Dynamics of the Nonlinear Rational Difference Equation Xn+1 = AXn + BXn−k + (pXn+Xn−k) / (q+Xn-k)

Elsayed M. Zayed

Abstract

In this article, we study the global stabitity and the asymptotic properties of the nonnegative solutions of the nonlinear di

Xn+1 = AXn + BXn−k + (pXn + Xn−k) / (q + Xn−k) , n = 0, 1, 2, .....

where the parameters

A, B, p, q and the initial conditions x−k,..., x−1, x0 are arbitrary nonnegative real numbers, while k is a positive integer number. Some numerical examples will be given to illustrate our results.fference equation

Keywords

Difference equations, Prime period two solution, Locally asymptotically stable, Global attractor, Global stability

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