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Acta Biotheoretica

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

Topological Analysis of Chaos in a Three-Variable Biochemical Model

  • Christophe Letellier
Article

Abstract

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.

Keywords

Time Series Control Parameter Bifurcation Diagram Single Time Topological Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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