Dynamics and pattern formation in a reaction-diffusion-advection mussel–algae model

This paper investigates the dynamics and pattern formation of a system modeling the interaction of mussels and algae in the water layer overlying the mussel bed, where the algae are the main food source for mussels, and the advection of algae is directed from the open sea toward the shore. For such...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2022-06, Vol.73 (3), Article 117
Main Authors: Wang, Jinfeng, Tong, Xue, Song, Yongli
Format: Article
Language:English
Subjects:
Advection
Algae
Diffusion rate
Dynamic stability
Dynamics
Engineering
Mathematical Methods in Physics
Mollusks
Mussels
Steady state
Theoretical and Applied Mechanics
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Summary:This paper investigates the dynamics and pattern formation of a system modeling the interaction of mussels and algae in the water layer overlying the mussel bed, where the algae are the main food source for mussels, and the advection of algae is directed from the open sea toward the shore. For such a class of systems, we first provide a clear picture on the local dynamics of the semi-trivial steady state in terms of diffusion rate of algae and advection rate, and then the global dynamics is presented by persistence theory and global stability of the semi-trivial steady state. Finally, the existence of the positive steady state is also investigated.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01744-6