Bookcover of Efficient Methods for Symbolic Analysis of Complex Reaction Networks
Booktitle:

Efficient Methods for Symbolic Analysis of Complex Reaction Networks

Südwestdeutscher Verlag für Hochschulschriften (2014-10-22 )

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ISBN-13:

978-3-8381-3970-8

ISBN-10:
3838139704
EAN:
9783838139708
Book language:
English
Blurb/Shorttext:
In this Book, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ 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 then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded.
Publishing house:
Südwestdeutscher Verlag für Hochschulschriften
Website:
https://www.svh-verlag.de
By (author) :
Hassan Errami
Number of pages:
108
Published on:
2014-10-22
Stock:
Available
Category:
General Natural Sciences
Price:
47.90 €
Keywords:
Stability, Hopf bifurcations, chemical reaction networks, Oscillations, Muldowney´s criteria, symbolic methods

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