Synchronization in symmetric bipolar population networks

TL;DR

This paper investigates synchronization phenomena in symmetric bipolar networks of Kuramoto oscillators, revealing how frequency distribution and topology influence the critical coupling needed for global synchronization.

Contribution

It provides analytical estimations for the minimum coupling strength for synchronization in bipolar oscillator networks, validated by numerical simulations.

Findings

Synchronization is enhanced when nodes are surrounded by nodes of opposite frequency.

Analytical estimations closely match numerical simulation results.

Frequency distribution and topology significantly affect synchronization thresholds.

Abstract

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either generated or consumed at different locations, we assume that the frequencies can take only two different values. Correlations between the value of the frequency of a given node and its topological localization are considered in both regular and random topologies. Synchronization is enhanced when nodes are surrounded by nodes of the opposite frequency. We find analytical estimations for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state, getting a very good agreement with the numerical simulations.