On a close to symmetric system of difference equations of second order

Abstract

Closed form formulas of the solutions to the following system of difference equations:

xn=yn−1yn−2 / xn−1(an+bnyn−1yn−2), yn=xn−1xn−2 / yn−1(αn+βnxn−1xn−2), n ∈ N0,

where an, bn, αn, βn, n∈N0, and initial values x−i, y−i, i∈{1,2} are real numbers, are found. The domain of undefinable solutions to the system is described. The long-term behavior of its solutions is studied in detail for the case of constant an, bn, αn and βn, n∈N0.