双寡头Bertrand博弈模型动态分析与混沌控制

Dynamic Analysis and Chaos Control in Duopoly Bertrand Game Model

基于价格博弈的Bertrand模型,文章构建四维的离散系统。依据现实经济活动,加入技术吸收效益讨论价格、利润和成本之间的关系。通过构建非线性离散动力系统,对系统的稳定性进行数值仿真。根据Sch-ur-Cohn判断得出内部趋于稳定的条件,延迟结构的时滞系数对系统的稳定性及复杂性有重要影响。并利用反馈控制对延时系统进行混沌控制,混沌现象在延时系统下成功的得到控制,使混沌行为运行于稳定轨迹,企业的市场竞争处于稳定状态,增加了企业的利润和收益。

This paper is based on the Bertrand model of price game to build a four-dimensional discrete system. Firstly, ac- cording to the realistic economic activities, the paper puts in technology absorption efficiency to discuss the relationship between price, profit and cost. Secondly, the paper conducts a numerical simulation of the system＇ s stability by building a non-linear dis- crete dynamic system. Thirdly, according to Schur-Cohn criterion, the paper obtains the condition that tends to be stable inside, and the significant impact of the lag coefficient of delayed system on the stability and complexity of the system. Finally the paper uses feedback to control the chaos of the delayed system and the chaos phenomenon is controlled successfully, which makes the chaos behavior operate in a stable orbit, market competition in a stable status and enterprises get more profit and income.