非线性非均衡蛛网模型的稳定性分析

发布时间：2018-06-22 05:09

本文选题：混沌 + 非均衡　；参考：《华侨大学》2002年硕士论文

【摘要】： 通常，关于单商品市场价格波动的稳定性问题，是在供需均衡的条件下进行研究的，称为“蛛网模型”。传统的蛛网模型假定供给函数和需求函数均为线性且每一期的供给与需求均衡，在现实的经济系统中，这两个假定条件都是难以成立的。其“线性”假定只能描述蛛网模型中的收敛、发散、2个周期闭合3种运动类型，不能刻画最常出现的各种周期运动及混沌现象。其“均衡”假定不能反映现实经济运行经常处于非均衡状态这一基本现象。据此，，本文将非均衡理论及非线性混沌理论同时应用于市场价格模型中进行研究，对传统的蛛网模型加以改进，从现实经济系统运作的实际情况出发，建立更加准确、科学，更能反映经济现实的非线性非均衡蛛网模型，并对所建立的模型进行动态分析，研究了各种参数条件下价格波动的稳定性问题，从而得到若干结论。这些结论都是通过严格的数理经济学方法推导而得，因此，结论是可信的，符合经济现实。本文不论是对于经济的理论分析还是实际的经济预测都有一定的参考价值。因此，本项工作是有创新价值和重要意义的。本文研究的基本结构如下：第一章：引言本章简要阐述论文主题思想和分析方法，包括选题来源、理论意义和分析方法三个部分。第二章：混沌经济学、非均衡经济学的基本知识与研究现状本章主要涉及与本文有关的混沌经济学、非均衡经济学的基本概念，混沌理论的产生和发展简介以及混沌理论、非均衡理论在经济学中的应用三个方面。第三章：一般化蛛网模型的分析本章是本文研究的核心和重点之一。主要研究了对形如模型(Ⅰ)的一般化蛛网模型的动态分析与稳定性问题，主要包括三个方面工作：一是建立模型并给出经济含义；二是对模型进行动态分析，证明了由模型(Ⅰ)所生成的价格系列在一定的条件下不会出现3以上周期运动和混沌现象；三是对模型进行稳定性分析，并得到模型(Ⅰ)关于均衡价格稳定的六个定理。第四章：对具体几个蛛网模型的分析本章是本文研究的核心和重点之二，主要研究了对于供给函数或需求函数为特定非线性形式的几个蛛网模型的动态分析与稳定性问题，分别对需求函数或供给函数为非线性函数时的蛛网模型，进行了动态分析和稳定性分析，从而得出了其均衡价格的存在条件及稳定区间。第五章：逻辑斯蒂方程在蛛网模型分析中的应用本章研究了逻辑斯蒂方程的演化机制，并将它应用在一类蛛网模型的研究中，对模型进行动态分析和稳定性分析，研究了各种参数条件下的性态，确定了经济系统达到稳定状态的参数范围及进入混沌状态的参数范围。第六章：基于混沌经济学的我国边际消费倾向分析本章从混沌经济学的角度对我国居民的边际消费倾向进行了分析，得出我国的消费系统正处于稳定状态，符合我国经济实际。
[Abstract]:The traditional cobweb model assumes that both the supply function and the demand function are linear and the supply and demand of each stage are balanced . In the real economic system , the two assumption conditions are difficult to be established .

In this paper , the non - equilibrium theory and nonlinear chaos theory are applied to the market price model , and the traditional cobweb model is improved . Based on the actual situation of the operation of the real economy system , this paper establishes a more accurate , scientific and more realistic nonlinear non - equilibrium cobweb model , and studies the stability of price fluctuation under various parameters . Therefore , the conclusion is credible and conforms to the economic reality .

The basic structure of this study is as follows :

Chapter One : Introduction This chapter provides a brief description of the paper ' s theme thoughts and analysis methods , including the source of choice , the theoretical significance and the analysis method .

Chapter 2 : The basic knowledge and research status of chaos economics and non - equilibrium economics mainly deals with the basic concepts of chaos economics , non - equilibrium economics , the generation and development of chaos theory , and the application of chaos theory and non - equilibrium theory in economics .

Chapter 3 : The analysis of generalized cobweb model is one of the core and focus of this paper . The dynamic analysis and stability of generalized cobweb model like model ( I ) are studied , including three aspects : firstly , establishing model and giving economic meaning ;
Second , the dynamic analysis of the model proves that the price series generated by the model ( I ) does not exhibit more than 3 cycles of motion and chaos under certain conditions ;
Thirdly , the stability analysis of the model is carried out , and six theorems for equilibrium price stability are obtained .

In the fourth chapter , this chapter is the core and key part of the study , which mainly studies the dynamic analysis and stability of several cobweb models in the form of supply function or demand function for a certain nonlinear form . The cobweb model of the demand function or the supply function as non - linear function is analyzed and the stability analysis is carried out respectively , and the existence condition and stable interval of equilibrium price are obtained .

In the fifth chapter , the logistic equation is applied to the analysis of cobweb model , the evolution mechanism of logistic equation is studied , and it is applied in the research of a kind of spider - net model . The dynamic analysis and stability analysis of the model are carried out , and the characteristics under various parameters are studied . The parameters range of the economic system reaching the steady state and the parameter range of entering the chaos state are determined .

Chapter 6 : This chapter analyzes the marginal consumption tendency of Chinese residents from the perspective of chaos economics , and concludes that our country ' s consumption system is in a stable state and conforms to our country ' s economic reality .
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2002
【分类号】：F019

【参考文献】