非线性自治差分方程模型的稳定性分析  

Convergent Analysis of Nonlinear Autonomous Difference Equations Models

作　　者：董庆华[1] 戴桂冬[1] DONG Qing-hua DAI Gui-dong(Elements Department, Beijing Institute of Fashion Technology, Beijing 100029, China)

机构地区：[1]北京服装学院基础教学部,北京100029

出　　处：《北京服装学院学报（自然科学版）》2016年第2期79-84,共6页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：北京服装学院创新团队与优秀人才选拔与培养计划项目(编号:PTTBIFT005)的阶段性研究成果之一

摘　　要：以动态分析的方法将西方经济学中一些重要经济系统抽象为自治差分方程,在深化线性自治差分方程稳定性的基础上,以矩阵和相图为研究工具,探索了非线性自治差分方程和方程组在均衡值附近的稳定性,给出了非线性自治差分方程和方程组局部收敛于均衡值的充要条件.In this paper,autonomous difference equation models were established based on some important dynamic economic systems. Upon the analysis of the convergence of linear autonomous difference equations,a detail study using matrix and phase portrait as research tools was conducted to explore the convergence of nonlinear autonomous difference equations near their equilibrium values.The sufficient and necessary conditions for local convergence of nonlinear autonomous difference equations and equations systems to their equilibrium values were given.

关 键 词：动态经济系统 自治差分方程 稳定性分析 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]