Chaos Control and Synchronization in Fractional-Order Lorenz-Like System
The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/623234 |
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| _version_ | 1832545409903362048 |
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| author | Sachin Bhalekar |
| author_facet | Sachin Bhalekar |
| author_sort | Sachin Bhalekar |
| collection | DOAJ |
| description | The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback. |
| format | Article |
| id | doaj-art-f0e41b875045484690be9618f0c3121a |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-f0e41b875045484690be9618f0c3121a2025-02-03T07:26:03ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/623234623234Chaos Control and Synchronization in Fractional-Order Lorenz-Like SystemSachin Bhalekar0Department of Mathematics, Shivaji University, Vidyanagar, Kolhapur 416004, IndiaThe present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback.http://dx.doi.org/10.1155/2012/623234 |
| spellingShingle | Sachin Bhalekar Chaos Control and Synchronization in Fractional-Order Lorenz-Like System International Journal of Differential Equations |
| title | Chaos Control and Synchronization in Fractional-Order Lorenz-Like System |
| title_full | Chaos Control and Synchronization in Fractional-Order Lorenz-Like System |
| title_fullStr | Chaos Control and Synchronization in Fractional-Order Lorenz-Like System |
| title_full_unstemmed | Chaos Control and Synchronization in Fractional-Order Lorenz-Like System |
| title_short | Chaos Control and Synchronization in Fractional-Order Lorenz-Like System |
| title_sort | chaos control and synchronization in fractional order lorenz like system |
| url | http://dx.doi.org/10.1155/2012/623234 |
| work_keys_str_mv | AT sachinbhalekar chaoscontrolandsynchronizationinfractionalorderlorenzlikesystem |