Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 364083, 13 pages
doi:10.1155/2010/364083
Research Article

On Global Attractivity of a Class of Nonautonomous Difference Equations

Wanping Liu,1 Xiaofan Yang,1,2 and Jianqiu Cao2

1College of Computer Science, Chongqing University, Chongqing 400044, China
2School of Computer and Information, Chongqing Jiaotong University, Chongqing 400074, China

Received 28 February 2010; Accepted 28 June 2010

Academic Editor: Guang Zhang

Copyright © 2010 Wanping Liu 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.

Abstract

We mainly investigate the global behavior to the family of higher-order nonautonomous recursive equations given by yn=(p+ryn-s)/(q+ϕn(yn-1,yn-2,…,yn-m)+yn-s), n∈ℕ0, with p≥0,r,q>0,s,m∈ℕ and positive initial values, and present some sufficient conditions for the parameters and maps ϕn:(ℝ+)m→ℝ+,n∈ℕ0, under which every positive solution to the equation converges to zero or a unique positive equilibrium. Our main result in the paper extends some related results from the work of Gibbons et al. (2000), Iričanin (2007), and Stević (vol. 33, no. 12, pages 1767–1774, 2002; vol. 6, no. 3, pages 405–414, 2002; vol. 9, no. 4, pages 583–593, 2005). Besides, several examples and open problems are presented in the end.