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首页> 外文期刊>Nonlinear studies >Effect of delay on growth function of zooplankton in plankton ecosystem model and its consequence on the formation of plankton bloom
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Effect of delay on growth function of zooplankton in plankton ecosystem model and its consequence on the formation of plankton bloom

机译：延迟对浮游生物生态系统模型浮游动物生长功能的影响及其对浮游生物开花形成的影响

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Models of plankton-based ecosystems with delay have received a great deal of attention for the last few decades. This paper deals with a plankton-based ecosystem involving nutrient, phyto- plankton and zooplankton. The model system is studied analytically and the threshold conditions for the existence and stability of various steady states are worked out. Next, we have introduced discrete time delay due to gestation in the functional response term involved with the growth equation of zooplankton. With delay differential equation model system we have studied the effect of time delay on the stability behavior. Next, we have obtained an estimate for the length of time delay to preserve the stability of the model system. Moreover, the existence of Hopf bifurcating small amplitude periodic solutions is derived by considering time delay as a bifurcation parameter. Finally, it is observed that constant nutrient input and dilution rate of nutrient play important role to change the steady state behavior in presence of time lag in gestation of the zooplankton. Computer simulations have been carried out to illustrate various analytical results.
机译：在过去的几十年中，基于浮游生物的具有延迟的生态系统模型受到了广泛的关注。本文讨论了一个基于浮游生物的生态系统，其中包括营养素，浮游植物和浮游动物。对模型系统进行了分析研究，得出了各种稳态存在和稳定性的阈值条件。接下来，由于浮游动物的生长方程所涉及的功能响应项中的妊娠，我们引入了离散的时间延迟。利用时滞微分方程模型系统，我们研究了时延对稳定性行为的影响。接下来，我们获得了时延长度的估计值，以保持模型系统的稳定性。此外，通过将时间延迟作为分叉参数来推导Hopf分叉小振幅周期解的存在。最后，观察到恒定的养分输入和养分的稀释率在浮游动物妊娠中存在时滞的情况下改变稳态行为起着重要作用。已经进行了计算机模拟以说明各种分析结果。

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