Global dynamics of the chemostat with variable yields

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.