Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization
In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/3713789 |
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| _version_ | 1832558862506393600 |
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| author | Yan Cui Hongjun He Guan Sun Chenhui Lu |
| author_facet | Yan Cui Hongjun He Guan Sun Chenhui Lu |
| author_sort | Yan Cui |
| collection | DOAJ |
| description | In this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm and C0 algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process. |
| format | Article |
| id | doaj-art-611a239798014976bc47c81b523a2106 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-611a239798014976bc47c81b523a21062025-02-03T01:31:21ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/37137893713789Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time SynchronizationYan Cui0Hongjun He1Guan Sun2Chenhui Lu3Shanghai University of Engineering and Science, Shanghai 201620, ChinaShanghai University of Engineering and Science, Shanghai 201620, ChinaShanghai University of Engineering and Science, Shanghai 201620, ChinaShanghai University of Engineering and Science, Shanghai 201620, ChinaIn this paper, we present a corresponding fractional order three-dimensional autonomous chaotic system based on a new class of integer order chaotic systems. We found that the fractional order chaotic system belongs to the generalized Lorenz system family by analyzing its linear term and topological structure. We also found that the equilibrium point generated by the fractional order system belongs to the unstable saddle point through the prediction correction method and the fractional order stability theory. The complexity of fractional order chaotic system is given by spectral entropy algorithm and C0 algorithm. We concluded that the fractional order chaotic system has a higher complexity. The fractional order system can generate rich dynamic behavior phenomenon with the values of the parameters and the order changed. We applied the finite time stability theory to design the finite time synchronous controller between drive system and corresponding system. The numerical simulations demonstrate that the controller provides fast and efficient method in the synchronization process.http://dx.doi.org/10.1155/2019/3713789 |
| spellingShingle | Yan Cui Hongjun He Guan Sun Chenhui Lu Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization Advances in Mathematical Physics |
| title | Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization |
| title_full | Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization |
| title_fullStr | Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization |
| title_full_unstemmed | Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization |
| title_short | Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization |
| title_sort | analysis and control of fractional order generalized lorenz chaotic system by using finite time synchronization |
| url | http://dx.doi.org/10.1155/2019/3713789 |
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