Detection of Hopf bifurcations in chemical reaction networks using convex coordinates

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

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jcp.2015.02.050

Title :

Detection of Hopf bifurcations in chemical reaction networks using convex coordinates

Author(s) :

Errami, Hassan [Auteur]
Institut für Informatik II [Bonn]
Eiswirth, Markus [Auteur]
Fritz-Haber-Institut der Max-Planck-Gesellschaft [FHI]
Grigoriev, Dima [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut für Mathematik [Kassel]
Seiler, Werner [Auteur]
Institut für Mathematik [Kassel]
Sturm, Thomas [Auteur]
Max-Planck-Institut für Informatik [MPII]
Modeling and Verification of Distributed Algorithms and Systems [VERIDIS]
Weber, Andreas [Auteur]
Institut für Informatik II [Bonn]

Journal title :

Journal of Computational Physics

Pages :

279–302

Publisher :

Elsevier

Publication date :

2015-06

ISSN :

0021-9991

HAL domain(s) :

Informatique [cs]

English abstract : [en]

We present efficient algorithmic methods to detect Hopf bifurcation fixed points in chemical reaction networks with symbolic rate constants, thereby yielding information about the oscillatory behavior of the networks. Our ...
Show more >We present efficient algorithmic methods to detect Hopf bifurcation fixed 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 fixed points to a first-order formula over the ordered field of the reals that can be solved using computational logic packages. The second method uses ideas from tropical geometry to formulate a more efficient 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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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