TY - JOUR
T1 - Nonlocal Interaction Induces the Self-Organized Mussel Beds
AU - Sun , Guiquan
AU - Liu , Shumin
AU - Li , Li
AU - Li , Jing
AU - Jin , Zhen
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 617
EP - 646
PY - 2022
DA - 2022/06
SN - 3
DO - http://doi.org/10.12150/jnma.2021.617
UR - https://global-sci.org/intro/article_detail/jnma/20687.html
KW - Nonlocal interaction, Mussel-algae system, Hopf bifurcation, Turing pattern, Multi-scale analysis.
AB - <p style="text-align: justify;">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.</p>