Dynamical clustering in oscillator ensembles with time-dependent interactions

TL;DR

This paper studies how inhomogeneous internal time scales in coupled oscillators lead to a critical transition from order to incoherence, with dynamical clustering as an intermediate regime.

Contribution

It introduces a model of oscillator ensembles with time-dependent interactions influenced by internal variables with diverse evolution rates, revealing a new transition mechanism.

Findings

Critical transition from order to incoherence with increasing inhomogeneity.

Dynamical clustering as an intermediate regime during transition.

Recurrent splitting into subpopulations based on internal variable dynamics.

Abstract

We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so that the ensemble is inhomogeneous with respect to the internal variable. Interactions between oscillators depend on this variable and thus vary with time. We show that as the inhomogeneity of time scales in the internal evolution grows, the system undergoes a critical transition between ordered and incoherent states. This transition is mediated by a regime of dynamical clustering, where the ensemble recurrently splits into groups formed by varying subpopulations.