Stability and Dynamical Analysis of a Biological System
This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic prop...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/952840 |
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| _version_ | 1850160102881886208 |
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| author | Xinhong Pan Min Zhao Yapei Wang Hengguo Yu Zengling Ma Qi Wang |
| author_facet | Xinhong Pan Min Zhao Yapei Wang Hengguo Yu Zengling Ma Qi Wang |
| author_sort | Xinhong Pan |
| collection | DOAJ |
| description | This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton. |
| format | Article |
| id | doaj-art-af09f2fd1ca64c01b0433e5a354f8420 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-af09f2fd1ca64c01b0433e5a354f84202025-08-20T02:23:15ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/952840952840Stability and Dynamical Analysis of a Biological SystemXinhong Pan0Min Zhao1Yapei Wang2Hengguo Yu3Zengling Ma4Qi Wang5School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaSchool of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaZhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, ChinaThis study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.http://dx.doi.org/10.1155/2014/952840 |
| spellingShingle | Xinhong Pan Min Zhao Yapei Wang Hengguo Yu Zengling Ma Qi Wang Stability and Dynamical Analysis of a Biological System Abstract and Applied Analysis |
| title | Stability and Dynamical Analysis of a Biological System |
| title_full | Stability and Dynamical Analysis of a Biological System |
| title_fullStr | Stability and Dynamical Analysis of a Biological System |
| title_full_unstemmed | Stability and Dynamical Analysis of a Biological System |
| title_short | Stability and Dynamical Analysis of a Biological System |
| title_sort | stability and dynamical analysis of a biological system |
| url | http://dx.doi.org/10.1155/2014/952840 |
| work_keys_str_mv | AT xinhongpan stabilityanddynamicalanalysisofabiologicalsystem AT minzhao stabilityanddynamicalanalysisofabiologicalsystem AT yapeiwang stabilityanddynamicalanalysisofabiologicalsystem AT hengguoyu stabilityanddynamicalanalysisofabiologicalsystem AT zenglingma stabilityanddynamicalanalysisofabiologicalsystem AT qiwang stabilityanddynamicalanalysisofabiologicalsystem |