An extension of the Fiedler–Mochizuki theory to time-delay systems

Abstract

We extend the analysis of regulatory networks, represented by differential equations, to account for time delays, which are often critical in modeling biological systems such as gene regulatory networks. Building on the framework of Fiedler et al. (2013), who identified determining nodes influencing long-term network dynamics based solely on the network structure, we introduce a novel method for incorporating time delays into this analysis. Our approach enhances the precision of studying complex biological systems by providing a more accurate representation of dynamic interactions over time.