Feedback control of the genetic networks with time delay

In this paper, the modeling and oscillation of the genetic network are studied. The circadian rhythm model consists of three Michaelis-Menten equations. With singular perturbation theory, the system can be transferred to a two-dimension one, and the period oscillation is caused by the positive and negative feedback loops in the biochemical networks. The effects of time delay on the system stability are also analyzed. The simulations are presented to show our theoretical results.