Copyright © 2009 Meseret Tuba Gülpinar and Mustafa Bayram. 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.
Our aim is to
investigate the global behavior of the following
fourth-order rational difference equation:
, where and the initial values . To verify that the positive equilibrium point of the
equation is globally asymptotically stable, we used the rule of
the successive lengths of positive and negative semicycles of
nontrivial solutions of the aforementioned equation.