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

Thursday, 19 October, 2017

Published in: 

arXiv:1710.07240

In an earlier paper, we proved the validity of large deviations theory for the particle approximation of quite general chemical reaction networks (CRNs). In this paper, we 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 (WF) theory, together with some examples.

Author(s): 

Andrea Agazzi
Amir Dembo
Jean-Pierre Eckmann