# An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems

## TL;DR

This paper provides an efficient method to identify when polynomial or power-law dynamical systems originate from reaction networks with properties like complex balancing, detailed balancing, or weak reversibility, which are linked to stability and thermodynamic equilibrium.

## Contribution

It introduces a computationally efficient characterization technique for recognizing systems derived from reaction networks with special properties such as complex balancing and weak reversibility.

## Key findings

- Characterization method for complex-balanced systems
- Identification of detailed-balanced systems
- Recognition of weakly reversible systems

## Abstract

Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction networks. On the other hand, networks with special properties (such as reversibility or weak reversibility) are known or conjectured to give rise to dynamical systems that have special properties: existence of positive steady states, persistence, permanence, and (for well-chosen parameters) complex balancing or detailed balancing. These last two are related to thermodynamic equilibrium, and therefore the positive steady states are unique and stable. We describe a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex-balanced, detailed-balanced, weakly reversible, and reversible mass-action systems.