在线咨询
中国工业与应用数学学会会刊
主管:中华人民共和国教育部
主办:西安交通大学
ISSN 1005-3085  CN 61-1269/O1

工程数学学报 ›› 2021, Vol. 38 ›› Issue (5): 662-678.doi: 10.3969/j.issn.1005-3085.2021.05.006

• • 上一篇    下一篇

具有非局部捕食效应的藻类--贻贝系统空间分布模式研究

李  静1,   孙桂全2,3   

  1. 1. 山西财经大学应用数学学院,太原 030006
    2. 中北大学理学院,太原 030051
    3. 山西大学复杂系统研究所,太原 030006
  • 出版日期:2021-10-15 发布日期:2021-12-15
  • 通讯作者: 孙桂全 E-mail: gquansun@126.com
  • 基金资助:
    重点研发计划政府间国际合作重点资助项目 (2018YFE0109600);国家自然科学基金 (11671241; 12001340);山西省自然科学基金 (201901D211411);山西省高等学校科技创新计划 (2019L0472).

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).

摘要:

贻贝种群作为海岸生态系统食物链网络的一个关键环节,其空间分布模式对海岸生态系统的健康发展具有重要影响.目前的研究工作忽略了某一位置贻贝生物量的增加是由其它位置的贻贝移动到此处并捕食藻类引起的.本文构建了具有非局部捕食效应的藻类--贻贝空间扩散模型,首先计算出无扩散系统存在两个平衡点并给出其局部渐进稳定的条件,然后基于 Turing 失稳理论,推导出扩散系统在贻贝生存平衡点附近发生 Turing 失稳的条件.进一步,通过数值模拟展示出贻贝种群随时间演化的空间分布模式,该模式最终形成高密度点状分布结构.最后,参数敏感性分析表明:两种群的扩散速率显著影响了贻贝种群的空间分布模式,说明两种群移动规律的改变可能会破坏海岸生态系统的稳定演化;而非局部捕食效应的影响效果不明显,更利于贻贝种群的持续生存.本研究有助于人们更好地从数学层面理解贻贝种群的发展演化规律,为海岸生态系统资源的合理开发与利用提供理论支撑.

关键词: 藻类--贻贝模型, 非局部捕食效应, 空间分布模式, 参数敏感性分析

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

中图分类号: