How to grow an oscillator network with enhanced synchronization

TL;DR

This paper proposes a new method for setting natural frequencies in growing oscillator networks to improve synchronization, outperforming traditional approaches across various conditions.

Contribution

It introduces a link-wise order parameter-based scheme for enhancing synchronization in growing oscillator networks, validated through analytical and numerical methods.

Findings

Link-wise order parameter outperforms global order parameter.

Proposed method achieves larger synchronization enhancement.

Approach is effective over a wide range of coupling strengths.

Abstract

We study a way to set the natural frequency of a newly added oscillator in a growing network to enhance synchronization. Population growth is one of the typical features of many oscillator systems for which synchronization is required to perform their functions properly. Despite this significance, little has been known about synchronization in growing systems. We suggest effective growing schemes to enhance synchronization as the network grows under a predetermined rule. Specifically, we find that a method based on a link-wise order parameter outperforms that based on the conventional global order parameter. With simple solvable examples, we verify that the results coincide with intuitive expectations. The numerical results demonstrate that the approximate optimal values from the suggested method show a larger synchronization enhancement in comparison to other naive strategies. The results also show that our proposed approach outperforms others over a wide range of coupling strengths.