Explosive synchronization with partial degree-frequency correlation

Author(s)

Pinto, Rafael S. ; Saa, Alberto

• Document type: Journal article
• Source: Physical Review E; v. 91, n. 2, p. 10-pg., 2015-02-27.

Abstract

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so-called explosive synchronization behavior, which is nowunder intensive investigation. Here we study and discuss explosive synchronization in a situation that has not yet been considered, namely when only a part, typically a small part, 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 a mean-field analysis and our conclusions were corroborated by exhaustive numerical experiments for synthetic networks and also for the undirected and unweighed version of a typical benchmark biological network, namely 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. (AU)

• FAPESP's process: 13/09357-9 - Physics and geometry of spacetime
• Grantee: Alberto Vazquez Saa
• Support Opportunities: Research Projects - Thematic Grants