Copyright © 2010 Guo-Mei Tang et al. 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 consider the higher-order nonlinear difference equation , , where parameters are positive real numbers and initial conditions are
nonnegative real numbers, . We investigate the periodic character, the invariant
intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the unique equilibrium of the equation is globally
asymptotically stable under certain conditions.