时滞浮游动植物营养圈的稳定性分析

Stability Analysis in a Nutrient-phytoplankton-zooplankton Model

主要对含时滯的浮游动植物营养圈模型的稳定性进行分析.首先分析了模型平衡点稳定的条件,然后利用多项式理论分析了特征根的分布,得到分支周期解存在的条件,最后用几组数值模拟对文中出现的现象进行了解释.进一步预测了该模型存在由平衡点到周期解,再到平衡点的稳定性开关现象.

In this paper,nutrient-phytoplankton-zooplankton model with delay is considered.Firstly,stability and Hopf bifurcation of the coexisting equilibrium are given.Then the existence of bifurcation periodic solutions via employing the polynamial theorem to analyze the distributions of the roots of the characteristic.Finnaly,some numerical simulations are carried out to illustrate the obtained results.Furthermore,we forecast that delay can induce the occurrence of the stability switches.