Stability and bifurcation of genetic regulatory networks with delays

A four-dimension genetic regulatory network model with double genes and four delays is considered. The existence of Hopf bifurcation is first considered and then explicit formulas are derived by using the normal form method and center manifold theory to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions. Finally, numerical simulations are carried out to support the theoretical analysis of the research.