Chaotic tatonnement

Summary Debreu's theorem on excess demand functions is used to demonstrate the possibilities of ergodic and topological chaos in a discrete-time tatonnement process with only two goods. The result is in sharp contrast with the well-known result of Arrow and Hurwicz on system stability in a continuous time model of price adjustment with two commodities.We would like to thank Professors Jess Benhabib, Richard Day, John Guckenheimer, Philip Holmes, Nicholas Kiefer and Tapan Mitra.     

Simulating tatonnement in a production economy

Summary. The paper presents some simulation results for a tatonnement process in a simple general equilibrium model with production. It shows that the discrete time tatonnement process can generate periodic and chaotic paths. Received December 14, 1994 revised version April 29, 1996     

A pitchfork bifurcation in the tatonnement process★

Summary . This note extends the example of Gale (1963) by considering the continuous time tatonnement process for a class of two agent, two commodity exchange economies, parametrized by a number μ∈(0,1). We demonstrate that as the parameter passes a threshold value μ^* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as μ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter μ approaches 1, the economy tends to the example considered by Gale, as does the limiting behavior of the tatonnement. Received: February 28, 1996; revised version August 5, 1996     

Trade Gains in Chaotic Equilibria

It is shown by means of an overlapping-generations (OLG) example that free international trade may be both deterministically chaotic and gainful in the sense of Pareto to a participating country.     

中国证券市场的混沌性检验

本文研究发现上证综指和深成指的日、周和月序列均是协方差平稳的,但是由于它们表现出随时间变化的易变性、长程相关性和过度的偏度与峰度,而这些又是非线性系统的特征,所以它们是非线性动力系统。本文对它们进行了混沌检验,发现我国证券市场中含有奇异吸引子,它控制着价格的运动,它是混沌过程。     

Chaotic Equilibrium Dynamics in Endogenous Growth Models

We study a class of two-sector endogenous growth models in the presence of a positive external effect. The class of models exhibits global indeterminacy of equilibria. The qualitative properties of a set of examples are analyzed by means of analytical and numerical methods. We also construct robust examples of both topological and ergodic chaos. Journal of Economic Literature Classification Numbers: E30, O41.     

Chaotic implications of the natural rate of unemployment

By means of a discrete time, dynamic model this paper shows that, despite correct short-term expectations about price change by all agents concerned, the economy may exhibit chaotic behaviour rather than convergence to a natural, equilibrium rate, when wage bargain takes place according to the usual specification of the Phillips curve while firms maximize profit. The lack of coordination between profit-maximizing firms and wage-bargaining workers may result in an irregular dynamic path which questions whether the natural rate, even if it exists, is at all knowable in these circumstances.     

混沌经济时间序列的建模与系统识别

利用时间序列分析方法对混沌经济时间序列进行研究。通过介绍有关时间序列分析的理论及混沌时间序列的建模方法,阐述了混沌经济时间序列中非线性(混沌)信息的提取方法,并对系统进行混沌识别,讨论了混沌系统混沌临界点的区间确定问题。     

Chaotic consumption patterns in a simple2-D addiction model

Summary.  Consumption fluctuations in a simple 2-D addiction model are investigated. The behavioural equations of the model are suggested by a related ‘rational addiction’ model of Becker and Murphy [2]. Our model generates erratic, seemingly unpredictable consumption patterns of the addicted persons. The occurence of chaos is proven by locating a so called horseshoe map in the phase space. Received: April 4, 1994; revised version March 25, 1996     

On the Existence of Chaotic Policy Functions in Dynamic Optimization

Applying the characterization results from Mitra and Sorger (1999), we show that topological chaos is a robust phenomenon in standard aggregative growth models even under arbitrary mild discounting. Furthermore, we state exact discount factor restrictions, under which two of the most popular examples of chaotic dynamics, the logistic map and the tent map, can be optimal policy functions of aggregative growth models.
JEL Classification Numbers: C61, O41.     

混沌理论在我国货币政策制定和执行中的应用

我国货币政策环境可视作混沌的复杂系统。混沌理论表明,系统在时空上的复杂结构通常隐含着简单的决定性准则,一旦这样的准则被发现,管理当局则可以观察或者控制系统内部的复杂状况,以达到预期目标。运用于货币政策的混沌理论,是指将货币政策环境看作是具有高度复杂性和长期行为不可预测性的混沌系统,其中必然隐含着复杂系统内普遍适用的简单决定性准则。如果我们掌握并始终遵循这一准则,就可以观察并控制货币政策环境这一复杂混沌系统,使货币政策目标向预期的方向发展。     

基于混沌理论的高科技企业创立及管理过程研究

高科技企业的创立和成长过程基本呈现混沌特征,可用Logistic方程进行描述。根据其混沌特性对科技企业进行动态管理,即通过调整研发投入和管理力度的方式,实现对科技创业企业的混沌控制,保证企业的稳定发展。     

Chaotic Equilibria in a Small, Open, Overlapping-Generations Economy with Child–Parent Externality

This paper presents a simple overlapping-generations model of a small open economy with child–parent externality that exhibits chaotic equilibrium dynamics.     

我国证券市场经济混沌探测研究--一种基于小波变换的噪声处理

经济时间序列的变化有长期趋势变动、周期变动以及日常细微波动(噪声),噪声的存在有时会影响系统的分辨率、稳定性,甚至会淹没正常信号。利用小波变换对上证指数和深成指的日收盘价序列进行去噪处理,用去噪后的日收盘价序列计算出日收益率序列,仍能较好地保留序列自身固有的特性,这种方法能满足探测我国证券市场的混沌性所需要的大样本、低噪声的要求。