Solvability and semi-cycle analysis of a class of nonlinear systems of difference equations

An analysis of semi-cycles of positive solutions to eight systems of difference equations of the following form xn=a+pn-1qn-2pn-1+qn-2,yn=a+rn-1sn-2rn-1+sn-2,n is an element of N0,where a is an element of [0, + infinity), the sequences p(n), q(n), r(n), s(n) are some of the sequences x(n) and y(n), with positive initial values x(-j),y(-j), j = 1,2, is conducted in detail, and it is shown that these systems can be solved in closed-form, which is the main result here. Two methods for showing the solvability are described.