一类差分方程的稳定性研究  

ON THE STABILITIES OF A CLASS OF DIFFERENCE EQUATIONS

作　　者：徐胜荣[1] 王希超[1] 周营营[1] 

机构地区：[1]山东农业大学信息科学与工程学院,山东泰安271000

出　　处：《山东农业大学学报（自然科学版）》2013年第4期624-629,共6页Journal of Shandong Agricultural University：Natural Science Edition

摘　　要：本文研究差分方程x n+1=βx n-k+γx n-l/A+Bx n-k+Cx n-l,n=1,2,…,其中系数β,γ,A,B,C和初始变量x-l,…,x-k,…,x-1,x0均为正实数,k∈{0,1,2,…},l∈{1,2,…},k<l.在变量代换的基础上,通过线性化方程及其特征方程的根,讨论正平衡点的局部渐近稳定性;通过单调性和有界性的研究,讨论正平衡点的全局吸引性.得到了正平衡点局部渐近稳定的充分条件和全局渐近稳定的充分条件。In this paper, we study the difference equation xn＋1=βxn-k＋γxn-l/A＋Bxn-k＋Cxn-l,n=1,2,…,where the parameters β,γ,A,B,C and the initial conditions x-1,…,x-k,…,x-1,x0 are all positive real numbers,k∈{0,1,2,…},l∈{1,2,…},k〈2 Based on the change of variables, we investigate the local asymptote stability by linearized equation and the roots of its characteristic equation, and investigate the global asymptote stability by considering the monotonicity and the boundedness . We obtain the sufficient conditions in which the positive equilibria is locally asymptotically stable, and those in which the positive equilibria is globally asymptotically stable.

关 键 词：差分方程 平衡点 局部渐近稳定 全局渐近稳定 

分 类 号：O241.84[理学—计算数学]