Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 214309 8 pages doi 2009 214309 Research Article Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation Chang-you Wang 1 2 3 Fei Gong 2 4 Shu Wang 3 Lin-rui Li 3 and Qi-hong Shi3 1 College of Mathematics and Physics Chongqing University of Posts and Telecommunications Chongqing 400065 China 2 Key Laboratory of Network Control Intelligent Instrument Chongqing University of Posts and Telecommunications Ministry of Education Chongqing 400065 China 3 College of Applied Sciences Beijing University of Technology Beijing 100124 China 4 College of Automation Chongqing University of Posts and Telecommunications Chongqing 400065 China Correspondence should be addressed to Chang-you Wang wangcy@ Received 17 February 2009 Accepted 17 September 2009 Recommended by Elena Braverman We study the asymptotic behavior of the solutions for the following nonlinear difference equation xn 1 2i 1 Aktxn-kt B0 S 1 BiỊxn-iì n 0 1 where the initial conditions x-r x-r 1 x1 x0 are arbitrary nonnegative real numbers k1 ks l1 it are nonnegative integers r max k1 ks l1 lt and Ak1 Aks B0 Bi1 Bit are positive constants. Moreover some numerical simulations to the equation are given to illustrate our results. Copyright 2009 Chang-you Wang 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. 1. Introduction Difference equations appear naturally as discrete analogues and in the numerical solutions of differential and delay differential equations having applications in biology ecology physics and so forth 1 . The study of nonlinear difference equations is of paramount importance not only in their own field but in understanding the behavior of their differential counterparts. There has been a lot of work .