Center Bifurcation for the Smallest Bimolecular Mass-Action System

Abstract

This paper investigates the centre bifurcation of the smallest bimolecular mass-action system. A three-dimensional reaction network, consisting of three species and four reactions, governed by mass-action kinetics with a positive equilibrium point, is considered. In addition to the stability analysis of the equilibrium point, the dynamic directions of the model in its planes are examined. In \cite{Banaji2023}, it is shown that the equilibrium point is classified as a centre when the reaction rate constants satisfy a specific condition, leading to a vertical Andronov-Hopf bifurcation. It is demonstrated that only one limit cycle can bifurcate from the centre equilibrium point using a bifurcation technique.