中文摘要：

浮游植物＂水花＂的形成机制和动态是海洋生态学研究的一个重要问题.浮游植物＂水花＂表现为浮游植物种群密度呈周期性的快速增长和快速消退等动态,从数学模型上看就是可激励系统.本文利用简单的浮游生物捕食模型,研究了浮游植物产生的毒性对具有浮游动物稀释毒性系统可激励的影响.通过对所建微分方程模型的分析,得到了系统产生hopf分支的条件.结果表明,在没有浮游动物稀释毒性的系统中,浮游植物产生的毒性不能使系统呈周期性动态;可在浮游动物稀释毒性时,适中的毒性会诱导系统产生极限环.通过模拟,得到了由于浮游动物对毒性的稀释而能够促进＂水花＂形成的结论.

英文摘要：

The mechanisms and dynamics of plankton bloom are the important problems in aquatic ecological system.The studies on plankton bloom show that the density of plankton is found to exhibit the periodical fast increase and quick decrease.From viewpoints of mathematics it is an excitable system.In this paper,we explore the effects of the toxin produced by plankton on a simple predator-prey system with the dilution of toxin by zooplankton.The observation in nature showed that the concentration of toxin will decline with zooplankton and has significant influences on the life of zooplankton.Here we build the simplest predator-prey model with dilution of toxin so that the effects of dilution of toxin could be clearly examined.By the analysis of a set of differential equations,we obtain the condition of parameters on which the system oscillates through hopf bifurcation.It is indicated that without the dilution of zooplankton the toxin of plankton can not induce the system excitable and with dilution intermediate toxin by plankton will produce limit cycle.It is concluded that the dilution of toxin by zooplankton can promote the bloom of plankton in this simple system.Of course,the roles of the dilution of toxin with other biological mechanisms will be further explored in the future.