具有恐惧效应和离散时滞的IGP模型的动力学分析
首发时间:2021-04-15
摘要:本文以简单的IGP(Intraguild Predation)模型为基础,建立了一类具有恐惧效应和离散时滞的IGP模型. 稳定性分析表明,平凡解是不稳定的;当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 IGP模型 恐惧效应 基本再生数 稳定性
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Dynamic analysis of IGP model with fear effect and discrete time delay
Abstract:In this paper, based on the simple intraguild predation(IGP) model, a class of IGP models with fear effect and discrete time delay have been 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 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 and boundary equilibrium (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 was large, the population densities of IG prey and IG predator would be small or even become extinct.
Keywords: Dynamic system Intraguild predation model Fear effect Basic reproduction number Stability
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