DYNAMICAL ANALYSIS OF A NON-LINEAR DIFFERENCE EQUATION.

In this article, we investigate the dynamics of the solutions of the following non-linear di¤erence equation xn+1 = xn-2xn-3 - 1; n ∞ N0 with arbitrary initial conditions x-2; x-1; x0. Besides, we have studied periodic behaviours of related di¤erence equation especially asymptotic periodicity and eventually periodicity. Then, we have researched unbounded solutions of di¤erence equation. [ABSTRACT FROM AUTHOR]