Stability Analysis for Chemical Reaction Networks with Time Delays by Decomposing them into Weakly Reversible Sub-Networks

In recent works, we considered a class of non-weakly reversible chemical reaction networks, and proved that any positive solution to ODEs that describe the dynamics of networks in the class converges to an equilibrium point. Our method for stability analysis is based on decomposing the network into some weakly reversible sub-networks and applying the Deficiency Zero Theorem (DZT) to them. In the present paper, we show that our method can be applied to stability analysis for the same class of non-weakly reversible networks with arbitrary time delays, by extending the DZT to be applicable to delayed networks.