动态经济分析中自治差分方程组的均衡值与收敛性

Equilibrium Value and Convergence of Autonomous Difference Equations in Dynamic Economic Analysis

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组,并给出自治差分方程组的均衡值及其存在条件;以坐标变换为研究工具将自治差分方程组的通解表达为关于系数矩阵的特征根与特征向量的标准型,研究了通解随时间收敛于均衡值的充要条件,以及收敛性与系数矩阵之间的关系问题,借以分析动态经济系统的稳定性.

This paper forms autonomous equations from some important economic models,and points out the equilibrium value and its existent condition. It expresses the general solution of a difference equations in a standard form of eigenvalues and eigenvectors,and gives a detail study on the condition in which autonomous difference equations solution is converged to equilibrium value in accordance with time and the relation between equation coefficients matrix and convergence,so as to analyze the stable situation of dynamic economic models.