Bifurcation analysis of a chemostat model with two distributed delays

Beretta and Takeuchi [Differ. Equat. Dyn. Syst. 2 (1994) 19] proposed and studied a chemostat-type model with two distributed delays. For this model, He et al. [SIAM J. Math. Anal. 29 (1998) 681] showed that the positive equilibrium can be globally asymptotically stable if the mean delays are sufficiently small. In this paper, using the average time delay as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations. Computer simulations illustrate the result. The mistakes in [Chaos, Solitons & Fractals 17 (2003) 879] are pointed out and corrected.