Acta Biotheoretica

, Volume 50, Issue 1, pp 1–13 | Cite as

Topological Analysis of Chaos in a Three-Variable Biochemical Model

  • Christophe Letellier


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.


Time Series Control Parameter Bifurcation Diagram Single Time Topological Analysis 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Christophe Letellier
    • 1
  1. 1.CORIA UMR 6614Université de RouenSaint-Etienne du Rouvray cedexFrance

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