On a class of systems of rational second-order difference equations solvable in closed form

Abstract

We show that the following nonlinear system of difference equations (Formula presented.) where parameters a,b,c,d and initial values x−1,x0,y−1,y0 are real numbers, is solvable in closed form, considerably generalizing some recent results. To do this, we use the method of transformation along with several tricks, transforming the system to some known solvable difference equations, by use of which we obtain some closed-form formulas for general solution to the system. The following five cases are considered separately: (1) c=0; (2) d=0; (3) a=0; (4) b=0; and (5) abcd≠0.