A Stability Aanalysis of a Time-Varying Chemostat with Pointwise Delay

Frederic Mazenc (1, 2) , Gonzalo Robledo (3) , Daniel Sepulveda (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]; Sciences du Vivant [q-bio]

Frederic Mazenc, Gonzalo Robledo, Daniel Sepulveda. A Stability Aanalysis of a Time-Varying Chemostat with Pointwise Delay. Mathematical Biosciences and Engineering, 2024, 21 (2), pp.38. ⟨10.3934/mbe.2024119⟩. ⟨hal-04412087⟩