Chaos Control for the Duopoly Cournot-Puu Model

DU Lin; ZHANG Ying; HU Gao-ge; LEI You-ming

doi:10.21656/1000-0887.370256

Volume 38 Issue 2

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DU Lin, ZHANG Ying, HU Gao-ge, LEI You-ming. Chaos Control for the Duopoly Cournot-Puu Model[J]. Applied Mathematics and Mechanics, 2017, 38(2): 224-232. doi: 10.21656/1000-0887.370256

Citation:

DU Lin, ZHANG Ying, HU Gao-ge, LEI You-ming. Chaos Control for the Duopoly Cournot-Puu Model[J]. Applied Mathematics and Mechanics, 2017, 38(2): 224-232. doi: 10.21656/1000-0887.370256

Citation:

DU Lin, ZHANG Ying, HU Gao-ge, LEI You-ming. Chaos Control for the Duopoly Cournot-Puu Model[J]. Applied Mathematics and Mechanics, 2017, 38(2): 224-232. doi: 10.21656/1000-0887.370256

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Chaos Control for the Duopoly Cournot-Puu Model

doi: 10.21656/1000-0887.370256

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）

Received Date: 2016-08-18
Rev Recd Date: 2016-09-19
Publish Date: 2017-02-15

Abstract

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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References(19)

References

[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.