Independent, Incidence Independent and Weakly Reversible Decompositions of Chemical Reaction Networks

Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions arcs. A CRN is weakly reversible if each of its connected components strongly connected. Weakly can be considered the most important class networks. Now, stoichiometric subspace a network linear span vectors (i.e., difference between complexes). decomposition independent (incidence independent) direct sum subspaces maps) subnetworks equals map) whole network. Decompositions used to study relationships positive steady states system (induced from partitioning set underlying network) those subsystems. In this work, we revisit our novel method finding decomposition, use it expand applicability on (vector) states. We also explore CRNs embedded deficiency zero subnetworks. addition, establish for incidence CRN. determine all forms decompositions network, provide number such decompositions. Lastly, networks, that independence sufficient condition weak reversibility identify subclasses where any reversible.