Campuses:

Part II:<br/><br/>Homotopy methods for counting reaction network equilibria

Monday, May 12, 2008 - 3:50pm - 4:20pm
EE/CS 3-180
Ruth Williams (University of California, San Diego)
Based on joint work with G. Craciun and J. W. Helton.

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.
MSC Code: 
70G60