Homotopy methods for counting reaction network equilibria

Details Homotopy methods for counting reaction network equilibria Homotopy methods for counting reaction network equilibria

2007-11-09

arxiv.org/abs/0711.1552v2

Mathematics

Dynamical Systems

27 pages

Scientific paper

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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