On a nonlinear second order system of difference equations

We prove that all positive solutions of the next system of difference equationsxn+1=A+ynpxn-1q,yn+1=A+xnpyn-1q,n∈N0,where parameters A,pA,p and q   are positive numbers, are bounded if one of the following conditions is satisfied p2<4qp2<4q, or 2q⩽p<1+q,q∈(0,1), and that the system has positive unbounded solutions when p2⩾4q>4p2⩾4q>4, or p⩾1+qp⩾1+q, q⩽1q⩽1, completely describing the boundedness character of the system in this case.