Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method
The dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. The chao...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6316235 |
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| _version_ | 1832556619991351296 |
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| author | Guo Feng Ding Yin Li Jiacheng |
| author_facet | Guo Feng Ding Yin Li Jiacheng |
| author_sort | Guo Feng |
| collection | DOAJ |
| description | The dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. The chaotic motion is controlled on the stable periodic period-1 orbit using the implementation of the hybrid control strategy. The factor affecting the control time of chaos is also studied. Numerical simulations are consistent with the theoretical analysis. The results of this research prove that the chaos control method can be extended to the higher-dimensional biological model and can be realized. |
| format | Article |
| id | doaj-art-8f4d5bbc5b1a4194b54cd929525af2ff |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8f4d5bbc5b1a4194b54cd929525af2ff2025-02-03T05:44:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/63162356316235Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY MethodGuo Feng0Ding Yin1Li Jiacheng2School of Data and Computer Science, Shandong Women’s University, Jinan 250300, ChinaWater Conservancy of Shandong Technician College, Zibo 255130, ChinaLaiwu No. 4 Senior High School, Jinan 250000, ChinaThe dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. The chaotic motion is controlled on the stable periodic period-1 orbit using the implementation of the hybrid control strategy. The factor affecting the control time of chaos is also studied. Numerical simulations are consistent with the theoretical analysis. The results of this research prove that the chaos control method can be extended to the higher-dimensional biological model and can be realized.http://dx.doi.org/10.1155/2021/6316235 |
| spellingShingle | Guo Feng Ding Yin Li Jiacheng Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method Discrete Dynamics in Nature and Society |
| title | Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method |
| title_full | Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method |
| title_fullStr | Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method |
| title_full_unstemmed | Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method |
| title_short | Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method |
| title_sort | neimark sacker bifurcation and controlling chaos in a three species food chain model through the ogy method |
| url | http://dx.doi.org/10.1155/2021/6316235 |
| work_keys_str_mv | AT guofeng neimarksackerbifurcationandcontrollingchaosinathreespeciesfoodchainmodelthroughtheogymethod AT dingyin neimarksackerbifurcationandcontrollingchaosinathreespeciesfoodchainmodelthroughtheogymethod AT lijiacheng neimarksackerbifurcationandcontrollingchaosinathreespeciesfoodchainmodelthroughtheogymethod |