tailieunhanh - báo cáo hóa học:" Research Article Asymptotic Behavior of Equilibrium Point for a Family of Rational Difference Equations"

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 Family of Rational Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 505906 10 pages doi 2010 505906 Research Article Asymptotic Behavior of Equilibrium Point for a Family of Rational Difference Equations Chang-you Wang 1 2 3 Qi-hong Shi 4 and Shu Wang3 1 College of Mathematics and Physics Chongqing University of Posts and Telecommunications Chongqing 400065 China 2 Key Laboratory of Network Control and 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 Fundamental Department Hebei College of Finance Baoding 071051 China Correspondence should be addressed to Chang-you Wang wangcy@ Received 7 August 2010 Accepted 19 October 2010 Academic Editor Rigoberto Medina Copyright 2010 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. This paper is concerned with the following nonlinear difference equation xn 1 2Í 1 As xn-Si B cn 1xn-tj Dxn n 0 1 . where the initial data x-m x-m 1 . x-1 x0 e R m max s1 . si t1 . tk s1 . Si t1 . tk are nonnegative integers and ASi B C and D are arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium x 0 of this equation is globally asymptotically stable which extends and includes corresponding results obtained in the work of Cinar 2004 Yang et al. 2005 and Berenhaut et al. 2007 . In addition some numerical simulations are also shown to support our analytic results. 1. Introduction Difference equations appear naturally as discrete analogues and in the numerical solutions of differential and delay differential equations and they have applications in biology ecology physics and so forth 1 . The study of properties of nonlinear .