Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems
It is of practical significance to realize a stable and controllable financial system by using chaotic synchronization theory. In this paper, the dynamics and synchronization are studied for a class of fractional-order chaotic financial systems. First, the stability and dynamics of the fractional-or...
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MDPI AG
2024-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/10/562 |
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| author | Panhong Zhang Qingyi Wang |
| author_facet | Panhong Zhang Qingyi Wang |
| author_sort | Panhong Zhang |
| collection | DOAJ |
| description | It is of practical significance to realize a stable and controllable financial system by using chaotic synchronization theory. In this paper, the dynamics and synchronization are studied for a class of fractional-order chaotic financial systems. First, the stability and dynamics of the fractional-order chaotic financial system are analyzed by using the phase trajectory diagram, time series diagram, bifurcation diagram, and Lyapunov exponential diagram. Meanwhile, we obtain the range of each parameter that puts the system in a periodic state, and we also reveal the relationship of the derivative order and the chaotic behaviors. Then, the adaptive control strategy is designed to achieve synchronization of the chaotic financial system. Finally, the theoretical results and control method are verified by numerical simulations. |
| format | Article |
| id | doaj-art-5b1bb674409f4a78a53d563a2c949e6b |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-5b1bb674409f4a78a53d563a2c949e6b2025-08-20T02:11:04ZengMDPI AGFractal and Fractional2504-31102024-09-0181056210.3390/fractalfract8100562Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial SystemsPanhong Zhang0Qingyi Wang1School of Finance, Hubei University of Economics, Wuhan 430205, ChinaSchool of Automation, China University of Geosciences, Wuhan 430074, ChinaIt is of practical significance to realize a stable and controllable financial system by using chaotic synchronization theory. In this paper, the dynamics and synchronization are studied for a class of fractional-order chaotic financial systems. First, the stability and dynamics of the fractional-order chaotic financial system are analyzed by using the phase trajectory diagram, time series diagram, bifurcation diagram, and Lyapunov exponential diagram. Meanwhile, we obtain the range of each parameter that puts the system in a periodic state, and we also reveal the relationship of the derivative order and the chaotic behaviors. Then, the adaptive control strategy is designed to achieve synchronization of the chaotic financial system. Finally, the theoretical results and control method are verified by numerical simulations.https://www.mdpi.com/2504-3110/8/10/562dynamics analysischaotic financial systemsfractional ordersynchronization |
| spellingShingle | Panhong Zhang Qingyi Wang Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems Fractal and Fractional dynamics analysis chaotic financial systems fractional order synchronization |
| title | Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems |
| title_full | Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems |
| title_fullStr | Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems |
| title_full_unstemmed | Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems |
| title_short | Dynamics Analysis and Adaptive Synchronization of a Class of Fractional-Order Chaotic Financial Systems |
| title_sort | dynamics analysis and adaptive synchronization of a class of fractional order chaotic financial systems |
| topic | dynamics analysis chaotic financial systems fractional order synchronization |
| url | https://www.mdpi.com/2504-3110/8/10/562 |
| work_keys_str_mv | AT panhongzhang dynamicsanalysisandadaptivesynchronizationofaclassoffractionalorderchaoticfinancialsystems AT qingyiwang dynamicsanalysisandadaptivesynchronizationofaclassoffractionalorderchaoticfinancialsystems |