Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 860152, 12 pages
doi:10.1155/2008/860152
Research Article
On the Global Asymptotic Stability of a Second-Order System of Difference Equations
Department of Mathematics, Faculty of Education, University of Selcuk, 42099 Meram Yeni Yol, Konya, Turkey
Received 4 June 2008; Accepted 8 September 2008
Academic Editor: Guang Zhang
Copyright © 2008 Ibrahim Yalcinkaya. 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.
Abstract
A sufficient condition is obtained for the global asymptotic
stability of the following system of difference equations zn+1=(tnzn−1+a)/(tn+zn−1), tn+1=(zntn−1+a)/(zn+tn−1), n=0,1,2,…, where the parameter aϵ(0,∞) and the initial values (zk,tk)ϵ(0,∞) (for k=−1,0).