Global convergence of quorum-sensing networks

TL;DR

This paper analyzes how synchronization occurs in networks where nodes communicate via shared environmental signals, extending to cases where the environment's dynamics are integral, with applications in systems biology.

Contribution

It introduces a general framework for understanding synchronization in networks mediated by shared dynamical variables, including cases where the environment's dynamics are significant.

Findings

Provides conditions for synchronization in environmental coupling networks

Applies the framework to biological systems demonstrating practical relevance

Extends existing models to include environmental dynamics as central elements

Abstract

In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general non- linear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quan- tities, typically provided by the nodes' environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from systems biology illustrate the approach.