On the Solutions of Four Second-Order Nonlinear Difference Equations

Abstract

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations \[x_{n+1} &=\frac{\pm 1}{x_{n}\left( x_{n-1}\pm 1\right) -1} \\ x_{n+1} &=\frac{\pm 1}{x_{n}\left( x_{n-1}\mp 1\right) +1}\text{.} \].