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

Co-author(s): Hassan Errami, Markus Eiswirth, Dima Grigoriev, Thomas Sturm and Andreas Weber

Reference: Computer Algebra in Scientific Computing - CASC 2013, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2013, Lecture Notes in Computer Science 8136, pp. 88-99

Description: In this paper we build an our previous work to compute Hopf bifurcation 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 with 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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