The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation

Abstract We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable Andronov–Hopf bifurcation (from here on abbreviated to ‘Hopf bifurcation’). It is easily shown that any such network must have at least three species and four irreversible reactions, one example a with exactly reactions was previously known due Wilhelm. In this paper, we develop both theory computational tools fully classify three-species, four-reaction, bimolecular CRNs, according whether they admit or forbid Hopf bifurcation. show there are, up natural equivalence, 86 minimal nondegenerate Amongst these, able decide supercritical subcritical bifurcations. Indeed, 25 bifurcations, can confirm all Bautin A total 31 more than periodic orbit. Moreover, 29 these coexistence stable equilibrium Thus, fairly complex behaviours not very rare in networks. Finally, use developed inheritance dynamical CRNs predict occurrence larger include find as subnetworks sense.