Nonlocal Interaction Induces the Self-Organized Mussel Beds (Journal of Nonlinear Modeling and Analysis, 2024)
Mussel beds are important habitats and food sources for biodiversity in coastal ecosystems. The predation of mussel on algae depends not onlyon the current time and location, but also on the quantity of algae at otherspatial location and time. To know the impacts of such predation behavior onthe dynamics of mussel beds well, we pose a reaction-diffusion mussel-algaemodel coupling nonlocal interaction with kernel function. By calculating thecritical conditions of Hopf bifurcation and Turing bifurcation, the conditionsfor the generation of Turing pattern are obtained. We find that the diffusionrate and predation rate of mussels have effect on the structure and density ofspatial pattern of mussels under the nonlocal interaction, and the predationrate of mussels can produce different pattern types, while the diffusion rateplays a more important role on the pattern density. Moreover, the nonlocal interaction promotes the stability of the mussel beds. These results suggest thatthe nonlocal interaction between mussels and algaes is one of the importantmechanisms for the formation of the spatial structure of mussel beds.