Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect
The refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as peri...
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| Format: | Article |
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AIMS Press
2024-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024201?viewType=HTML |
| _version_ | 1797256711036207104 |
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| author | Parvaiz Ahmad Naik Muhammad Amer Rizwan Ahmed Sania Qureshi Zhengxin Huang |
| author_facet | Parvaiz Ahmad Naik Muhammad Amer Rizwan Ahmed Sania Qureshi Zhengxin Huang |
| author_sort | Parvaiz Ahmad Naik |
| collection | DOAJ |
| description | The refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as period-doubling and Neimark-Sacker (NS) bifurcations. The bifurcating and fluctuating behavior of the system was controlled via feedback and hybrid control methods. In addition, numerical simulations were performed as evidence to back up our theoretical findings. According to our findings, maintaining an optimal level of refuge availability was critical for predator and prey population cohabitation and stability. |
| first_indexed | 2024-04-24T22:26:05Z |
| format | Article |
| id | doaj.art-74246e62bf0f44d79bf43b66b2a7a856 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-24T22:26:05Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-74246e62bf0f44d79bf43b66b2a7a8562024-03-20T01:18:24ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-02-012134554458610.3934/mbe.2024201Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effectParvaiz Ahmad Naik0Muhammad Amer 1Rizwan Ahmed 2Sania Qureshi 3Zhengxin Huang41. Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise 533000, China2. Department of Mathematics, Air University Multan Campus, Multan, Pakistan2. Department of Mathematics, Air University Multan Campus, Multan, Pakistan3. Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon 4. Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Pakistan 5. Department of Mathematics, Near East University, Mersin, Turkey1. Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise 533000, ChinaThe refuge effect is critical in ecosystems for stabilizing predator-prey interactions. The purpose of this research was to investigate the complexities of a discrete-time predator-prey system with a refuge effect. The analysis investigated the presence and stability of fixed points, as well as period-doubling and Neimark-Sacker (NS) bifurcations. The bifurcating and fluctuating behavior of the system was controlled via feedback and hybrid control methods. In addition, numerical simulations were performed as evidence to back up our theoretical findings. According to our findings, maintaining an optimal level of refuge availability was critical for predator and prey population cohabitation and stability.https://www.aimspress.com/article/doi/10.3934/mbe.2024201?viewType=HTMLpredator-prey systemrickerrefugestabilityperiod-doubling bifurcationneimark-sacker (ns) bifurcationchaos control |
| spellingShingle | Parvaiz Ahmad Naik Muhammad Amer Rizwan Ahmed Sania Qureshi Zhengxin Huang Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect Mathematical Biosciences and Engineering predator-prey system ricker refuge stability period-doubling bifurcation neimark-sacker (ns) bifurcation chaos control |
| title | Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect |
| title_full | Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect |
| title_fullStr | Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect |
| title_full_unstemmed | Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect |
| title_short | Stability and bifurcation analysis of a discrete predator-prey system of Ricker type with refuge effect |
| title_sort | stability and bifurcation analysis of a discrete predator prey system of ricker type with refuge effect |
| topic | predator-prey system ricker refuge stability period-doubling bifurcation neimark-sacker (ns) bifurcation chaos control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024201?viewType=HTML |
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