On a second order rational systems of difference equations
The authors study the system of second-order rational difference equations \[ x_{n+1}=\frac{y_n\,x_{n-1}}{\pm x_{n-1}\pm y_n}, \quad y_{n+1}=\frac{x_n\,y_{n-1}}{\pm x_n\pm y_{n-1}}, \quad n\in{\mathbb N}_0, \] with nonzero initial conditions. They derive an explicit form of the solution in terms of the Fibonacci sequence and the initial values.
system of second-order rational difference equations
scientific article; zbMATH DE number 6537496