(untitled) (European Journal of Pure and Applied Mathematics, 2025)
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 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.