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| Nonlocal Interaction Induces the Self-organized Mussel Beds |
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| KeyWord:Nonlocal interaction Mussel-algae system Hopf bifurcation Turing pattern Multi-scale analysis |
| Author Name | Affiliation | | Guiquan Sun | Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
Complex System Research Center, Shanxi University, Taiyuan, Shanxi 030006, China | | Shumin Liu | Complex System Research Center, Shanxi University, Taiyuan, Shanxi 030006, China | | Li Li | School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, China
Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan, Shanxi 030051, China | | Jing Li | School of Applied Mathematics, Shanxi University of Finance and Economics, Shanxi, Taiyuan, Shanxi 030006, China | | Zhen Jin | Complex System Research Center, Shanxi University, Taiyuan, Shanxi 030006, China |
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| Abstract: |
| Mussel beds are important habitats and food sources for biodiversity in coastal ecosystems. The predation of mussel on algae depends not only on the current time and location, but also on the quantity of algae at other spatial location and time. To know the impacts of such predation behavior on the dynamics of mussel beds well, we pose a reaction-diffusion mussel-algae model coupling nonlocal interaction with kernel function. By calculating the critical conditions of Hopf bifurcation and Turing bifurcation, the conditions for the generation of Turing pattern are obtained. We find that the diffusion rate and predation rate of mussels have effect on the structure and density of spatial pattern of mussels under the nonlocal interaction, and the predation rate of mussels can produce different pattern types, while the diffusion rate plays a more important role on the pattern density. Moreover, the nonlocal interaction promotes the stability of the mussel beds. These results suggest that the nonlocal interaction between mussels and algaes is one of the important mechanisms for the formation of the spatial structure of mussel beds. |
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