In this paper, we analyze a nutrient-phytoplankton model with toxic effects governed by a Holling-type Ⅲ functional. We show the model can undergo two saddle-node bifurcations and a Hopf bifurcation. This results in very interesting dynamics: the model can have at most three positive equilibria and can exhibit relaxation oscillations. Our results provide some insights on understanding the occurrence and control of phytoplankton blooms.

中文翻译：

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具有毒性作用的营养浮游植物模型的分叉与稳定性分析

在本文中，我们分析了具有HollingⅢ类功能的毒性效应的营养性浮游植物模型。我们显示该模型可以经历两个鞍节点分叉和一个霍普夫分叉。这产生了非常有趣的动态：该模型最多可以具有三个正平衡，并且可以表现出松弛振荡。我们的结果为了解浮游植物水华的发生和控制提供了一些见识。