Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model
This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system u...
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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/10.1155/2017/6312964 |
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| author | Qamar Din A. A. Elsadany Hammad Khalil |
| author_facet | Qamar Din A. A. Elsadany Hammad Khalil |
| author_sort | Qamar Din |
| collection | DOAJ |
| description | This work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model. |
| format | Article |
| id | doaj-art-8181dcd1941e4eebb6833ff21d669dc6 |
| 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-8181dcd1941e4eebb6833ff21d669dc62025-02-03T06:08:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/63129646312964Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore ModelQamar Din0A. A. Elsadany1Hammad Khalil2Department of Mathematics, The University of Poonch Rawalakot, Rawalakot 12350, PakistanBasic Science Department, Faculty of Computers and Informatics, Suez Canal University, New Campus, Ismailia 41522, EgyptDepartment of Mathematics, University of Education, Attock Campus, Lahore, Punjab, PakistanThis work is related to dynamics of a discrete-time 3-dimensional plant-herbivore model. We investigate existence and uniqueness of positive equilibrium and parametric conditions for local asymptotic stability of positive equilibrium point of this model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation for positive equilibrium with the help of an explicit criterion for Neimark-Sacker bifurcation. The chaos control in the model is discussed through implementation of two feedback control strategies, that is, pole-placement technique and hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the model.http://dx.doi.org/10.1155/2017/6312964 |
| spellingShingle | Qamar Din A. A. Elsadany Hammad Khalil Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model Discrete Dynamics in Nature and Society |
| title | Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model |
| title_full | Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model |
| title_fullStr | Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model |
| title_full_unstemmed | Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model |
| title_short | Neimark-Sacker Bifurcation and Chaos Control in a Fractional-Order Plant-Herbivore Model |
| title_sort | neimark sacker bifurcation and chaos control in a fractional order plant herbivore model |
| url | http://dx.doi.org/10.1155/2017/6312964 |
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