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

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Published

2010-04-09

How to Cite

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

Issue

Vol. 3 No. 2: (April 2010)

Section

Nonlinear Analysis

License

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European Journal of Pure and Applied Mathematics will be Copyright Holder.