Asymptotology of Chemical Reaction Networks

TL;DR

This paper develops a comprehensive theoretical framework and algorithms for analyzing the asymptotic behavior of multiscale chemical reaction networks, focusing on eigenvalues, eigenvectors, and their approximations.

Contribution

It extends the concept of the limiting step to multiscale networks and provides explicit algorithms with proven accuracy for linear systems, with discussions on nonlinear extensions.

Findings

Algorithms accurately approximate eigenvalues and eigenvectors.

Theoretical proofs confirm the accuracy of the estimates.

Demonstrations on simple examples validate the approach.

Abstract

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.