Globally delay-independent stability of ring-structured genetic regulatory networks

Modeling genetic regulatory networks in terms of differential equations with time delays provides a powerful tool for understanding gene regulatory processes in living organisms. In this paper we studied the globally delay-independent stability ring-structured genetic regulatory networks. We first present a sufficient condition for globally delay-independent stability of such genetic regulatory networks, based on the M-matrix theory. Then this sufficient condition is reduced to determine if the roots of a polynomial lie in the right complex plane. Finally, autoregulatory network and repressilatory network are employed to illustrate the theorems developed in this study.