Reachability Analysis of Low-Order Discrete State Reaction Networks Obeying Conservation Laws

Figure 3

Graphical explanation of how the reaction network structure of in the proof of Proposition 15 is constructed. (a) Reaction network structure of an -dimensional d-CRN . (b) Reaction network structure of resulting from merging the species and of along their shared reaction (and reverse counterpart reaction ). Note that by merging and we obtain a stoichiometric matrix having redundant reactions (e.g., , resulting in , ) and zero reaction vectors (i.e., self-loops on ), but they are omitted in (b). A directed cycle on which the chosen reaction lies is depicted in gray.

(a)

(b)