Global stability of perturbed complex-balanced systems

TL;DR

This paper demonstrates that complex-balanced systems, which are usually stable but not robust to parameter changes, remain globally stable when their rate constants are perturbed, provided they are robustly permanent.

Contribution

It proves that robustly permanent complex-balanced systems retain global stability despite perturbations in rate constants.

Findings

Robustly permanent complex-balanced systems are globally stable.

Small parameter perturbations do not compromise stability in these systems.

The stability of such systems is preserved under rate constant perturbations.

Abstract

A class of polynomial dynamical systems called complex-balanced are locally stable and conjectured to be globally stable. In general, complex-balancing is not a robust property, i.e., small changes in parameter values may result in the loss of the complex-balanced property. We show that robustly permanent complex-balanced systems are globally stable even after the rate constants have been perturbed.