Abstract: This paper studies the dynamical behavior of oscillatory expression in E.coli with negative state feedback. Results show that the bifurcation happens when the sum of the time delay reaches a critical value. Interestingly, after adding the control of negative state feedback, the Hopf bifurcation phenomenon is delayed, which indicates that the model can keep steady within a bigger range. What’s more, numerical simulations are carried out to support the theoretical analysis.

Key words: genetic regulatory, stability, Hopf bifurcation, delay, bifurcation control, state feedback