Hopf bifurcation analysis for a model of RNA silencing with two delays

In this paper, a four-dimension genetic regulatory network model with two time delays is considered. Firstly, the existence of Hopf bifurcation is considered. Then, by using the normal form method and center manifold theory, the explicit formulas are derived to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, one numerical example is exploited to support the theoretical analysis of the research.