一种双寡头垄断Cournot-Puu模型的混沌控制研究

都琳; 张莹; 胡高歌; 雷佑铭

doi:10.21656/1000-0887.370256

一种双寡头垄断Cournot-Puu模型的混沌控制研究

doi: 10.21656/1000-0887.370256

西北工业大学理学院, 西安 710072

基金项目: 国家自然科学基金（11672233;11302169；11672232）；中央高校基本科研业务费（3102014JCQ01081）

详细信息

作者简介:
都琳(1981—)，女，副教授，博士(通讯作者. E-mail：lindu@nwpu.edu.cn).

中图分类号: O415.5
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- 被引次数: 0
出版历程
- 收稿日期: 2016-08-18
- 修回日期: 2016-09-19
- 刊出日期: 2017-02-15

Chaos Control for the Duopoly Cournot-Puu Model

School of Natural and Applied Sciences, Northwestern Polytechnical University,Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11672233; 11302169；11672232）

摘要

摘要: 基于非线性动力学的基本原理，研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本，离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上，结合Cournot-Puu模型的基本特征，应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下，对该模型的输出进行调整并实现混沌控制.
- Cournot-Puu模型 /
- 混沌控制 /
- 延迟反馈控制 /
- 自适应控制
Abstract: Based on the linearization method for nonlinear dynamics and the linear stability theorem, the duopoly Cournot-Puu model and the associated chaos control methods were investigated. In view of the essential features of the model, the delayed feedback control (DFC) method and the adaptive control method were applied to address the chaotic behavior of this system and to control chaos during the output adjustment process in the actual economic sense. The theoretical formulations were numerically simulated. Furthermore, the rational value ranges of the control parameters were given and the economic meanings of both the introduced control methods were discussed.
- Cournot-Puu model /
- chaos control /
- delayed feedback control /
- adaptive control

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参考文献(19)

[1]	Lorenz E N. Deterministic nonperiodic flow[J]. Journal of the Atmospheric Sciences,1963,20(2): 130-141.
[2]	Mackey M C, Glass L. Oscillation and chaos in physiological control systems[J]. Science,1977,197(4300): 287-288.
[3]	Lüscher E, Hübler A. Resonant stimulation of complex systems[J]. Helvetica Physica Acta,1989,62(5): 544-551.
[4]	Ott E, Grebogi C, Yorke J A. Controlling chaos[J]. Physical Review Letters,1990,64(11): 1196-1199.
[5]	Matsumoto A. Controlling the Cournot-Nash chaos[J]. Journal of Optimization Theory and Applications,2006,128(2): 379-392.
[6]	YANG Tao, YANG Lin-bao, YANG Chun-mei. Theory of control of chaos using sampled data[J]. Physics Letters A,1998,246(3/4): 284-288.
[7]	Medio A, Pireddu M, Zanolin F. Chaotic dynamics for maps in one and two dimensions: a geometrical method and applications to economics[J]. International Journal of Bifurcation and Chaos,2009,19(10): 3283-3309.
[8]	Akhmet M, Akhmetova Z, Fen M O. Chaos in economic models with exogenous shocks[J]. Journal of Economic Behavior & Organization,2014,106: 95-108.
[9]	YI Qi-guo, ZENG Xiang-jin. Complex dynamics and chaos control of duopoly Bertrand model in Chinese air-conditioning market[J]. Chaos, Solitons & Fractals,2015,76: 231-237.
[10]	Tacha O I, Volos Ch K, Kyprianidis I M, et al. Analysis, adaptive control and circuit simulation of a novel nonlinear finance system[J]. Applied Mathematics and Computation,2016,276: 200-217.
[11]	Puu T. Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in Economics [M]. New York: Springer, 2000.
[12]	Cánovas J S, Medina D L. Topological entropy of Cournot-Puu duopoly[J]. Discrete Dynamics in Nature and Society,2010,2010: 506940. doi: 10.1155/2010/506940.
[13]	Cánovas J S. Reducing competitors in Cournot-Puu oligopoly[J]. Nonlinear Analysis: Real World Applications,2012,13(4): 1772-1779.
[14]	Tramontana F, Elsadany A A, Xin B, et al. Local stability of the Cournot solution with increasing heterogeneous competitors[J]. Nonlinear Analysis: Real World Applications,2015,26: 150-160.
[15]	HU Gao-ge, GAO She-sheng, GAO Bing-bing. Chaos control in Cournot-Puu model[C]// Shao J, Zhang Y Q, ed. Current Development of Mechanical Engineering and Energy . 2014: 1189-1194.
[16]	Ahmed E, Elettreby M F. Controls of the complex dynamics of a multi-market Cournot model[J]. Economic Modelling,2014,37: 251-254.
[17]	李佼瑞, 白冰冰. 时滞异质三寡头模型的分岔和混沌控制[J]. 数学的实践与认识, 2015,45(6): 212-219.(LI Jiao-rui, BAI Bing-bing. Bifurcation and chaos control of a delayed heterogenous trioploly model[J]. Mathematics in Practice and Theory,2015,45(6): 212-219.(in Chinese))
[18]	WU Wen-juan, CHEN Zeng-qiang, Ip W H. Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model[J]. Nonlinear Analysis: Real World Applications,2014,11(5): 4363-4377.
[19]	CHEN Liang, CHEN Guan-rong. Controlling chaos in an economics model[J]. Physica A: Statistical Mechanics and Its Applications,2007,374(1): 349-358.