Trichotomy of a system of two difference equations

AbstractIn this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations xn+1=A+∑i=1kaixn−pi∑j=1mbjyn−qj,yn+1=B+∑i=1kciyn−pi∑j=1mdjxn−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<q2<⋯