qj , where k,m ∈ {1, 2, . . .}, A,B, ai, ci,bj ,dj , i ∈ {1, . . ., k}, j ∈ {1, . . .,m}, are positive constants, pi , qj , i ∈ {1, . . . , k}, j ∈ {1, . . . , m}, are positive integers such that p1 < p2 < ··· < pk, q1