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Discrete Dynamics in Nature and Society
Volume 2007, Article ID 73849, 6 pages
Research Article

Dynamics of a Class of Higher Order Difference Equations

Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Beograd 11000, Serbia

Received 16 October 2007; Revised 11 November 2007; Accepted 29 November 2007

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.


We prove that all positive solutions of the autonomous difference equation xn=αxnk/(1+xnk+f(xn1,,xnm)),n0, where k,m, and f is a continuous function satisfying the condition βmin{u1,,um}f(u1,,um)βmax{u1,,um} for some β(0,1), converge to the positive equilibrium x¯=(α1)/(β+1) if α>1.