Detection of Hopf bifurcations in chemical reaction networks using convex 
coordinates

Errami, Hassan; Eiswirth, Markus; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas

doi:10.1016/j.jcp.2015.02.050

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Detection of Hopf bifurcations in chemical reaction networks using convex coordinates

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Eiswirth, Markus
Physical Chemistry, Fritz Haber Institute, Max Planck Society;
Ertl Center for Electrochemisty and Catalysis, Gwangju Institute of Science and Technology (GIST);

Sturm, Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;

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Citation

Errami, H., Eiswirth, M., Grigoriev, D., Seiler, W. M., Sturm, T., & Weber, A. (2015). Detection of Hopf bifurcations in chemical reaction networks using convex coordinates. Journal of Computational Physics, 291, 279-302. doi:10.1016/j.jcp.2015.02.050.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0025-77FE-C

Abstract

We present ecient algorithmic methods to detect Hopf bifurcation xed
points in chemical reaction networks with symbolic rate constants, thereby
yielding information about the oscillatory behavior of the networks. Our
methods use the representations of the systems on convex coordinates that
arise from stoichiometric network analysis. One of our methods then reduces
the problem of determining the existence of Hopf bifurcation xed points to a
rst-order formula over the ordered eld of the reals that can be solved using
computational logic packages. The second method uses ideas from tropical
geometry to formulate a more ecient method that is incomplete in theory
but worked very well for the examples that we have attempted; we have
shown it to be able to handle systems involving more than 20 species.