Stability of genetic regulatory networks with time delay

We present a model for genetic regulatory networks with time delays, which is described by functional differential equations or delay differential equations (DDE), provide necessary and sufficient conditions for simplifying the genetic network model, and further analyze nonlinear properties of the model in terms of local stability and bifurcation. The proposed model transforms the original interacting network into several simple transcendental equations at an equilibrium, thereby significantly reducing the computational complexity and making analysis of stability and bifurcation tractable for even large-scale networks. Finally, to test the theory, a repressilator model is used as an example for numerical simulation.