Kuramoto oscillators in random networks

TL;DR

This paper investigates how Kuramoto oscillators synchronize in random networks, showing that synchronization occurs across various network connectivities and sizes, with phase transitions observed in large networks.

Contribution

It provides numerical analysis of synchronization phenomena in random networks, highlighting the effects of network size and connectivity on phase coherence.

Findings

Synchronization occurs regardless of network connectivity levels.

Phase transitions are observed in large networks.

Synchronization persists near the connectivity threshold.

Abstract

By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators synchronize and achieve phase coherence, and this process is not significantly affected by the level of connectivity of the network. If the probability that two oscillators are coupled is around the network connectivity threshold synchronization still occurs, although in a more attenuated way. If the size of the network is sufficiently large the oscillators have a phase transition.