Dominance and Deficiency for Petri Nets and Chemical Reaction Networks

TL;DR

This paper investigates the long-term behavior of discrete chemical reaction networks using Petri net theory, providing conditions under which certain reactions cannot fire in recurrent configurations, especially for networks with deficiency one.

Contribution

It introduces a new sufficient condition linking Petri net properties to CRN behavior, extending previous results and analyzing deficiency one networks.

Findings

Identifies conditions preventing non-terminal reactions from firing in recurrent states

Provides a comparison with existing results by Anderson et al.

Analyzes implications for CRNs with deficiency one.

Abstract

Inspired by Anderson et al. [J. R. Soc. Interface, 2014] 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 all 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.