Competitive Exclusion for Chemostat Equations with Variable Yields

Tewfik Sari (1, 2)

1 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles
2 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme

In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu (SIAM J. Appl. Math. 34:760-763, 1978) and by Wolkowicz and Lu (SIAM J. Appl. Math. 52:222-233, 1992) in the case when growth rates are proportional to food uptakes. Our result generalizes a large variety of previous results obtained by Lyapunov techniques.

Mots clés: LYAPUNOV FUNCTION; GLOBAL ASYMPTOTIC STABILITY; VARIABLE YIELD; VARIABILITE; FONCTION MATHEMATIQUE; CHEMOSTAT COMPETITIVE EXCLUSION PRINCIPLE

Domaines: Sciences de l'environnement

Tewfik Sari. Competitive Exclusion for Chemostat Equations with Variable Yields. Acta Applicandae Mathematicae, 2012, 123 (1), p. 201 - p. 219. ⟨10.1007/s10440-012-9761-8⟩. ⟨hal-00780065⟩