Fast-slow vector fields of reaction-diffusion systems

V. Bykov, Y. Cherkinsky, V. Gol'dshtein, N. Krapivnik, U. Maas

Research output: Contribution to journalArticlepeer-review


A geometrically invariant concept of fast-slow vector fields perturbed by transport terms describing molecular diffusion is proposed in this paper. It is an extension of our concept of singularly perturbed vector fields for ODEs to reaction-diffusion systems with chemical reactions having wide range of characteristic time scales, while transport processes remain comparatively slow. Under this assumption we developed a decomposition into a fast and slow subsystems. It is assumed that the transport terms for the fast subsystem can be neglected to the leading order. For the slow subsystem we modify a concept of singularly perturbed profiles proposed in our previous works. The results are used to justify and to modify an algorithm of reaction-diffusion manifolds (REDIMs). The modified REDIM method is applied to the Michaelis-Menten model to illustrate the suggested approach.

Original languageEnglish
Pages (from-to)67-86
Number of pages20
JournalIMA Journal of Applied Mathematics
Issue number1
StatePublished - 28 Feb 2020


  • invariant manifolds
  • reaction-diffusion systems
  • singularly perturbed systems

ASJC Scopus subject areas

  • Applied Mathematics


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