Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)
This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide...
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| Main Authors: | , , , , |
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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/10.1155/2018/6719341 |
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| author | A. Al-khedhairi S. S. Askar A. E. Matouk A. Elsadany M. Ghazel |
| author_facet | A. Al-khedhairi S. S. Askar A. E. Matouk A. Elsadany M. Ghazel |
| author_sort | A. Al-khedhairi |
| collection | DOAJ |
| description | This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations. |
| format | Article |
| id | doaj-art-e2ab4f6a9d07419dae3b0d9f3fa8f7e3 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e2ab4f6a9d07419dae3b0d9f3fa8f7e32025-02-03T01:23:44ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/67193416719341Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)A. Al-khedhairi0S. S. Askar1A. E. Matouk2A. Elsadany3M. Ghazel4Department of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Basic Engineering Sciences, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi ArabiaMathematics Department, College of Sciences and Humanities Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi ArabiaMathematics Department, Faculty of Science, Hail University, Hail 2440, Saudi ArabiaThis paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.http://dx.doi.org/10.1155/2018/6719341 |
| spellingShingle | A. Al-khedhairi S. S. Askar A. E. Matouk A. Elsadany M. Ghazel Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) Complexity |
| title | Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) |
| title_full | Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) |
| title_fullStr | Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) |
| title_full_unstemmed | Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) |
| title_short | Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2) |
| title_sort | dynamics chaos control and synchronization in a fractional order samardzija greller population system with order lying in 0 2 |
| url | http://dx.doi.org/10.1155/2018/6719341 |
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