In this article, we investigate the dynamics of the solutions of the following non-linear difference equation xn+1 = xn-2xn-3 - 1; n ? ?0 with arbitrary initial conditions x-2; x-1; x0. Besides, we have studied peri- odic ...

In this paper we investigate the stability of solutions of difference equation x(n+1) = x(n-1)x(n-4) - 1. We also study periodic solutions of related difference equation especially asymptotic periodicity.