Dynamical quorum sensing and clustering dynamics in a population of spatially distributed active rotators

TL;DR

This paper introduces a model for clustering in spatially distributed active rotators, highlighting how increased local density induces a transition to oscillatory behavior, facilitating rapid formation of a dominant cluster through dynamical quorum sensing.

Contribution

It presents a novel model demonstrating how local density triggers a transition to oscillatory dynamics, leading to efficient clustering via dynamical quorum sensing.

Findings

Phase waves propagate without decay in the oscillation regime.

Dynamical quorum sensing accelerates clustering and results in a single dominant cluster.

An exact localized solution for a simplified model is derived.

Abstract

A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted as dynamical quorum sensing. In the oscillation regime, phase waves propagate without decay, which generates an effectively long-range interaction in the clustering dynamics. The clustering process becomes facilitated and only one dominant cluster appears rapidly as a result of the dynamical quorum sensing. An exact localized solution is found to a simplified model equation, and the competitive dynamics between two localized states is studied numerically.