Abstract:
The dynamics of biochemical reaction networks can be described by ODEs with polynomial right hand side. Due to high measurement uncertainty, few experimental repetitions and a limited number of measurable components, parameters are subject to high uncertainty and can vary in large intervals. One therefore effectively has to study families of parametrized polynomial ODEs. In this presentation networks are considered where the steady state variety can be parameterized by monomials. I discuss how one can exploit these parameterizations to derive polynomial conditions for the occurrence of multistationarity or Hopf bifurcations.
For zoom link (available shortly ahead of the talk) please see Seminar on the Mathematics of Reaction Networks: