# Building oscillatory chemical reaction networks by adding reversible reactions

## TL;DR

This paper demonstrates that adding reversible reactions to a chemical reaction network that admits oscillation can preserve that oscillatory behavior under certain conditions, extending understanding of network inheritance properties.

## Contribution

It establishes conditions under which oscillation is inherited when reversible reactions are added to a CRN, advancing the theory of oscillatory network construction.

## Key findings

- Oscillation inheritance is possible with reversible reactions under mild conditions.
- The results extend previous inheritance theorems for multistationarity.
- Provides criteria for designing larger oscillatory networks from smaller ones.

## 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.