Explosive synchronization with partial degree-frequency correlation

TL;DR

This paper demonstrates that partial degree-frequency correlation, especially among hubs, can induce explosive synchronization in networks, even when full correlation does not, through extensive numerical experiments.

Contribution

It reveals that partial degree-frequency correlation, focusing on hubs, can induce explosive synchronization, expanding understanding beyond full correlation scenarios.

Findings

Partial correlation among hubs induces explosive synchronization.

Partial correlation can enable explosive synchronization where full correlation cannot.

Neural network of C. elegans exhibits explosive synchronization with partial correlation.

Abstract

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of the their corresponding vertices exhibits the so-called explosive synchronization behavior, which is now under intensive investigation. Here, we study and report explosive synchronization in a situation that has not yet been considered, namely when only a part, typically small, of the vertices is subjected to a degree frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform exhaustive numerical experiments for synthetic networks and also for the undirected and unweighted version of the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.