Enhanced synchronization with proportional coupling in Kuramoto oscillator networks

TL;DR

This paper proposes a new coupling method for Kuramoto oscillator networks that enhances synchronization by scaling interactions based on frequency differences, inducing explosive transitions and improving efficiency.

Contribution

It introduces a proportional coupling scheme that maximizes synchronization and alters the criticality of the system, offering a new approach for engineered network synchronization.

Findings

Synchronization is enhanced by the proposed coupling scheme.

The system transitions from a continuous to an explosive phase transition.

The method provides insights into the critical behavior of the Kuramoto model.

Abstract

We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency detuning, synchronization is enhanced. The coupling scheme induces a change in criticality, driving the system from a continuous phase transition to an explosive transition by changing a single parameter. Our work offers a general route to efficient synchronization in engineered networks and provides insight into the critical behavior of the Kuramoto model.