AN EXTENSION OF THE FIEDLER-MOCHIZUKI THEORY FOR REGULATORY NETWORKS OF ODES TO TIME-DELAY SYSTEMS

Abstract

We consider the dynamics of a system of differential equations called a Regulatory Network, which represents complex regulatory relationships such as gene regulatory networks. The paper by Fiedler-Mochizuki et al.[3] showed that it is possible to identify a set of determining nodes that determines the asymptotic dynamics of the Regulatory Network from its network structure alone. We extend this theory to the case where the regulatory network contains time delays.