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HOMOTOPY METHODS FOR COUNTING REACTION NETWORK EQUILIBRIA
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G. Craciun, J. W. Helton and R. J. Williams
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Abstract

Dynamical system models of complex biochemical reaction networks are usually
high-dimensional, nonlinear, and contain many unknown parameters.
In some cases the
reaction network structure dictates that positive equilibria must be unique for all
values of the parameters in the model.
In other cases multiple equilibria exist if and
only if special relationships between these parameters are satisfied.
We describe
methods based on homotopy invariance of degree which allow us
to determine the number of
equilibria for complex biochemical reaction networks
and how this number depends on
parameters in the model.

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Published in Mathematical Biosciences, Volume 216, Issue 2, December 2008, pages 140-149.
For the published article, click
here.
For a copy of a preprint, for personal
scientific non-commercial use, click
here
for pdf. *

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Software Complement: Mathematica Notebooks for Computing Chemical Reaction Network Jacobians
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For many of the examples in this paper, the determinant of the Jacobian
of the right hand side of the dynamic equations was computed
symbolically using Mathematica.
The webpage accessed by
clicking here contains
Mathematica notebooks for many
of the examples in this paper, as well as a demonstration notebook
that readers may edit to run their own examples.
These notebooks were developed by
Igor Klep, Karl Fredrickson and J. William Helton.

Last updated December 26, 2008.