Advances in Difference Equations
Volume 2010 (2010), Article ID 679409, 9 pages
Research Article

Dynamical Properties in a Fourth-Order Nonlinear Difference Equation

1School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China
2College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, China

Received 21 October 2009; Accepted 29 March 2010

Academic Editor: Jianshe S. Yu

Copyright © 2010 Yunxin Chen and Xianyi Li. 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.


The rule of trajectory structure for fourth-order nonlinear difference equation xn+1=(xan2+xn3)/(xan2xn3+1), n=0,1,2,, where a[0,1) and the initial values x3,x2,x1,x0[0,), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4+,3,1+,2,2+,1,1+, 1 in a period. By utilizing this rule its positive equilibrium point is verified to be globally asymptotically stable.