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

Banaji, Murad and Boros, Balázs and Hofbauer, Josef (2023) The smallest bimolecular mass-action system with a vertical Andronov–Hopf bifurcation. Applied Mathematics Letters, 143: 108671. ISSN 0893-9659

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, up to a natural equivalence, the only such mass-action system that admits a center via an Andronov–Hopf bifurcation.