Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities
We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium po...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/7384150 |
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| _version_ | 1832565321792225280 |
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| author | Hongliang Tu Xueli Zhan Xiaobing Mao |
| author_facet | Hongliang Tu Xueli Zhan Xiaobing Mao |
| author_sort | Hongliang Tu |
| collection | DOAJ |
| description | We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos. |
| format | Article |
| id | doaj-art-ac43d60e4734455e83cdf2083002f2b4 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ac43d60e4734455e83cdf2083002f2b42025-02-03T01:08:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/73841507384150Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D ActivitiesHongliang Tu0Xueli Zhan1Xiaobing Mao2School of Information and Management, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaSchool of Economics, Beijing Wuzi University, Beijing 101149, ChinaSchool of Information and Management, Jiangxi University of Finance and Economics, Nanchang 330013, ChinaWe study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.http://dx.doi.org/10.1155/2017/7384150 |
| spellingShingle | Hongliang Tu Xueli Zhan Xiaobing Mao Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities Discrete Dynamics in Nature and Society |
| title | Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities |
| title_full | Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities |
| title_fullStr | Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities |
| title_full_unstemmed | Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities |
| title_short | Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities |
| title_sort | complex dynamics and chaos control on a kind of bertrand duopoly game model considering r d activities |
| url | http://dx.doi.org/10.1155/2017/7384150 |
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