Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems

TL;DR

This paper explicitly constructs minimal invariant and globally attracting regions for reaction systems with two reversible reactions, where rate constants vary within bounds, enhancing understanding of their dynamical behavior.

Contribution

It introduces a novel explicit construction method for minimal invariant and attracting regions in variable-rate reaction systems with two reversible reactions.

Findings

Explicit construction of minimal invariant regions

Explicit construction of minimal globally attracting regions

Applicable to systems with time-varying rate constants within bounds

Abstract

The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal globally attracting regions for dynamical systems consisting of two reversible reactions, where the rate constants are allowed to vary in time within a bounded interval.