Global Behavior of Nonnegative Solutions to a Higher Order Difference Equation  

作　　者：SHI Qi-hong YANG Jian-wei WANG Chang-you 

机构地区：[1]Department of Basic Sciences,Hebei Finance University,Baoding 071051,China [2]College of Mathematics and Information Science,North China University of Water Resources and Electric Power,Zhengzhou 450011,China [3]College of Mathematics and Physics,Chongqing University of Posts and Telecommunications,Chongqing 400065,China [4]Key Laboratory of Network control and Intelligent Instrument,Ministry of Education,Chongqing 400065,China

出　　处：《Chinese Quarterly Journal of Mathematics》2012年第2期280-285,共6页数学季刊（英文版）

基　　金：Supported by the Science and Technology Project of Chongqing Municiple Education Commission(KJ110501);Supported by the Research Initiation Project for High-level Talents of North China University of Water Resources and Electric Power(201035);Supported by the NSF of the Hebei Higher Education Institutions(Z2011111)

摘　　要：This paper is concerned with the following nonlinear difference equation:x_(n+1)=sum from i=1 to l A_(s_i)x_(n-s_i)/B+C multiply from j=1 to k x_(n-t_j) +D_x_n,n=0,1,…(1.1).The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique,which extends and includes partially corresponding results obtained in the references [6-9].The global behavior of the solutions is investigated.In addition,in order to support analytic results,some numerical simulations to the special equations are presented.This paper is concerned with the following nonlinear difference equation： xn＋1=∑l i=1Asi xn-s;/B＋CП k j=1xn-tj＋Dxn,n=0,1,… The more simple sufficient conditions of asymptotic stability are obtained by using a smart technique, which extends and includes partially corresponding results obtained in the references [6-9]. The global behavior of the solutions is investigated. In addition, in order to support analytic results, some numerical simulations to the special equations are presented.

关 键 词：local stability difference equation equilibrium point global attractor 

分 类 号：O175.07[理学—数学]