Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks. / Feliu, Elisenda; Kruff, Niclas; Walcher, Sebastian.
In: Journal of Nonlinear Science, Vol. 30, No. 4, 2020, p. 1355-1380.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
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 -
ID: 225521967