Explosive synchronization with partial degree-frequency correlation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Rafael S Pinto, Alberto Saa

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 now under 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 ...Continue Reading

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Citations

May 16, 2018·Physical Review. E·Alberto Saa
Jan 15, 2016·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rafael S Pinto, Alberto Saa
Jan 20, 2018·Physical Review. E·Pedro E HarunariC E Fiore
Jan 20, 2018·Physical Review. E·Prosenjit KunduPinaki Pal
Feb 24, 2016·Scientific Reports·Can XuShuguang Guan
Aug 23, 2017·Scientific Reports·P Palaniyandi, Govindan Rangarajan

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