Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function
In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With cha...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9978320 |
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| _version_ | 1832554112420413440 |
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| author | Hui Li Wei Zhou Tong Chu |
| author_facet | Hui Li Wei Zhou Tong Chu |
| author_sort | Hui Li |
| collection | DOAJ |
| description | In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures (also called Isoperiodic Stable Structures) and different shape basins of attraction of coexisting attractors. The eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary. |
| format | Article |
| id | doaj-art-bf1db8b031864edabb1e153b050abea5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-bf1db8b031864edabb1e153b050abea52025-02-03T05:52:27ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99783209978320Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand FunctionHui Li0Wei Zhou1Tong Chu2School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, ChinaSchool of Law, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, ChinaIn this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures (also called Isoperiodic Stable Structures) and different shape basins of attraction of coexisting attractors. The eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary.http://dx.doi.org/10.1155/2021/9978320 |
| spellingShingle | Hui Li Wei Zhou Tong Chu Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function Complexity |
| title | Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function |
| title_full | Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function |
| title_fullStr | Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function |
| title_full_unstemmed | Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function |
| title_short | Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function |
| title_sort | stability multistability and complexity analysis in a dynamic duopoly game with exponential demand function |
| url | http://dx.doi.org/10.1155/2021/9978320 |
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