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

Authors

  • Elsayed M. Zayed Prof

Keywords:

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

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

Author Biography

  • Elsayed M. Zayed, Prof
    no

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Published

2010-04-09

Issue

Section

Nonlinear Analysis

How to Cite

Dynamics of the Nonlinear Rational Difference Equation Xn+1 = AXn + BXn−k + (pXn+Xn−k) / (q+Xn-k). (2010). European Journal of Pure and Applied Mathematics, 3(2), 254-268. https://ejpam.com/index.php/ejpam/article/view/447

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