Stability and bifurcation of delayed bidirectional gene regulatory networks with negative feedback loops

This paper studies the stability and bifurcation of three cases of bidirectional gene regulatory networks with negative feedback loops and time delays. The uniqueness of the positive equilibrium point of the gene regulatory networks is verified. The delay independent stability conditions of the networks are established by analyzing their corresponding characteristic equations. The existence of the Hopf bifurcation of the networks with or without time delays is presented. Numerical simulations demonstrate the correctness of the obtained theoretical results.