Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control
We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcat...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/970205 |
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| _version_ | 1849403928466161664 |
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| author | Junhai Ma Fang Zhang Yanyan He |
| author_facet | Junhai Ma Fang Zhang Yanyan He |
| author_sort | Junhai Ma |
| collection | DOAJ |
| description | We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players. |
| format | Article |
| id | doaj-art-97dc5a789c5b4ee2b5ebc9b2b1ae7336 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-97dc5a789c5b4ee2b5ebc9b2b1ae73362025-08-20T03:37:08ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/970205970205Complexity Analysis of a Master-Slave Oligopoly Model and Chaos ControlJunhai Ma0Fang Zhang1Yanyan He2College of Management and Economics, Tianjin University, Tianjin 300072, ChinaCollege of Management and Economics, Tianjin University, Tianjin 300072, ChinaDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaWe establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.http://dx.doi.org/10.1155/2014/970205 |
| spellingShingle | Junhai Ma Fang Zhang Yanyan He Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control Abstract and Applied Analysis |
| title | Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control |
| title_full | Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control |
| title_fullStr | Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control |
| title_full_unstemmed | Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control |
| title_short | Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control |
| title_sort | complexity analysis of a master slave oligopoly model and chaos control |
| url | http://dx.doi.org/10.1155/2014/970205 |
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