Stability and Bifurcation of Delayed Gene Regulatory Network with Self-Feedback, Positive Feedback and Negative Feedback

摘要

This letter investigates the stability and bifurcation of delayed gene regulatory network with self-feedback, positive feedback and negative feedback. The stability condition of the network without time delays is obtained. The establishment of the existence condition of Hopf bifurcation of the network is given by considering its characteristic equation. With the variation of the time delays, the network appears Hopf bifurcation and loses its stability which is theoretically and numerically illustrated. The bistability of the network is also numerically presented.