General solution to subclasses of a two-dimensional class of systems of difference equations

Abstract

We show practical solvability of the following two-dimensional systems of difference equations x(n+1) = u(n-2)v(n-3) + a/u(n-2) + v(n-3), y(n+1) = w(n-2)s(n-3) +a/w(n-2 )+ s(n-3), n is an element of N-0, where u(n), v(n), w(n) and s(n) are x(n) or y(n), by presenting closed-form formulas for their solutions in terms of parameter a, initial values, and some sequences for which there are closed-form formulas in terms of index n. This shows that a recently introduced class of systems of difference equations, contains a subclass such that one of the delays in the systems is equal to four, and that they all are practically solvable, which is a bit unexpected fact.