Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 610467, 17 pages
doi:10.1155/2010/610467

Boundedness and global attractivity of a higher-order nonlinear difference equation

Xiu-Mei Jia1 and Wan-Tong Li2

1Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China
 2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

Abstract

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn+1=(r+pyn+yn−k)/(qyn+yn−k), n∈ℕ0, where the parameters p,q,r∈(0,∞),k∈{1,2,3,…} and the initial conditions y−k,…,y0∈(0,∞). We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.