中文摘要：

针对一类浮游生物模型,根据非线性分析和偏微分方程性质,利用椭圆方程不动点指数理论研究了此模型共存解的存在性.由于此模型的特殊性,不能直接应用不动点指数理论,本文给出了此类问题的一般性解决方法,然后通过数值方法给出了模型的一组数值模拟结果.结果表明当营养物浓度变化时,浮游植物密度与浮游动物密度产生变化,一定程度上印证了赤潮现象产生的原因.

英文摘要：

A kind of model about plankton is studied .According to the nonlinear analysis and partial dif‐ferential equations ,the existence of positive steady solutions of the model is obtained by using the theory of fixed point index .The conclusion can′t be get directly due to the particularity of the model ,and the general solution of this kind of situation is given .T hen a set of numerical result is given by numerical method ,which indicates that the change of density of zooplankton and phytoplankton during nutrition in‐creasing of the numerical result can reflect the red tide to some degree .