[1]赵 娜,周 伟*,王文瑞.一类混合双寡头模型的分岔分析与混沌控制[J].江西师范大学学报(自然科学版),2019,(06):605-612.[doi:10.16357/j.cnki.issn1000-5862.2019.06.09]
　ZHAO Na,ZHOU Wei*,WANG Wenrui.The Bifurcation Analysis and Chaos Control of a Mixed Duopoly Model[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(06):605-612.[doi:10.16357/j.cnki.issn1000-5862.2019.06.09]
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一类混合双寡头模型的分岔分析与混沌控制()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年06期
页码:
605-612
栏目:
数学与应用数学
出版日期:
2019-12-10

文章信息/Info

Title:
The Bifurcation Analysis and Chaos Control of a Mixed Duopoly Model
文章编号:
1000-5862(2019)06-0605-08
作者:
赵 娜1; 周 伟1*; 王文瑞2
1.兰州交通大学数理学院,甘肃 兰州 730070; 2.兰州交通大学经济管理学院,甘肃 兰州 730070
Author(s):
ZHAO Na1; ZHOU Wei1*; WANG Wenrui2
1.School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou Gansu 730070,China; 2.School of Economics and Management,Lanzhou Jiaotong University,Lanzhou Gansu 730070,China
关键词:
混合寡头;  分岔;  吸引子共存;  混沌控制
Keywords:
mixed duopoly;  bifurcation;  coexistence of attractors;  chaos control
分类号:
F 224
DOI:
10.16357/j.cnki.issn1000-5862.2019.06.09
文献标志码:
A
摘要:
在有限理性的假设下,建立了由公私合营企业和外资企业组成的生产同质产品的动态混合双寡头模型,分析了该系统的均衡点的存在性和稳定性,并推导出均衡点不会通过Neimark-Sacker分岔失去稳定性.利用Matlab数值模拟了系统在选取不同参数时的动力学行为,结果表明:系统会通过flip分岔进入混沌状态,并且在特定的参数条件下会出现多吸引子共存的现象.此外,还发现调整速度的大小会影响系统的稳定状态,当调整速度较大时,系统更容易变得不稳定而进入混沌状态.对于系统的混沌状态,使用延迟反馈方法实施了有效控制.
Abstract:
Under the assumption of bounded rationality,a dynamical mixed duopoly model consisting of a public-private joint firm and a foreign enterprise is established.The existence and stability of equilibrium point of the system are analyzed,and it is concluded that the equilibrium point cannot loss its stability via Neimark-Sacker bifurcation.The dynamical behaviors of the system when selecting different parameters is numerically simulated by Matlab,the results show that the system will enter the chaotic state through the flip bifurcation.And under some certain parameter conditions,the phenomenon of coexistence of multiple attractors can be found.In addition,it is also found that the speed of adjustment affects the steady state of the built model.When the speed of adjustment is selected large enough,the system is more likely to become unstable and enter a chaotic state.The chaotic state of the system is controlled successfully using the so-called delay feedback method.

参考文献/References:

[1] Agiza H N,Hegazi A S,Elsadany A A.Complex dynamics and synchronization of a duopoly game with bounded rationality[J].Mathematics and Computers in Simulation,2002,58(2):133-146.
[2] Puu T.The chaotic duopolists revisited[J].Journal of Economic Behavior and Organization,1998,33(3/4):385-394.
[3] Ding Zhanwei,Wang Qiao,Jiang Shumin.Analysis on the dynamics of a Cournot investment game with bounded rationality[J].Economic Modelling,2014,39:204-212.
[4] Agliari A,Naimzada A K,Pecora N.Nonlinear dynamics of a Cournot duopoly game with differentiated products[J].Applied Mathematics and Computation,2016,281:1-15.
[5] Cavalli F,Naimzada A.Complex dynamics and multistability with increasing rationality in market games[J].Chaos,Solitons and Fractals,2016,93:151-161.
[6] Zhou Jie,Zhou Wei,Chu Tong,et al.Bifurcation,intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation[J].Applied Mathematics and Computation,2019,341:358-378.
[7] Zhang Yahui,Zhou Wei,Chu Tong,et al.Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production[J].Nonlinear dynamics,2018,91(2):819-835.
[8] 黄东卫,付玉霞,于沈新.同质企业研发竞争行为的动力学性态分析[J].天津工业大学学报,2015,34(3):73-77,84.
[9] 张芳,张婷婷,马小林.双渠道供应链博弈模型的复杂性分析[J].天津工业大学学报,2015,34(3):78-84.
[10] Matsumura T.Partial privatization in mixed duopoly[J].Journal of Public Economics,1998,70(3):473-483.
[11] Bárcena-Ruiz J C,Garzón M B.Endogenous timing in a mixed oligopoly with semipublic firms[J].Portuguese Economic Journal,2010,9(2):97-113.
[12] Fujiwara K.Partial privatization in a differentiated mixed oligopoly[J].Journal of Economics,2007,92(1):51-65.
[13] 徐晓慧,李杰.混合寡头市场下的民营化和战略政策[J].中国经济问题,2016(6):96-108.
[14] 张伟.基于外资渗透和部分私有化的混合多寡头研发投入研究[J].科技管理研究,2015,35(9):105-109.
[15] 张伟,于良春.混合寡头厂商的合作研发及反垄断控制研究[J].中国工业经济,2014(5):44-56.
[16] 叶光亮,邓国营.最优关税和部分私有化战略:产品差异的混合寡头模型[J].经济学:季刊,2010,9(2):597-608.
[17] Askar S S,Alshamrani A M,Alnowibet K.Dynamic cournot duopoly games with nonlinear demand function[J].Applied Mathematics and Computation,2015,259:427-437.
[18] Pyragas K.Continuous control of chaos by self-controlling feedback[J].Physics Letters A,1992,170(6):421-428.

备注/Memo

备注/Memo:
收稿日期:2019-05-10
基金项目:国家自然科学基金(61863022)资助项目.
通信作者:周 伟(1980-),男,山东聊城人,副教授,博士,主要从事非线性动力学研究.E-mail:wei_zhou@vip.126.com
更新日期/Last Update: 2019-12-10