A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos
One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE) with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/8434765 |
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| _version_ | 1832552617309372416 |
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| author | Shiyun Shen Meihua Ke Ping Zhou |
| author_facet | Shiyun Shen Meihua Ke Ping Zhou |
| author_sort | Shiyun Shen |
| collection | DOAJ |
| description | One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE) with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme. |
| format | Article |
| id | doaj-art-1091defb2b014f8c82ae24172501b954 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1091defb2b014f8c82ae24172501b9542025-02-03T05:58:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/84347658434765A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling ChaosShiyun Shen0Meihua Ke1Ping Zhou2Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaKey Laboratory of Network Control and Intelligent Instrument, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaCenter of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaOne 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE) with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.http://dx.doi.org/10.1155/2017/8434765 |
| spellingShingle | Shiyun Shen Meihua Ke Ping Zhou A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos Discrete Dynamics in Nature and Society |
| title | A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos |
| title_full | A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos |
| title_fullStr | A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos |
| title_full_unstemmed | A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos |
| title_short | A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos |
| title_sort | 3d fractional order chaotic system with only one stable equilibrium and controlling chaos |
| url | http://dx.doi.org/10.1155/2017/8434765 |
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