Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2021, Vol. 38 ›› Issue (5): 662-678.doi: 10.3969/j.issn.1005-3085.2021.05.006

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The Spatial Distribution Pattern of an Algae-mussel Model with Nonlocal Predation Effect

LI Jing1,   SUN Guiquan2,3   

  1. 1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006
    2. School of Science, North University of China, Taiyuan 030051
    3. Complex Systems Research Center, Shanxi University, Taiyuan 030006
  • Online:2021-10-15 Published:2021-12-15
  • Contact: G. Sun. E-mail address: gquansun@126.com
  • Supported by:
    The National Key R&D Program of China (2018YFE0109600); the National Natural Science Foundation of China (11671241; 12001340); the Natural Science Foundation of Shanxi Province (201901D211411); the Science and Technology Innovation Project of Universities in Shanxi Province (2019L0472).

Abstract:

Mussel population is a key link in the food chain network of coastal ecosystem, and its spatial distribution pattern plays an important role in the healthy development of coastal ecosystem. The current researches ignore that the increase of mussel biomass in one location is caused by the mussels of other locations moving to this location and preying on algae. In this paper, an algae-mussel spatial diffusion model with nonlocal predation effect is established. Firstly, the existences of two equilibria in the non-diffusion system are calculated and the corresponding conditions of locally asymptotic stability are given. Then, the conditions for Turing instability of the diffusion system near the mussel survival equilibrium are derived based on Turing instability theory. Furthermore, the spatial distribution pattern of mussel population with time evolution was demonstrated by numerical simulations, which eventually formed a high density spot distribution structure. Finally, the parameter sensitivity analysis shows that the diffusion rates of the two populations significantly affect the spatial distribution pattern of the mussel population, which indicates that the changes of the movement laws of two populations may destroy the stable evolution of the coastal ecosystem; While the influence of nonlocal predation effect is not obvious, which is more conducive to the sustainable survival of mussel population. This work helps people to better understand the evolution law of mussel population from the mathematical level, and provides theoretical support for the rational development and utilization of coastal ecosystem resources.

Key words: algae-mussel model, nonlocal predation effect, spatial distribution pattern, parameter sensitivity analysis

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