自然科学版
陕西师范大学学报(自然科学版)
数学与计算机科学
动态Bertrand模型的复杂现象与混沌控制
姚洪兴1, 王梅2
(1 江苏大学 财经学院; 2 理学院, 江苏 镇江 212013 )
姚洪兴,男,教授,博士生导师,研究方向为经济系统复杂性建模与分析。E-mail:hxyao@ujs.edu.cn
摘要:
建立了基于特定需求函数的Bertrand双寡头垄断模型,分析了垄断市场下生产同质产品的企业竞争现象。应用有限理性法和不完全信息法实现了竞争模型由静态到动态的转化过程。进一步求解了动态模型的价格均衡解,并分析了均衡点的稳定状态。针对模型中出现的复杂现象提出了不同的混沌控制法,实现了垄断市场由混乱到稳定的回归。
关键词:
Bertrand模型; 有限理性; 不完全信息; 分叉; 混沌
收稿日期:
2014-10-10
中图分类号:
O211; F224.9; F270
文献标识码:
A
文章编号:
1672-4291(2015)02-0024-04doi:10.15983/j.cnki.jsnu.2015.02.221
基金项目:
国家自然科学基金资助项目(71271103,71371087,71271107)
Doi:
The complex phenomena and the chaos control of Bertrand model
YAO Hongxing1,WANG Mei2
(1 School of Economic; 2 School of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China)
Abstract:
Based on the specific demand function, a duopoly Bertrand model is established.The enterprise competition phenomenon in producing homogeneous products under the monopoly market is analyzed. The competition model is transformed from static medel to dynamic model by bounded rationality and incomplete information method. Under such condition, the price equilibrium solution of the dynamic model and the steady state of equilibrium points are obtained. The regression of monopoly market from chaos to stable is achieved by different chaos control methods.
KeyWords:
Bertrand model; bounded rationality; incomplete information; bifurcation; chaos