A global convergence result for strongly monotone systems with positive translation invariance

TL;DR

This paper proves that strongly monotone ODE systems with a specific translation-invariance property ensure all solutions converge to a unique equilibrium, extending known results and including a biochemical application.

Contribution

It introduces a new convergence theorem for strongly monotone systems with translation invariance, complementing existing conservation law results.

Findings

All solutions in such systems converge to a unique equilibrium.

The theorem applies to biochemical reaction models.

Provides a practical example in biochemistry.

Abstract

We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. An application to a reaction of interest in biochemistry is provided as an illustration.