EMERGENCE AND COLLAPSE OF LIMIT CYCLES IN THE GLYCOLYSIS MODEL

Abstract

The main question in this paper is to show that, for appropriated fixed 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-diffusion system modeling glycolysis. To do so, we use Lyapunovs method.