一类高维指数型差分方程正解的渐近性  

Asymptotic Behavior of the Positive Solutions of A High-Dimensional System of Difference Equations Having Exponential Terms

作　　者：韦志坚[1] 吴琪琪 WEI Zhi-jian;WU Qi-qi(College of Mathematics and Econometrics, Hunan University, Changsha 410082 ,China)

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2017年第5期639-641,共3页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：教育部留学回国人员科研启动基金资助项目(教外司留(2013)693号)

摘　　要：研究一类高维指数型差分方程模型x_(n+1)^(i)=a_i+b_ix_(n-1)^(i+1)e^(-x(ni)(i=1,2,…,m)正解的渐近性,其中a_i和b_i是正常数,且初始值x_(-1)^(i)和x_0^(i)是正实数值,x_(n-1)^(m+1)=x_(n-1)^(1)(n=0,1,2,…),获得该方程正平衡点的存在唯一性及正解的有界性、持久性和收敛性的一些充分条件,所得结果推广了已有文献的相关结论.A asymptotic behavior of the positive solutions of the high-dimensional exponential system of difference equationsxn＋1^（i）=ai＋bixn-1i＋1e^（-x（ni）（i=1,2,…,m）,is studied where ai,bi are positive constants, the initial values x（-1）^（i）,x0^（i） are positive real numbers and xn-1m＋1=xn-11（n=0,1,2,…）. We investigate the existence and uniqueness of positive equilibrium point,the boundedness,persistence and asymptotic behavior of the positive solutions of such a system. In particular, our results extend the corresponding ones in the literature.

关 键 词：差分方程系统 正平衡点 有界性 持久性 收敛性 

分 类 号：O175.7[理学—数学]