|
This article is cited in 1 scientific paper (total in 1 paper)
IN MEMORIAM OF V. A. PLISS
Qualitative studies of some biochemical models
C. Panteaa, V. G. Romanovskibc a West Virginia University, PO Box 6201, Morgantown, West Virginia, USA
b University of Maribor, SI-2000 Maribor, Slovenia
c Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000 Maribor, Slovenia
Abstract:
A computational approach to detect Andronov - Hopf bifurcations in polynomial systems of ordinary differential equations depending on parameters is proposed. It relies on algorithms of computational commutative algebra based on the Groebner bases theory. The approach is applied to the investigation of two models related to the MAPK (mitogen-activated protein kinases) double phosphorylation, a biochemical network that occurs in many cellular pathways. For the models we perform the analysis of roots of the characteristic polynomials of the Jacobians at the steady states and prove the absence of Andronov - Hopf bifurcations for biochemically relevant values of parameters. We also performed a search for algebraic invariant subspaces in the systems (which represent "weak" conservations laws) and find all subfamilies admitting linear invariant subspaces. The search is done using the Darboux method. That, is we look for Darboux polynomials and cofactors as polynomials with undetermined coefficients and then determine the coefficients using the algorithms of the elimination theory.
Keywords:
polynomial system of ODEs, Andronov - Hopf bifurcation, invariant subspace, biochemical reactions networks.
Received: 22.10.2019 Revised: 12.12.2019 Accepted: 12.12.2019
Citation:
C. Pantea, V. G. Romanovski, “Qualitative studies of some biochemical models”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:2 (2020), 319–330; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 214–222
Linking options:
https://www.mathnet.ru/eng/vspua193 https://www.mathnet.ru/eng/vspua/v7/i2/p319
|
Statistics & downloads: |
Abstract page: | 17 | Full-text PDF : | 11 |
|