一类浮游生物捕食-食饵模型的分歧解

摘要

研究了一类海洋生态系统中浮游生物捕食-食饵模型平衡态正解的存在性，其功能反应函数为HollingⅡ型。利用线性稳定性理论得到正常数平衡解的稳定性。借助分歧理论，以扩散系数为分歧参数，构造了发自正常数平衡解分支的非常数平衡解分支，从而给出了模型非常数平衡态正解的存在性。%T he existence of positive solutions of the steady-state system for the predator-prey model be-tween plankton in a marine ecosystem with Holling type II functional response is studied .Firstly ,by the linearized stability theory ,the stability of positive constant steady-state solution is discussed .Secondly , by means of the bifurcation theory ,non-constant steady-state solutions bifurcating from the positive con-stant steady-state solution are given by treating the diffusion coefficient as the bifurcation parameter , w hich implies the existence of non-constant steady-state solutions .