经济动态系统的一种几何描述框架——Lagrange体系模型

A Kind of Geometric Framework of Economic Dynamic Systems——Lagrangian Models

为方便地将物理学中的对称性分析方法应用到经济动态系统的研究中,从而揭示经济系统所内蕴的特性及其运行规律,给出了一种以Lagrange体系模型形式将主流经济学中的大多数经济动态模型纳入到统一的描述框架中,建立了所谓的经济Vakonomic模型.这种描述框架的特点是:经济动态系统被赋予了一种几何结构,其中应用了微分流形和辛结构的数学方法,同时揭示了经济动态系统与物理系统之间具有某种相似性.

The aim of the research is the achievement of conveniently applying the method of physic symmetric analysis in economic dynamic systems in order to uncover characteristics and evolving laws implied in economic dynamic systems. A unified framework which can be well adapted to describe a majority of dynamic economic models in mainstream economics by using the form of a kind of Lagrangian model was presented, and a so-called economic Vakonomic model was built. The feature of this framework is. the dynamic economic systems are endowed with a geometric structure by means of the mathematical method of differential manifold and symplectic structure, meanwhile some analogue between the economic dynamic systems and physic systems was established.