Finding complex balanced and detailed balanced realizations of chemical reaction networks

TL;DR

This paper presents efficient linear programming methods to find complex balanced and detailed balanced realizations of chemical reaction networks, which are crucial for understanding system stability.

Contribution

It introduces novel numerical procedures for identifying balanced realizations in chemical reaction networks using linear programming techniques.

Findings

Procedures successfully applied to numerical examples

Methods efficiently identify balanced realizations

Potential implications for stability analysis

Abstract

Reversibility, weak reversibility and deficiency, detailed and complex balancing are generally not "encoded" in the kinetic differential equations but they are realization properties that may imply local or even global asymptotic stability of the underlying reaction kinetic system when further conditions are also fulfilled. In this paper, efficient numerical procedures are given for finding complex balanced or detailed balanced realizations of mass action type chemical reaction networks or kinetic dynamical systems in the framework of linear programming. The procedures are illustrated on numerical examples.