T. F. Ibrahim, “Dynamics of a Rational Recursive Sequence of Order Two,” International Journal of Mathematics and Computation, Vol. 5, No. D09, 2009, pp. 98105.
has been cited by the following article:
- TITLE: Periodicity and Solution of Rational Recurrence Relation of Order Six
- AUTHORS: Tarek F. Ibrahim Ibrahim
- KEYWORDS: Difference Equation; Solutions; Periodicity; Local Stability
JOURNAL NAME: Applied Mathematics
Sep 05, 2014
- ABSTRACT: Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system an+1=f(an) determines a difference equation and vise versa. We ob-tain in this paper the solution and periodicity of the following difference equation. xn+1=(xnxn-2xn-4)/(xn-1xn-3xn-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.