The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation

TL;DR

This paper introduces the smallest known three-species bimolecular mass-action system that exhibits a vertical Andronov-Hopf bifurcation, leading to a center with a surface filled with periodic orbits.

Contribution

It identifies the unique minimal bimolecular chemical reaction network capable of producing a center through an Andronov-Hopf bifurcation.

Findings

System exhibits a degenerate Andronov-Hopf bifurcation of infinite codimension.

The system is the only three-species bimolecular network with this property.

System dynamics include a center with a two-dimensional invariant surface.

Abstract

We present a three-dimensional differential equation, which robustly displays a degenerate Andronov-Hopf bifurcation of infinite codimension, leading to a center, i.e., an invariant two-dimensional surface that is filled with periodic orbits surrounding an equilibrium. The system arises from a three-species bimolecular chemical reaction network consisting of four reactions. In fact, it is the only such mass-action system that admits a center via an Andronov-Hopf bifurcation.