EMERGENCE AND COLLAPSE OF LIMIT CYCLES IN THE GLYCOLYSIS MODEL

Resumen

The main question in this paper is to show that, for appropriated xed values of the rate for the
low activity state in the system modeling a type of glycolysis, a single limit cycle emerges after a
supercritical Hopf Bifurcation as the bifurcation parameter increases, while continuously increasing
the bifurcation parameter, this limit cycle collapses after a subcritical Hopf bifurcation. The mo-
tivation is in the study of Hopf bifurcations about the spatially homogeneous equilibrium in the
reaction-diusion system modeling glycolysis. To do so, we use Lyapunovs method.
KEYWORDS: non-degenerate Hopf bifurcation, pattern formation, asymptotic expansion, glyco-
lysis model, reaction-diusion.
MSC: 35B32, 35B36, 35C20, 92E20, 35K57, 35B40