Author(s)

Tarek F. Ibrahim Ibrahim

Department of Mathematics, Faculty of Sciences and arts (S. A.) King Khalid University, Abha , Saudi Arabia.

Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system a_n+1=f(a_n) determines a difference equation and vise versa. We ob-tain in this paper the solution and periodicity of the following difference equation. xn+1=(x_nx_n-2x_n-4)/(x_n-1x_n-3x_n-5, (1) n=0,1,... where the initial conditions x_-5,x_-4,x_-3,x_-2,x_-1 and x₀ are arbitrary real numbers with x_-1,x_-3 and x_-5 not equal to be zero. On the other hand, we will study the local stability of the solutions of Equation (1). Moreover, we give graphically the behavior of some numerical examples for this difference equation with some initial conditions.

Difference Equation; Solutions; Periodicity; Local Stability

T. Ibrahim, "Periodicity and Solution of Rational Recurrence Relation of Order Six," Applied Mathematics, Vol. 3 No. 7, 2012, pp. 729-733. doi: 10.4236/am.2012.37107.