Dynamical quorum-sensing and synchronization of nonlinear oscillators coupled through an external medium

TL;DR

This paper presents a theoretical model explaining how populations of oscillators synchronize through an external medium, revealing diverse transition mechanisms including a novel 'dynamic death' phenomenon, aligning with experimental observations.

Contribution

The study introduces a unified analytical framework for dynamical quorum sensing, identifying multiple transition mechanisms and a new 'dynamic death' phase in oscillator synchronization.

Findings

Identifies four distinct mechanisms for population-dependent oscillation transitions.

Derives analytic equations for phase boundaries based on population density.

Model reproduces key features observed in experiments with catalytic particles and engineered bacteria.

Abstract

Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via signaling molecules distributed through an external media. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common media. We show that this model exhibits a rich phase diagram with four qualitatively distinct mechanisms fueling population-dependent transitions to global oscillations, including a new type of transition we term "dynamic death". We derive a single pair of analytic equations that allows us to calculate all phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments of BZ catalytic particles as well as synthetically engineered bacteria.