带防御机制的捕食者-食饵模型中恐惧因子的作用

doi:10.6040/j.issn.1671-9352.0.2019.670

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (3): 121-126.doi: 10.6040/j.issn.1671-9352.0.2019.670

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带防御机制的捕食者-食饵模型中恐惧因子的作用

王静,伏升茂

西北师范大学数学与统计学院, 甘肃 730070

发布日期:2020-03-27
作者简介:王静(1993— )女, 硕士研究生, 研究方向为偏微分方程与生物数学. E-mail: MNMYX520@163.com
基金资助:
国家自然科学基金资助项目(11761063,11361055)

Effect of fear factor on a predator-prey model with defense mechanish

WANG Jing, FU Sheng-mao

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2020-03-27

摘要/Abstract

摘要： 研究了一类具有恐惧因子且食饵防御机制的捕食者-食饵模型,得到了非负平衡点局部渐近稳定的条件以及 Hopf 分支存在的条件, 并讨论了恐惧因子对种群密度的影响,最后进行了数值模拟。结果表明, 恐惧程度的增加会导致捕食者种群密度的降低, 但对食饵种群密度无直接影响。

关键词: 捕食者-食饵模型, 恐惧因子, Hopf分支, 食饵防御机制

Abstract: A predator-prey model with fear factor and prey defense mechanism is studied. The conditions for the local asymptotic stability of positive equilibrium and the conditions for existence of Hopf bifurcation are obtained, and the effect of fear factor on population density is discussed. Finally, numerical simulation is carried out. As a result, it is shown that the increase of fear degree will lead to the decrease of predator population density, but has no direct effect on the density of prey population.

Key words: predator-prey model, fear factor, hopf bifurction, defense mechanism

中图分类号:

O175.26

王静,伏升茂. 带防御机制的捕食者-食饵模型中恐惧因子的作用[J]. 《山东大学学报(理学版)》, 2020, 55(3): 121-126.

WANG Jing, FU Sheng-mao. Effect of fear factor on a predator-prey model with defense mechanish[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 121-126.

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带防御机制的捕食者-食饵模型中恐惧因子的作用

Effect of fear factor on a predator-prey model with defense mechanish

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