A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control
A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The propose...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/6680399 |
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| _version_ | 1849306342859210752 |
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| author | Jie Ran Yonghui Zhou |
| author_facet | Jie Ran Yonghui Zhou |
| author_sort | Jie Ran |
| collection | DOAJ |
| description | A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results. |
| format | Article |
| id | doaj-art-2ea52b47700741c18ccde5f8debfad84 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2ea52b47700741c18ccde5f8debfad842025-08-20T03:55:07ZengWileyComplexity1099-05262024-01-01202410.1155/2024/6680399A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal ControlJie Ran0Yonghui Zhou1School of Mathematical SciencesSchool of Big Data and Computer ScienceA stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.http://dx.doi.org/10.1155/2024/6680399 |
| spellingShingle | Jie Ran Yonghui Zhou A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control Complexity |
| title | A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control |
| title_full | A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control |
| title_fullStr | A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control |
| title_full_unstemmed | A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control |
| title_short | A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control |
| title_sort | stochastic discrete fractional cournot duopoly game modeling stability and optimal control |
| url | http://dx.doi.org/10.1155/2024/6680399 |
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