Linear Conjugacy of Chemical Reaction Networks

TL;DR

This paper develops a unified theory called conjugate chemical reaction network theory, which identifies conditions under which different networks can exhibit identical qualitative dynamics, extending the understanding of network equivalences.

Contribution

It introduces a theorem that broadens the scope of weakly reversible systems by establishing conditions for different networks to have the same dynamics.

Findings

Identifies conditions for network conjugacy in chemical reaction networks.

Extends the theory of weakly reversible systems.

Provides a unified framework for analyzing network dynamics.

Abstract

Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant species. It is known that two networks may possess the same governing mass-action dynamics despite disparate network structure. To date, however, there has only been limited work exploiting this phenomenon even for the cases where one network possesses known dynamics while the other does not. In this paper, we bring these known results into a broader unified theory which we call conjugate chemical reaction network theory. We present a theorem which gives conditions under which two networks with different governing mass-action dynamics may exhibit the same qualitative dynamics and use it to extend the scope of the well-known theory of weakly reversible systems.