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一类三阶非线性递归差分方程的全局渐近稳定性与振动性(英文)
引用本文:曾春花,张建勋,罗永超,陈军刚.一类三阶非线性递归差分方程的全局渐近稳定性与振动性(英文)[J].生物数学学报,2010(3):431-441.
作者姓名:曾春花  张建勋  罗永超  陈军刚
作者单位:[1]凯里学院理学院,贵州凯里556011 [2]宁波大学理学院,浙江宁波315211 [3]宁波大学科技学院,浙江宁波315211
基金项目:Supported by the Science Foundation of Guizhou Educational Committee for Young Scholar(No.Qianjiaoke2008080); The Key Subject Programs of Kaili University (No.KZD2009001)
摘    要:研究了一类三阶方程x_(n+1)=x_nx_(n-2)+a/x_n+x_(n-2)+b,n=0,1,…的解的振动性和正解的全局渐近稳定性,证明了正平衡解的全局渐近稳定,非平衡解具有规律的振动性.

关 键 词:差分方程  正解  全局渐近稳定  半环

Global Asymptotic Stability and Oscillation of a Third Order Nonlinear Recursive Difference Equation
ZENG Chun-hua,ZHANG Jian-xun,LUO Yong-chao,CHEN Jun-gang.Global Asymptotic Stability and Oscillation of a Third Order Nonlinear Recursive Difference Equation[J].Journal of Biomathematics,2010(3):431-441.
Authors:ZENG Chun-hua  ZHANG Jian-xun  LUO Yong-chao  CHEN Jun-gang
Institution:1 College of Science,Kaili University,Kaili Guizhou 556011 China) (2 Faculty of science,Ningbo University,Ningbo Zhejiang 315211 China) (3 Faculty of science and technology,Ningbo University,Ningbo Zhejiang 315211 China)
Abstract:In this paper,we investigate the oscillatory behavior and the global asymptotic stability of solutions of the equation x_(n+1)=x_nx_(n-2)+a/x_n+x_(n-2)+b,n=0,1,...,where a0,b0.We show that trivial solutions have regular oscillatory behavior and the positive equilibrium of the equation is global asymptotic stability.
Keywords:Difference equation  Positive solution  Global asymptotic stability  Semicycle
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