Stability and hopf bifurcation of genetic regulatory networks with multiple delays

In this paper, we study the stability for a triple-gene expression model. We choose the sum of the delays as the bifurcation parameter. The bifurcation will occur when the sum of the delays passes through a critical value. The critical value of the delays is determined. Thus the triple-gene model can remain stable when the sum of the delays is smaller than the critical value. Finally, we verify the correctness of the theoretical results through the numerical simulations.