Critical Parameters for Singular Perturbation Reductions of Chemical Reaction Networks

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and depend on many parameters, it is frequently interest to obtain a reduction in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov Fenichel, provides path toward reductions. In the present paper we discuss values lead singular reductions (so-called Tikhonov-Fenichel values, or TFPVs). An algorithmic approach known, but feasible for small dimensions only. Here characterize conditions classes networks TFPVs turning off reactions (by setting rate parameters zero), removing species (which relates classical quasi-steady state model reduction). particular, definitive results class complex balanced (of deficiency zero) first order