Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates

  • Hassan Errami
  • Markus Eiswirth
  • Dima Grigoriev
  • Werner M. Seiler
  • Thomas Sturm
  • Andreas Weber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8136)


We build on our previous work to compute Hopf bifurcation fixed points for chemical reaction systems on the basis of reaction coordinates. For determining the existence of Hopf bifurcations the main algorithmic problem is to determine whether a single multivariate polynomial has a zero for positive coordinates. For this purpose we provide heuristics on the basis of the Newton polytope that ensure the existence of positive and negative values of the polynomial for positive coordinates. We apply our method to the example of the Methylene Blue Oscillator (MBO).


Hopf Bifurcation Lorenz System Hopf Bifurcation Point Toric Ideal Newton Polytope 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Hassan Errami
    • 1
  • Markus Eiswirth
    • 2
    • 3
  • Dima Grigoriev
    • 4
  • Werner M. Seiler
    • 1
  • Thomas Sturm
    • 5
  • Andreas Weber
    • 6
  1. 1.Institut für MathematikUniversität KasselKasselGermany
  2. 2.Fritz-Haber-Institut der Max-Planck-GesellschaftBerlinGermany
  3. 3.Ertl Center for Electrochemisty and CatalysisGISTSouth Korea
  4. 4.CNRS, MathématiquesUniversité de LilleVilleneuve d’AscqFrance
  5. 5.Max-Planck-Institut für InformatikSaarbrückenGermany
  6. 6.Institut für Informatik IIUniversität BonnBonnGermany

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