Boundedness of trajectories for weakly reversible, single linkage class reaction systems

TL;DR

This paper proves that in weakly reversible, single linkage class chemical reaction networks, the trajectories of the mass-action systems remain bounded over time, advancing understanding of their long-term behavior.

Contribution

It establishes the boundedness of trajectories for weakly reversible, single linkage class reaction systems, confirming a conjecture in this specific case.

Findings

Trajectories are bounded in weakly reversible, single linkage class systems.

The conjecture holds true for networks with one linkage class.

Provides a foundation for analyzing stability in chemical reaction networks.

Abstract

This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems biology. A basic question, whose answer remains largely unknown, is the following: for which network structures do trajectories of mass-action systems remain bounded in time? In this paper, we conjecture that the result holds when the reaction network is weakly reversible, and prove this conjecture in the case when the reaction network consists of a single linkage class, or connected component.