Global dynamics of the chemostat with different removal rates and variable yields

Tewfik Sari (1, 2) , Frédéric Mazenc (1)

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. We construct a Lyapunov function which reduces to the Lyapunov function which where considered by S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case where the response functions are of Michaelis-Menten type and the yields are constant. Various applications are given including constant, linear and quadratic yields.

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

Domaines: Systèmes dynamiques [math.DS]

Tewfik Sari, Frédéric Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. 2009. ⟨hal-00418676v1⟩