title: Qualitative studies of some biochemical models
metadata.name: dc.contributor.author
metadata.value: Pantea, Casian
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Romanovski, Valery G.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T17:52:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T17:52:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Pantea C., Romanovski V.G. Qualitative studies of some biochemical models. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 319–330.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.214
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17948
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Slovenian Research Agency (program P1-0306, projects N1-0063,
  BI-US/19-21-058).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: polynomial system of ODEs
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Andronov—Hopf bifurcation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: invariant subspace
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: biochemical reactions networks
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Qualitative studies of some biochemical models
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 319-330.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17948/1/319-330.pdf
resources.format: Adobe PDF
resources.size: 330,1 kB