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).
Type de document :
Communication dans un congrès
Vladimir P. Gerdt and Wolfram Koepf and Ernst W. Mayr and Evgenii V. Vorozhtsov. Computer Algebra in Scientific Computing, Sep 2013, Berlin, Germany. Springer, 8136, pp.88-99, 2013, Computer Algebra in Scientific Computing. 〈10.1007/978-3-319-02297-0_7〉
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https://hal.inria.fr/hal-00931946
Contributeur : Stephan Merz <>
Soumis le : jeudi 16 janvier 2014 - 10:13:58
Dernière modification le : jeudi 11 janvier 2018 - 06:23:13

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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. Vladimir P. Gerdt and Wolfram Koepf and Ernst W. Mayr and Evgenii V. Vorozhtsov. Computer Algebra in Scientific Computing, Sep 2013, Berlin, Germany. Springer, 8136, pp.88-99, 2013, Computer Algebra in Scientific Computing. 〈10.1007/978-3-319-02297-0_7〉. 〈hal-00931946〉

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