Stability analysis of genetic regulatory networks with multiple time delays

A genetic regulatory network is a dynamic system to describe interactions among genes (mRNA) and its products (proteins). From the statistic thermodynamics and biochemical reaction principle, a genetic regulatory network can be described by a group of nonlinear differential equations with time delays. Stability is one of interesting properties for genetic regulatory network. Previous studies have investigated stability of genetic regulatory networks with a single time delay. In this paper, we investigate properties of genetic regulatory networks with multiple time delays in the notion of delay-independent stability. We present necessary and sufficient condition for the local delay-independent stability of genetic regulatory network with multiple time delays which are independent or commensurate.