Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge
To study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type Ⅱ response function. The existence and stability of positive equilibria are disc...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017032 |
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| author | Juan Li Yongzhong Song Hui Wan Huaiping Zhu |
| author_facet | Juan Li Yongzhong Song Hui Wan Huaiping Zhu |
| author_sort | Juan Li |
| collection | DOAJ |
| description | To study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type Ⅱ response function. The existence and stability of positive equilibria are discussed. Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3. Numerical simulations are carried out to intuitively support our analytical results and help to explain the observed biological behaviors. Our findings finally show that both phytoplankton refuge and toxin have a significant impact on the occurring and terminating of algal blooms in freshwater lakes. |
| format | Article |
| id | doaj-art-cf2da2d3862b482aabb0bd7f8aae95f9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-cf2da2d3862b482aabb0bd7f8aae95f92025-01-24T02:39:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-03-0114252955710.3934/mbe.2017032Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refugeJuan Li0Yongzhong Song1Hui Wan2Huaiping Zhu3Jiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, ChinaJiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, ChinaJiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, ChinaLaboratory of Mathematical Parallel Systems (Lamps), Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, CanadaTo study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type Ⅱ response function. The existence and stability of positive equilibria are discussed. Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3. Numerical simulations are carried out to intuitively support our analytical results and help to explain the observed biological behaviors. Our findings finally show that both phytoplankton refuge and toxin have a significant impact on the occurring and terminating of algal blooms in freshwater lakes.https://www.aimspress.com/article/doi/10.3934/mbe.2017032phytoplanktonzooplanktonrefugetoxinalgal bloomsmultiple equilibriastabilityhopf bifurcationbogdanov-takens bifurcation |
| spellingShingle | Juan Li Yongzhong Song Hui Wan Huaiping Zhu Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge Mathematical Biosciences and Engineering phytoplankton zooplankton refuge toxin algal blooms multiple equilibria stability hopf bifurcation bogdanov-takens bifurcation |
| title | Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge |
| title_full | Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge |
| title_fullStr | Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge |
| title_full_unstemmed | Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge |
| title_short | Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge |
| title_sort | dynamical analysis of a toxin producing phytoplankton zooplankton model with refuge |
| topic | phytoplankton zooplankton refuge toxin algal blooms multiple equilibria stability hopf bifurcation bogdanov-takens bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017032 |
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