Mazenc Frédéric, Robledo Gonzalo, Sepúlveda Daniel
EPI DISCO Inria-Saclay, Laboratoire des Signaux et Systèmes (UMR CNRS 8506), CNRS, CentraleSupélec, Université Paris-Sud, 3 rue Joliot Curie, 91192, Gif-sur-Yvette, France.
Departamento de Matemáticas, Universidad de Chile, Casilla 653, Santiago, Chile.
Math Biosci Eng. 2024 Jan 22;21(2):2691-2728. doi: 10.3934/mbe.2024119.
This paper revisits a recently introduced chemostat model of one-species with a periodic input of a single nutrient which is described by a system of delay differential equations. Previous results provided sufficient conditions ensuring the existence and uniqueness of a periodic solution for arbitrarily small delays. This paper partially extends these results by proving-with the construction of Lyapunov-like functions-that the evoked periodic solution is globally asymptotically stable when considering Monod uptake functions and a particular family of nutrient inputs.
本文重新审视了一个最近引入的单物种恒化器模型，该模型具有单一营养物质的周期性输入，由一个时滞微分方程组描述。先前的结果提供了充分条件，确保对于任意小的时滞存在且唯一的周期解。本文通过构造类李雅普诺夫函数证明，在考虑莫诺德摄取函数和特定营养物质输入族时，所引发的周期解是全局渐近稳定的，从而部分扩展了这些结果。
