Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market
Recently, the insurance industry in China has been greatly developed. The number of domestic insurance companies and foreign investment insurance companies has greatly increased. Competition between different insurance companies is becoming increasingly fierce. <b>Grasping the</b> intern...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/5/270 |
| _version_ | 1797499780369219584 |
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| author | Peiluan Li Jinling Yan Changjin Xu Rong Gao Ying Li |
| author_facet | Peiluan Li Jinling Yan Changjin Xu Rong Gao Ying Li |
| author_sort | Peiluan Li |
| collection | DOAJ |
| description | Recently, the insurance industry in China has been greatly developed. The number of domestic insurance companies and foreign investment insurance companies has greatly increased. Competition between different insurance companies is becoming increasingly fierce. <b>Grasping the</b> internal competition law of different insurance companies is a very meaningful work. In this present work, we set up a novel fractional-order delayed duopoly game model in insurance market and discuss the dynamics including existence and uniqueness, non-negativeness, and boundedness of solution for the established fractional-order delayed duopoly game model in insurance market. By selecting the delay as a bifurcation parameter, we build a new delay-independent condition ensuring the stability and creation of Hopf bifurcation of the built fractional-order delayed duopoly game model. Making use of a suitable definite function, we explore the globally asymptotic stability of the involved fractional-order delayed duopoly game model. By virtue of hybrid controller which includes state feedback and parameter perturbation, we can effectively control the stability and the time of creation of Hopf bifurcation for the involved fractional-order delayed duopoly game model. The research indicates that time delay plays an all-important role in stabilizing the system and controlling the time of onset of Hopf bifurcation of the involved fractional-order delayed duopoly game model. To check the rationality of derived primary conclusions, Matlab simulation plots are explicitly presented. The established results in this manuscript are wholly novel and own immense theoretical guiding significance in managing and operating insurance companies. |
| first_indexed | 2024-03-10T03:52:20Z |
| format | Article |
| id | doaj.art-8e814161426c4a7f93e9791961d501c0 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:52:20Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8e814161426c4a7f93e9791961d501c02023-11-23T11:03:48ZengMDPI AGFractal and Fractional2504-31102022-05-016527010.3390/fractalfract6050270Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance MarketPeiluan Li0Jinling Yan1Changjin Xu2Rong Gao3Ying Li4School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaGuizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaRecently, the insurance industry in China has been greatly developed. The number of domestic insurance companies and foreign investment insurance companies has greatly increased. Competition between different insurance companies is becoming increasingly fierce. <b>Grasping the</b> internal competition law of different insurance companies is a very meaningful work. In this present work, we set up a novel fractional-order delayed duopoly game model in insurance market and discuss the dynamics including existence and uniqueness, non-negativeness, and boundedness of solution for the established fractional-order delayed duopoly game model in insurance market. By selecting the delay as a bifurcation parameter, we build a new delay-independent condition ensuring the stability and creation of Hopf bifurcation of the built fractional-order delayed duopoly game model. Making use of a suitable definite function, we explore the globally asymptotic stability of the involved fractional-order delayed duopoly game model. By virtue of hybrid controller which includes state feedback and parameter perturbation, we can effectively control the stability and the time of creation of Hopf bifurcation for the involved fractional-order delayed duopoly game model. The research indicates that time delay plays an all-important role in stabilizing the system and controlling the time of onset of Hopf bifurcation of the involved fractional-order delayed duopoly game model. To check the rationality of derived primary conclusions, Matlab simulation plots are explicitly presented. The established results in this manuscript are wholly novel and own immense theoretical guiding significance in managing and operating insurance companies.https://www.mdpi.com/2504-3110/6/5/270fractional-order duopoly game modelinsurance marketexistence and uniquenessnon-negativenessboundednessstability |
| spellingShingle | Peiluan Li Jinling Yan Changjin Xu Rong Gao Ying Li Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market Fractal and Fractional fractional-order duopoly game model insurance market existence and uniqueness non-negativeness boundedness stability |
| title | Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market |
| title_full | Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market |
| title_fullStr | Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market |
| title_full_unstemmed | Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market |
| title_short | Understanding Dynamics and Bifurcation Control Mechanism for a Fractional-Order Delayed Duopoly Game Model in Insurance Market |
| title_sort | understanding dynamics and bifurcation control mechanism for a fractional order delayed duopoly game model in insurance market |
| topic | fractional-order duopoly game model insurance market existence and uniqueness non-negativeness boundedness stability |
| url | https://www.mdpi.com/2504-3110/6/5/270 |
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