On the Geometry of Chemical Reaction Networks: Lyapunov Function and Large Deviations


Journal Article

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. In an earlier paper, we proved the validity of large deviations theory for the particle approximation of quite general chemical reaction networks. In this paper, we extend its scope and present a more geometric insight into the mechanism of that proof, exploiting the notion of spherical image of the reaction polytope. This allows to view the asymptotic behavior of the vector field describing the mass-action dynamics of chemical reactions as the result of an interaction between the faces of this polytope in different dimensions. We also illustrate some local aspects of the problem in a discussion of Wentzell–Freidlin theory, together with some examples.

Full Text

Duke Authors

Cited Authors

  • Agazzi, A; Dembo, A; Eckmann, JP

Published Date

  • July 1, 2018

Published In

Volume / Issue

  • 172 / 2

Start / End Page

  • 321 - 352

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-018-2035-8

Citation Source

  • Scopus