Advances in Difference Equations
Volume 2009 (2009), Article ID 235691, 13 pages
doi:10.1155/2009/235691
Dynamics for Nonlinear Difference Equation xn+1=(αxn−k)/(β+γxn−lp)
Dongmei Chen1
, Xianyi Li1
and Yanqin Wang3
1College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, China
3School of Physics \& Mathematics, Jiangsu Polytechnic University, Changzhou, 213164 Jiangsu, China
Abstract
We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ones.