恒化器中生物适应性生长模型的周期解

本文基于恒化器培养微生物代谢过程所建立的微分方程，考虑微生物对环境的适应性，并赋予营养基流速以周期输入，研究微分方程模型周期解的存在性与渐近性。该系统描述恒化器中因微生物赖以生存的一种营养基供给浓度的周期变化，而使微生物在快速吸收营养、快速繁殖与静止吸收营养、停止繁殖的两种生存状态之间转换，首先讨论各种可能生存状态周期解的存在性，共有3种类型的周期解，然后利用Poineare映射和方程的耗散性对周期解作定性分析。得出以下结论：当Floquet乘子时，二类生存状态的种群均会被淘汰出恒化器，此时种群会渐近地趋于只有快速吸收营养物种存活的稳定周期状态，或者是进入同类微生物快速吸收营养与静止吸收营养2种生存状态共存的周期状态。

Periodic Solutions of the Chemostate Model with Adaptive Nutrient Uptaking

A chemostate model of one microbe feeding on a single essential nutrient with adaptive nutrient uptake is considered.And the input speed of the essential nutrient is assumed varying periodically around a mean value.Firstly we discussed the existence of the periodic solutions about this model which considered the adaptive mechanism of the species by switching between cells with active and dormant state.Active cells means assimilating nutrient quickly and producing offspings quickly.Dormant ones don't assimil...