A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller
A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is q≥0.8477. The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractiona...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/4192824 |
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| _version_ | 1849396696856920064 |
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| author | Ping Zhou Meihua Ke Peng Zhu |
| author_facet | Ping Zhou Meihua Ke Peng Zhu |
| author_sort | Ping Zhou |
| collection | DOAJ |
| description | A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is q≥0.8477. The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order q is given. Furthermore, there are the coexisting “positive attractor” and “negative attractor” in this fractional-order chaotic system, and the necessary condition for “positive attractor” and “negative attractor” is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid. |
| format | Article |
| id | doaj-art-b03c06c88628404c9d68e4f36c8a17d6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b03c06c88628404c9d68e4f36c8a17d62025-08-20T03:39:15ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/41928244192824A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear ControllerPing Zhou0Meihua Ke1Peng Zhu2Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaA 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is q≥0.8477. The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order q is given. Furthermore, there are the coexisting “positive attractor” and “negative attractor” in this fractional-order chaotic system, and the necessary condition for “positive attractor” and “negative attractor” is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid.http://dx.doi.org/10.1155/2018/4192824 |
| spellingShingle | Ping Zhou Meihua Ke Peng Zhu A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller Complexity |
| title | A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller |
| title_full | A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller |
| title_fullStr | A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller |
| title_full_unstemmed | A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller |
| title_short | A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller |
| title_sort | fractional order system with coexisting chaotic attractors and control chaos via a single state variable linear controller |
| url | http://dx.doi.org/10.1155/2018/4192824 |
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