Bifurcation and controller design in a 3D delayed predator-prey model
Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this articl...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241617 |
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| author | Jinting Lin Changjin Xu Yiya Xu Yingyan Zhao Yicheng Pang Zixin Liu Jianwei Shen |
| author_facet | Jinting Lin Changjin Xu Yiya Xu Yingyan Zhao Yicheng Pang Zixin Liu Jianwei Shen |
| author_sort | Jinting Lin |
| collection | DOAJ |
| description | Delayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. The research explores how delays affect the stabilization of system and the adjustment of bifurcation. This paper provides computer simulation photos supporting the main obtained findings. The outcomes of this paper are groundbreaking and can provide critical guidance for the control and regulation of predator and prey population densities. |
| format | Article |
| id | doaj-art-067eec95cae14d14bc883f7720400a7b |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-067eec95cae14d14bc883f7720400a7b2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912338913392910.3934/math.20241617Bifurcation and controller design in a 3D delayed predator-prey modelJinting Lin0Changjin Xu1Yiya Xu2Yingyan Zhao3Yicheng Pang4Zixin Liu5Jianwei Shen6School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaGuizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, ChinaDelayed dynamical models demonstrate significant application value in depicting interactions and internal dynamics among different biological populations. Therefore, they have garnered significant interest from numerous scholars in both biology and mathematics. Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. The research explores how delays affect the stabilization of system and the adjustment of bifurcation. This paper provides computer simulation photos supporting the main obtained findings. The outcomes of this paper are groundbreaking and can provide critical guidance for the control and regulation of predator and prey population densities.https://www.aimspress.com/article/doi/10.3934/math.20241617predator-prey systemwell-posedness of solutionhopf bifurcationstabilityhybrid controller |
| spellingShingle | Jinting Lin Changjin Xu Yiya Xu Yingyan Zhao Yicheng Pang Zixin Liu Jianwei Shen Bifurcation and controller design in a 3D delayed predator-prey model AIMS Mathematics predator-prey system well-posedness of solution hopf bifurcation stability hybrid controller |
| title | Bifurcation and controller design in a 3D delayed predator-prey model |
| title_full | Bifurcation and controller design in a 3D delayed predator-prey model |
| title_fullStr | Bifurcation and controller design in a 3D delayed predator-prey model |
| title_full_unstemmed | Bifurcation and controller design in a 3D delayed predator-prey model |
| title_short | Bifurcation and controller design in a 3D delayed predator-prey model |
| title_sort | bifurcation and controller design in a 3d delayed predator prey model |
| topic | predator-prey system well-posedness of solution hopf bifurcation stability hybrid controller |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241617 |
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