李晓娜.具有时滞和毒素系统的动力学分析[J].数学研究及应用,2021,41(1):33~48
具有时滞和毒素系统的动力学分析
Dynamical Analysis of Toxin Producing Model with Delay
投稿时间:2019-09-20  修订日期:2020-11-13
DOI:10.3770/j.issn:2095-2651.2021.01.005
中文关键词:  浮游植物  浮游动物  毒素  时滞  稳定性
英文关键词:phytoplankton  zooplankton  toxin  delay  stability
基金项目:国家自然科学基金(Grant No.11261058).
作者单位
李晓娜 伊犁师范大学数学与统计学院, 新疆 伊宁 835000 
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中文摘要:
      本文研究了具有抑制底物和时滞的产毒浮游植物与浮游动物相互作用模型, 其中时滞是由浮游动物的繁殖及浮游植物的成熟产生的, 且浮游动植物的相互作用是通过Tissiet功能反映函数来实现的. 文章给出了两种物种共存及共存平衡点稳定的条件, 证明了当时滞参数小于时滞临界值时, 共存平衡点是稳定的, 当时滞参数大于时滞临界值时, 共存平衡点是不稳定的, 且当时滞参数经过时滞临界值时, 系统会出现 Hopf 分支, 并做了数值模拟验证了所得结论的正确性.
英文摘要:
      In this paper, a toxin producing phytoplankton-zooplankton model with inhibitory substrate and time delay is investigated. A discrete time delay is induced to both of the consume response function and distribution of toxic substance term. Moreover, Tissiet type function is used for zooplankton grazing to account for the effect of toxication by the TPP population. The conditions to guarantee the coexistence of two species and stability of coexistence equilibrium are given. In particular, we show that there exist critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. Some numerical simulations are executed to validate the analytical findings.
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