Complicate dynamical analysis of a discrete predator-prey model with a prey refuge
In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respective...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023768?viewType=HTML |
| _version_ | 1797829555967229952 |
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| author | A. Q. Khan Ibraheem M. Alsulami |
| author_facet | A. Q. Khan Ibraheem M. Alsulami |
| author_sort | A. Q. Khan |
| collection | DOAJ |
| description | In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model. |
| first_indexed | 2024-04-09T13:23:14Z |
| format | Article |
| id | doaj.art-6f50c9c9bc624996b8bdefa3481a9bb5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T13:23:14Z |
| publishDate | 2023-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6f50c9c9bc624996b8bdefa3481a9bb52023-05-11T01:26:54ZengAIMS PressAIMS Mathematics2473-69882023-04-0187150351505710.3934/math.2023768Complicate dynamical analysis of a discrete predator-prey model with a prey refugeA. Q. Khan0Ibraheem M. Alsulami 11. Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan2. Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi ArabiaIn this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model.https://www.aimspress.com/article/doi/10.3934/math.2023768?viewType=HTMLchaosdiscrete modelbifurcationsrefugenumerical simulation |
| spellingShingle | A. Q. Khan Ibraheem M. Alsulami Complicate dynamical analysis of a discrete predator-prey model with a prey refuge AIMS Mathematics chaos discrete model bifurcations refuge numerical simulation |
| title | Complicate dynamical analysis of a discrete predator-prey model with a prey refuge |
| title_full | Complicate dynamical analysis of a discrete predator-prey model with a prey refuge |
| title_fullStr | Complicate dynamical analysis of a discrete predator-prey model with a prey refuge |
| title_full_unstemmed | Complicate dynamical analysis of a discrete predator-prey model with a prey refuge |
| title_short | Complicate dynamical analysis of a discrete predator-prey model with a prey refuge |
| title_sort | complicate dynamical analysis of a discrete predator prey model with a prey refuge |
| topic | chaos discrete model bifurcations refuge numerical simulation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023768?viewType=HTML |
| work_keys_str_mv | AT aqkhan complicatedynamicalanalysisofadiscretepredatorpreymodelwithapreyrefuge AT ibraheemmalsulami complicatedynamicalanalysisofadiscretepredatorpreymodelwithapreyrefuge |