Hopf bifurcation analysis for genetic regulatory networks with two delays

In this paper, a genetic regulatory network with two time delays is considered. Firstly, the stabilities with one delay and two delays are investigated. It is shown that the stability switches for time delays, and Hopf bifurcation may occur within certain range of the model parameters. Then, combining the normal form method and the center manifold theorem, we derive the explicit formulas which determine the direction of the bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical examples are exploited to support our results.