Delayed Feedback Control and Bifurcation Analysis in a Chaotic Chemostat System

Abstract

In this paper, the effect of delay on a nonlinear chaotic chemostat system with delayed feedback is investigated by regarding delay as a parameter. At first, the stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, some numerical simulation examples are given, which indicate that the chaotic oscillation can be converted into a stable steady state or a stable periodic orbit when delay passes through certain critical values.