In this paper, we propose a class of resource-based growth models with delays in algal digestion and detritus-nutrient recycling, and investigate the model based on two different survival scenarios of algae during nutrient transformation. One scenario considers the survival rates of algae during nutrient uptake, while the other overlooks this factor. We find a significant difference in the estimated time window required for clearing the lake of detritus between the two models, and both are longer compared to the model without algal digestion delay. Moreover, the internal equilibria of both scenarios undergo an infinite number of stability switches, however, the key parameters leading to these stability switches differ. Notably, in the model accounting for algal death during nutrient uptake, there exists a safe zone where the stability of the internal equilibrium remains unaffected by the detritus-nutrient recycling delay, provided that the algal digestion delay falls within a suitable range. The findings derived from this study can provide valuable insights for the development of efficacious approaches in safeguarding the ecological integrity, managing algal blooms, facilitating sustainable fishery practices, and fostering favorable economic outcomes within the realm of water resources advancement.

中文翻译：

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鱼类生存受藻华影响：基于资源的生长模型，具有藻类消化延迟和碎屑养分回收延迟

在本文中，我们提出了一类延迟藻类消化和碎屑养分循环的基于资源的生长模型，并基于藻类在养分转化过程中的两种不同的生存情景对该模型进行了研究。一种情况考虑了藻类在营养吸收过程中的存活率，而另一种情况则忽略了这一因素。我们发现两个模型之间清除湖泊碎屑所需的估计时间窗口存在显着差异，并且与没有藻类消化延迟的模型相比，两者都更长。此外，两种情况的内部平衡都会经历无数次稳定性切换，然而，导致这些稳定性切换的关键参数不同。值得注意的是，在考虑养分吸收过程中藻类死亡的模型中，存在一个安全区，只要藻类消化延迟落在合适的范围内，内部平衡的稳定性就不会受到碎屑-养分循环延迟的影响。这项研究的结果可以为保护生态完整性、管理藻华、促进可持续渔业实践以及在水资源开发领域促进有利的经济成果等有效方法的开发提供宝贵的见解。