General solutions 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 =u v + a / u + v , y =w s + a / w + s , n ∈ N , where u , v , w and s are x or y , 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. n+1 n−2 n−3 n−2 n−3 n+1 n−2 n−3 n−2 n−3 0 n n n n n n