An entropy based clustering order parameter for finite ensembles of oscillators

TL;DR

This paper introduces a new entropy-based clustering order parameter for finite oscillator systems that effectively detects cluster formation and distinguishes the splay state, complementing existing synchronization measures.

Contribution

The paper proposes a novel entropy-based order parameter for finite oscillator ensembles that uniquely identifies the splay state and quantifies clustering.

Findings

The new order parameter singles out the splay state with zero value.

It provides a positive measure for clustering in oscillator systems.

It complements existing Kuramoto order parameters for system analysis.

Abstract

Based on the entropy concept, we define a new clustering order parameter $c$ feasible for finite systems of interacting oscillators. Unlike the generalized synchronization order parameters of the Kuramoto type, this new order parameter singles out the splay state as the unique state with $c = 0$, thus yielding a positive value whenever there is some kind of cluster formation in the system. It is therefore proposed to be monitored alongside the Kuramoto order parameters as a means to quantify the overall amount of clustering in the system.