Dominance and deficiency for Petri nets and chemical reaction networks
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Inspired by Anderson et al. (J R Soc Interface, 2014, doi: 10.1098/rsif.2013.0943) 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.
KeywordsChemical Reaction Network Incidence Matrix Outgoing Edge Terminal Vertex Mass Action Kinetic
We thank David Anderson for kindly explaining his work during the Banff International Research Station (BIRS) workshop on CRNs (14w5167). Also, we thank the organizers of this workshop during which this research was initiated. We are indebted to Matthew Johnston for carefully reading an earlier version of this paper and for providing useful comments. And in particular for finding a counterexample to a conjecture in an earlier version of this paper. We also thank David Anderson, Gheorghe Craciun and Matthew Johnston for noticing an omission in the definition of \(\le _d\) in the conference version of this paper. We finally thank the referees for their useful comments, and in particular for noticing an omission in an earlier version of Lemma 3.3. R.B. is a postdoctoral fellow of the Research Foundation—Flanders (FWO).
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