  Deciding whether and where a system of parametrized ordinary differential
equations displays bistability, that is, has at least two asymptotically stable
steady states for some choice of parameters, is a hard problem. For systems
modeling biochemical reaction networks, we introduce a procedure to determine,
exclusively via symbolic computations, the stability of the steady states for
unspecified parameter values. In particular, our approach fully determines the
stability type of all steady states of a broad class of networks. To this end,
we combine the Hurwitz criterion, reduction of the steady state equations to
one univariate equation, and structural reductions of the reaction network.
Using our method, we prove that bistability occurs in open regions in parameter
space for many relevant motifs in cell signaling.
