Dynamics of a Class of Higher Order Difference Equations

Iricanin, Bratislav D.

doi:https://doi.org/10.1155/2007/73849

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2007 | Article ID 073849 | https://doi.org/10.1155/2007/73849

Dynamics of a Class of Higher Order Difference Equations

Bratislav D. Iricanin¹

Received16 Oct 2007

Revised11 Nov 2007

Accepted29 Nov 2007

Published26 Feb 2008

Abstract

We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1.

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Copyright

Copyright © 2007 Bratislav D. Iričanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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