Synchronization in an evolving network

TL;DR

This paper investigates how synchronization emerges in a network of Kuramoto oscillators that evolves stochastically based on oscillator phases and degree distribution, highlighting the threshold for synchronization and its stability.

Contribution

It introduces a model linking network evolution with oscillator phases, demonstrating how synchronization depends on connection density and network resilience.

Findings

Synchronization occurs after reaching a critical connection density.

The synchronous state remains stable with additional links.

Network fluctuations are mitigated by increased connectivity.

Abstract

In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold connection density is reached. This cumulative effect of topology and dynamics has many real-world implications, where synchronization in a system emerges as a collective property of its components in a self-organizing manner. The synchronous state remains stable as long as the connection density remains above the threshold value, with additional links providing resilience against network fluctuations.