A two-patch prey-predator model with predator dispersal driven by the predation strength
Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile w...
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AIMS Press
2017-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017046 |
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| author | Yun Kang Sourav Kumar Sasmal Komi Messan |
| author_facet | Yun Kang Sourav Kumar Sasmal Komi Messan |
| author_sort | Yun Kang |
| collection | DOAJ |
| description | Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns. |
| format | Article |
| id | doaj-art-7f9c7e1cf45d488bab8c01da3657ad6d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-07-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7f9c7e1cf45d488bab8c01da3657ad6d2025-01-24T02:39:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-07-0114484388010.3934/mbe.2017046A two-patch prey-predator model with predator dispersal driven by the predation strengthYun Kang0Sourav Kumar Sasmal1Komi Messan2Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, USAAgricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, IndiaSimon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State University, Mesa, AZ 85212, USAForaging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions. We provide completed local and global analysis of our model. Our analytical results combined with bifurcation diagrams suggest that: (1) dispersal may stabilize or destabilize the coupled system; (2) dispersal may generate multiple interior equilibria that lead to rich bistable dynamics or may destroy interior equilibria that lead to the extinction of predator in one patch or both patches; (3) Under certain conditions, the large dispersal can promote the permanence of the system. In addition, we compare the dynamics of our model to the classic two patch model to obtain a better understanding how different dispersal strategies may have different impacts on the dynamics and spatial patterns.https://www.aimspress.com/article/doi/10.3934/mbe.2017046rosenzweig-macarthur prey-predator modelself-organization effectsdispersalpersistencenon-random foraging movements |
| spellingShingle | Yun Kang Sourav Kumar Sasmal Komi Messan A two-patch prey-predator model with predator dispersal driven by the predation strength Mathematical Biosciences and Engineering rosenzweig-macarthur prey-predator model self-organization effects dispersal persistence non-random foraging movements |
| title | A two-patch prey-predator model with predator dispersal driven by the predation strength |
| title_full | A two-patch prey-predator model with predator dispersal driven by the predation strength |
| title_fullStr | A two-patch prey-predator model with predator dispersal driven by the predation strength |
| title_full_unstemmed | A two-patch prey-predator model with predator dispersal driven by the predation strength |
| title_short | A two-patch prey-predator model with predator dispersal driven by the predation strength |
| title_sort | two patch prey predator model with predator dispersal driven by the predation strength |
| topic | rosenzweig-macarthur prey-predator model self-organization effects dispersal persistence non-random foraging movements |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017046 |
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