Some characteristics of the closed-form solutions of two nonlinear difference equations

We derive the closed-form solutions of the following difference equations xn+1=xn−3±1+xn−2xn, n=0,1,2,…, where x−3, x−2, x−1, x0 ∈ (0, ∞). We also investigate the behavior of their respective solutions. Particularly, we study the conver-gence, periodicity character, stability and boundedness of their solutions.