It is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem. We show that to find a strongly endotactic/endotactic/consistent/conservative realization that is dynamically equivalent to the mass-action system generated by a given network (when it exists), it suffices to consider only the source vertices of the given network. We also present a characterization of the dynamical relationships that exist between several types of weakly reversible deficiency one networks.
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