TY - JOUR

T1 - Critical Parameters for Singular Perturbation Reductions of Chemical Reaction Networks

AU - Feliu, Elisenda

AU - Walcher, Sebastian

AU - Wiuf, Carsten

N1 - Funding Information: SW acknowledges support by the bilateral project ANR-17-CE40-0036 and DFG-391322026 SYMBIONT. EF acknowledges support from the Independent Research Fund Denmark, and by the Novo Nordisk Foundation (Denmark), grant NNF18OC0052483. CW acknowledges support from the Novo Nordisk Foundation (Denmark), grant NNF19OC0058354. All three authors thank two anonymous reviewers for a very detailed reading of the first version, and for numerous constructive comments and helpful suggestions. Publisher Copyright: © 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - 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 may depend on many parameters, it is frequently of interest to obtain a reduction of dimension in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov and Fenichel, provides a path towards such reductions. In the present paper, we discuss parameter values that lead to singular perturbation reductions (so-called Tikhonov–Fenichel parameter values, or TFPVs). An algorithmic approach is known, but it is feasible for small dimensions only. Here, we characterize conditions for classes of reaction networks for which TFPVs arise by turning off reactions (by setting rate parameters to zero) or by removing certain species (which relates to the classical quasi-steady state approach to model reduction). In particular, we obtain definitive results for the class of complex-balanced reaction networks (of deficiency zero) and first-order reaction networks.

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

KW - Critical manifold

KW - Dimension reduction

KW - Invariant sets

KW - Quasi-steady state

KW - Reaction networks

U2 - 10.1007/s00332-022-09843-4

DO - 10.1007/s00332-022-09843-4

M3 - Journal article

AN - SCOPUS:85138181862

VL - 32

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 6

M1 - 83

ER -