TY - JOUR

T1 - Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks

AU - Feliu, Elisenda

AU - Kruff, Niclas

AU - Walcher, Sebastian

PY - 2020

Y1 - 2020

N2 - We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary. We apply the theoretical results to chemical reaction networkswith mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the fast subsystem admits complex-balanced steady states

AB - We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary. We apply the theoretical results to chemical reaction networkswith mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems, there exist canonical parameterizations of the variety of stationary points; hence, the theory is applicable in a natural manner. In particular, we obtain a closed form expression for the reduced system when the fast subsystem admits complex-balanced steady states

KW - math.DS

KW - q-bio.MN

KW - q-bio.QM

U2 - 10.1007/s00332-020-09610-3

DO - 10.1007/s00332-020-09610-3

M3 - Journal article

VL - 30

SP - 1355

EP - 1380

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 4

ER -