A stability analysis of a time-varying chemostat with pointwise delay

Frederic Mazenc (1, 2) , Gonzalo Robledo (3) , Daniel Sep Úlveda (4)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 L2S - Laboratoire des signaux et systèmes
3 UCHILE - Universidad de Chile = University of Chile [Santiago]
4 UTEM - Universidad Tecnológica Metropolitana

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.

Mots clés: chemostat; nonautonomous differential delay equations; Lyapunov like functions; Asymptotic stabilty; periodic solutions

Domaines: Mathématiques [math]

Frederic Mazenc, Gonzalo Robledo, Daniel Sep Úlveda. A stability analysis of a time-varying chemostat with pointwise delay. Mathematical Biosciences and Engineering, 2024, 21 (2), ⟨10.3934/mbe.2024xxx⟩. ⟨hal-04621063⟩