Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays

We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons and Fractals 2004;20:995-1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. The results are consistent with the numerical results in [Chaos, Solitons and Fractals 2004;20:995-1004]