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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

工程数学学报 ›› 2021, Vol. 38 ›› Issue (4): 586-600.doi: 10.3969/j.issn.1005-3085.2021.04.012

• • 上一篇    

具有Holling-II型和非局部时滞的植被模型斑图动力学（英）

梁   娟1,2,3,    李   莉4,   崔   亮5,   郭尊光1,2,3   

  1. 1- 太原工业学院理学系，太原  030008 2- 中北大学大数据学院，太原  030051 3- 中北大学理学院，太原  030051 4- 山西大学计算机与信息技术学院，太原  030006 5- 山西财经大学资源环境学院，太原  030006
  • 收稿日期:2020-12-06 接受日期:2021-03-19 出版日期:2021-08-15 发布日期:2021-10-15
  • 通讯作者: 李 莉 E-mail: lili831113@sxu.edu.cn
  • 基金资助:
    国家自然科学基金 (42075029)；国家重点研发计划 (2018YFE0109600)；山西省自然科学基金 (201901D111322)；太原工业学院青年(后备)学科带头人支持计划 (201808).

Pattern Dynamics of Vegetation System with Holling-type II and Nonlocal Delay

LIANG Juan1,2,3,   LI Li4,   CUI Liang5,   GUO Zun-guang1,2,3   

  1. 1- Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    2- Data Science and Technology, North University of China, Taiyuan 030051
    3- School of Science, North University of China, Taiyuan 030051
    4- School of Computer and Information Technology, Shanxi University, Taiyuan 030006
    5- College of Resources and Environment, Shanxi University of Finance and Economics, Taiyuan 030006
  • Received:2020-12-06 Accepted:2021-03-19 Online:2021-08-15 Published:2021-10-15
  • Contact: L. Li. E-mail address: lili831113@sxu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (42075029); the National Key Research and Development Program of China (2018YFE0109600); the Natural Science Foundation of Shanxi Province (201901D111322); the Program for the (Reserved) Discipline Leaders of Taiyuan Institute of Technology (201808).

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摘要： 在干旱半干旱地区，植被通过根部的非局部作用吸收水分．本文建立了一个具有非局部时滞项和Holling-II功能反应函数的数学模型．通过数学分析，得到了植被-水模型产生图灵斑图的条件，数值模拟得到了在不同时滞参数下植被的空间分布．结果显示时滞对植被密度的影响呈现“抛物现象”且时滞能够引起斑图结构的改变．具体来讲，随着时滞的增加，斑图从均匀分布向不均匀转化；当时滞小于阈值时，植被密度随着时滞的增加而减少，反之，植被密度随着时滞的增加而增加．此外，功能反应项系数与植被密度呈现正相关关系．数值模拟的结果揭示了非局部作用和Holling-II功能反应函数对植被斑图的影响，为植被保护提供了新的理论依据．

关键词: 非局部时滞, 植被, 沙漠化, 斑图

Abstract: In arid or semi-arid regions, vegetation absorbs water through the nonlocal effects of roots. The paper establishes a mathematical model with nonlocal delay and Holling-II functional response function. By mathematical analysis, the conditions under which the vegetation-water model generates the Turing pattern are obtained. The spatial distributions of vegetation under different delays are obtained by numerical simulation. The simulation results show that delay in vegetation density presents a ``parabolic phenomenon", and delay can cause a change in the pattern structure. Specifically, as delay increases, a pattern is transformed from uniform distribution to nonuniform distribution. When the delay parameter is less than the threshold, vegetation density increases with the decrease of delay. On the contrary, the density of vegetation will increase with the increase of delay. Besides, the functional response term coefficient is positively correlated with vegetation density. The numerical simulation results show the influence of nonlocal delay and Holling-II functional response function on vegetation pattern, which provide a new theoretical basis for vegetation protection.

Key words: nonlocal delay, vegetation, desertification, pattern

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