Topological analysis of chaos in a three-variable biochemical model.
A three-variable biochemical prototype involving two enzymes with autocatalytic regulation proposed by Decroly and Goldbeter (1987) is analyzed using a topological approach. A two-branched manifold, a so-called template, is thus identified. For certain control parameter values, this template is a horseshoe template with a global torsion of two half-turns. This implies that the bifurcation diagram can be described using the usual sequences associated with a unimodal map with a differentiable maximum as well as exemplified by the logistic map. Moreover, a type-I intermittency associated with a saddle-node bifurcation is exhibited. The dynamics from a single time series are also investigated to determine whether it is possible to investigate the dynamics of this biochemical model from the measure of a single concentration.
Letellier
Christophe
C
CORIA UMR 6614, Université de Rouen, Saint-Etienne du Rouvray, France. Christophe.Letellier@coria.fr
D002384:Catalysis; D006031:Glycosylation; D006593:Hexokinase / Q000378:metabolism; D008956:Models, Chemical; D025221:Phosphofructokinases / Q000378:metabolism
D025221:Phosphofructokinases; D006593:Hexokinase