Dominance and deficiency for Petri nets and chemical reaction networks

Abstract

Inspired by Anderson et al. (J R Soc Interface, 2014, doi:) we study the long-term behavior of discrete chemical reaction networks (CRNs). In particular, using techniques from both Petri net theory and CRN theory, we provide a powerful sufficient condition for a structurally-bounded CRN to have the property that none of the non-terminal reactions can fire for any of its recurrent configurations. We compare this result and its proof with a related result of Anderson et al. and show its consequences for the case of CRNs with deficiency one.