中文摘要：

利用简单的浮游生物捕食模型,研究浮游植物产生毒性在具有时间延迟下对系统的影响.通过对所建时滞微分方程的分析,得到了系统通过hopf分支产生可激励性质的时滞窗口.利用计算机模拟的手段进一步验证了分析的结果,并考察了毒性释放率在震荡状态下对频率和振幅的影响.结果表明毒性发作时间的延迟对系统的动态影响较大,不同延迟值对系统稳定性的影响可能不同.但在系统不稳定的条件下浮游植物产生的毒性降低了震荡的频率,增加振幅,一定程度上控制了＂水花＂的形成.

英文摘要：

This paper explores the effects of the time delay of toxin produced by phytoplankton on a simple predator-prey system of plankton.By the analysis of a set of delay differential equations,we obtain the window of time delay in which the system oscillates through hopf bifurcation.Furthermore,using computer simulation,we examine the influences of toxin on the frequency and amplitude of oscillation.It is concluded that the increase of toxin contributes to decreasing the frequency of oscillation and increasing the amplitude of oscillation.This indicates that the toxin with time delay controls the bloom of plankton to some extent.