Stability and Robustness Analysis for a Multispecies Chemostat Model with Delays in the Growth Rates and Uncertainties
Stability and Robustness Analysis for a Multispecies Chemostat Model with Delays in the Growth Rates and Uncertainties
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DOI：
10.3934/dcdsb.2018098
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发表时间：
2018-03
影响因子：
1.2
通讯作者：
F. Mazenc;G. Robledo;Michael A. Malisoff
中科院分区：
文献类型：
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作者：
F. Mazenc;G. Robledo;Michael A. Malisoff
我们研究了具有任意数量的竞争物种、一种底物和恒定稀释率的恒化器模型。我们允许增长率的延迟和附加的不确定性。使用某些物种的恒定输入，我们得出延迟大小的界限，以确保不确定性为零时平衡的渐近稳定性，这可以允许多个物种的持久性。在延迟和不确定性的情况下，我们提供了延迟和不确定性的界限，以确保输入状态在不确定性方面的稳定性。
We study a chemostat model with an arbitrary number of competing species, one substrate, and constant dilution rates. We allow delays in the growth rates and additive uncertainties. Using constant inputs of certain species, we derive bounds on the sizes of the delays that ensure asymptotic stability of an equilibrium when the uncertainties are zero, which can allow persistence of multiple species. Under delays and uncertainties, we provide bounds on the delays and on the uncertainties that ensure input-to-state stability with respect to uncertainties.