二阶有理型非线性差分方程二周期正解的局部稳定性  

Local Stability of Two Periodic Positive Solutions of a Second Order Rational Nonlinear Difference Equation

作　　者：张丽春[1] 黄庆道[2] 杨月婷[1] 蔡淑云[1] 

机构地区：[1]北华大学数学与统计学院,吉林吉林132033 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2016年第3期451-456,共6页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅"十二五"科学技术研究项目(批准号:2011152);吉林省教育厅"十二五"规划项目(批准号:GH150078)

摘　　要：应用稳定流形定理研究二阶有理型非线性差分方程x_(n+1)=a-bx_n/A+x_(n-1),n=0,1,2,…二周期正解的局部稳定性,其中A,b>0,a≥0均为实数,且初始条件x_(-1)和x_0为任意正实数.结果表明,该二阶非线性差分方程的正平衡点是稳定的,最小二周期正解是不稳定的.Using the stable manifold theorem,we studied the local stability of two periodic positive solutions of second order rational nonlinear difference equationa xn＋1=a-bxn/A＋xn-1,n=0,1,2,…where A,b〉0,a≥0were real numbers,and initial conditions x-1and x0 were arbitrary positive real numbers.The results show that the positive equilibrium point of the second order nonlinear difference equation is stable,and the minimum two periodic positive solution is unstable.

关 键 词：二阶 差分方程 二周期解 局部渐近稳定性 

分 类 号：O175[理学—数学]