具时滞增长的变输入恒化器模型的一致持续生存准则及周期情形的完全分析
Uniform persistence criteria for a variable inputs chemostat model with delayed response in growth and complete analysis of the periodic case
摘要：
研究了一类具有时滞（固定）生长反应的变稀释率、变营养输入的单种群恒化器模型。本文的第一个目标是证明持久性意味着一致持久性。然后，我们集中在特定的情况下，周期性的营养输入和相同的周期性稀释与延迟响应的增长。我们得到一个阈值的模型的（均匀）持久性或每个解决方案的生物量趋于消失。此外，我们证明了持久性等价于存在唯一的非平凡周期解。我们还证明了这种解决方案是有吸引力的。我们注意到，在任何情况下，我们都不需要对延迟的大小施加任何限制。
英文摘要：
We study a single-species chemostat model with variable nutrient input and variable dilution rate with delayed (fixed) response in growth. The first goal of this article is to prove that persistence implies uniform persistence. Then we concentrate in the particular case with periodic nutrient input and same periodic dilution with delayed response in growth. We obtain a threshold for either the (uniform) persistence of the model or that the biomass of every solution tends to vanish. Furthermore, we prove that persistence is equivalent to the existence of a unique non-trivial periodic solution. We also prove that this solution is attractive. We remark in no case we need to impose any restrictions on the size of the delay.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
