Building oscillatory chemical reaction networks by adding reversible reactions

Abstract

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.

updated to elucidate the proof

Cited by in corpus (3)

• Adding species to chemical reaction networks: preserving rank preserves nondegenerate behaviours
• Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits
• The inheritance of local bifurcations in mass action networks