Stability of steady states and algebraic parameterizations in chemical reaction networks.

Criteria such as Routh-Hurwitz are used to establish whether a steady state of a system of ordinary differential equations is asymptotically stable, by computing the Jacobian of the system and studying the sign of the real part of its eigenvalues. I am interested in determining the stability of positive steady states of reaction networks (using mass-action kinetics), when the values of the reaction rate constants are unknown. To this end, I combine the Routh-Hurwtiz criterion with algebraic parameterizations of the steady state variety. In this talk I will give an overview of this approach, and present algebraic and combinatoric tools used to detect bistability in chemical reaction networks.