tailieunhanh - Báo cáo hóa học: "Research Article On the Difference Equation xn"

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 On the Difference Equation xn | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 876936 7 pages doi 2008 876936 Research Article On the Difference Equation xn 1 axn ộxn-1 e Xn Xiaohua Ding1 and Rongyan Zhang2 1 Department of Mathematics Harbin Institute of Technology in Weihai Weihai Shandong 264209 China 2 Department of Mathematics Huang He Science and Technology College Zhengzhou Henan 264209 China Correspondence should be addressed to Xiaohua Ding mathdxh@ Received 22 September 2007 Accepted 14 December 2007 Recommended by Istvan Gyori We study a discrete delay Mosquito population equation. Firstly we study the stability of the equilibria of the system and the existence of period-two bifurcation by analyzing the characteristic equation. Secondly the direction and stability of the bifurcation are determined by using the normal form theory. Finally some computer simulations are performed to illustrate the analytical results found. Copyright 2008 X. Ding and R. Zhang. 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 and preliminaries Recently there has been a great interest in studying nonlinear difference equations and systems. One of the reasons for this is a necessity for some techniques which can be used in investigating equations arising in mathematical models describing real-life situations in population biology economy psychology sociology and so forth. Such equations also appear naturally as discrete analogues of differential equations which model various biological and economical systems 1-4 . In this paper we study the following discrete delay Mosquito population equation 1 xn 1 axn fxn e x0 x1 0 n 1 2 3 . where a 0 1 f 0 ot . The equilibrium points of are solutions of the following equation x ax fxfex. 2 Advances in Difference Equations It