  We show that if a chemical reaction network (CRN) admits nondegenerate
(resp., linearly stable) oscillation, and we add new reversible reactions
involving new species to this CRN, then the new CRN so created also admits
nondegenerate (resp., linearly stable) oscillation provided certain mild and
easily checked conditions are met. This claim that the larger CRN "inherits"
oscillation from the smaller one, provided it is built from the smaller CRN in
an appropriate way, follows an analogous result involving multistationarity. It
also adds to a number of prior results on the inheritance of oscillation; these
collectively often allow us to determine the capacity of a given network for
oscillation based on an analysis of its subnetworks.
