Global dynamics of the chemostat with variable yields

Tewfik Sari (1, 2)

1 MERE - Water Resource Modeling
2 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]

In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. LaSalle's extension theorem of the Lyapunov stability theory is the main tool.

Mots clés: chemostat; competitive exclusion principle; Lyapunov function; global asymptotic stability; variable yield model

Domaines: Systèmes dynamiques [math.DS]

Tewfik Sari. Global dynamics of the chemostat with variable yields. 2010. ⟨hal-00459923⟩