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

Critical parameters for singular perturbation reductions of chemical reaction networks