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

Abstract : 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).
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https://hal.inria.fr/hal-00931946
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Submitted on : Thursday, January 16, 2014 - 10:13:58 AM
Last modification on : Tuesday, February 19, 2019 - 3:40:03 PM

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Hassan Errami, Markus Eiswirth, Dima Grigoriev, Werner Seiler, Thomas Sturm, et al.. Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates. CASC 2013 - 15th International Workshop on Computer Algebra in Scientific Computing, Sep 2013, Berlin, Germany. pp.88-99, ⟨10.1007/978-3-319-02297-0_7⟩. ⟨hal-00931946⟩

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