Stability and convergence of a higher order rational difference Equation
Abstract
In this paper the asymptotic stability of equilibria and periodic points of the following higher order rational difference Equation xn+1 =(alpha xn-k)/(1+xn...xn-k), k>=1, n=0,1,... is studied where the parameters ?alpha, betta, and gamma are positive real numbers, and the initial conditions x-k, ..., x0 are given arbitrary real numbers. The forbidden set of this equation is found and then, the order reduction method is used to facilitate the analysis of its asymptotic dynamics
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