Hopf bifurcation analysis of a turbidostat model with discrete delay

In this contribution, the dynamic behaviors of a turbidostat model with discrete delay are investigated. With the delay of digestion chosen to be a bifurcation parameter, we find that Hopf bifurcations occur when the delay crosses some critical values. Also, by employing the normal form theory and the center manifold theorem, we determine the type and stability of the bifurcating periodic solutions. Finally, numerical simulations are offered to support our results.