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具有恐惧效应和离散时滞的IGP模型的动力学分析

发表时间:2021-12-31  浏览量:325  下载量:50
全部作者: 彭思樵,孟益民
作者单位: 湖南大学数学学院
摘 要: 建立了一类具有恐惧效应和离散时滞的共位群内捕食(intraguild predation,IGP)模型。稳定性分析表明,平凡解是不稳定的;当共位群(IG)食饵和IG捕食者的基本再生数都小于1时,半平凡解是全局渐近稳定的;当IG食饵的基本再生数小于1且IG捕食者的基本再生数大于1时,边界平衡点(IG食饵不存在时)是全局渐近稳定的。此外,正平衡点和边界平衡点(IG捕食者不存在时)的稳定性不仅与基本再生数有关,还与恐惧系数和离散时滞相关。数值模拟表明,当恐惧系数非常大时,IG食饵和IG捕食者的种群密度会非常小甚至趋于灭亡。
关 键 词: 动力系统;共位群内捕食(IGP)模型;恐惧效应;基本再生数;稳定性
Title: Dynamic analysis of IGP model with fear effect and discrete time delay
Author: PENG Siqiao, MENG Yimin
Organization: School of Mathematics, Hunan University
Abstract: A class of intraguild predation (IGP) models with fear effect and discrete time delay were established. The stability analysis shows that the trivial solution is unstable. The semi-trivial solution is globally asymptotically stable when the basic reproduction numbers of both intraguild (IG) prey and IG predator are less than 1. When the basic reproduction number of IG prey is less than 1 and the basic reproduction number of IG predator is greater than 1, the boundary equilibrium point (when IG prey does not exist) is globally asymptotically stable. In addition, the stabilities of positive equilibrium point and boundary equilibrium point (when IG predator does not exist) are not only related to the basic reproduction number, but also related to the fear coefficient and discrete time delay. Numerical simulations show that when the fear coefficient is large, the population densities of IG prey and IG predator will be small or even become extinct.
Key words: dynamical system; intraguild predation (IGP) model; fear effect; basic reproduction number; stability
发表期数: 2021年12月第4期
引用格式: 彭思樵,孟益民. 具有恐惧效应和离散时滞的IGP模型的动力学分析[J]. 中国科技论文在线精品论文,2021,14(4):425-439.
 
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