Synchronization in time-varying random networks with vanishing connectivity
File(s)
Published version
Author(s)
Rosas De Andraca, Fernando Ernesto
Faggian, Marco
Ginelli, Francesco
Levnajic, Zoran
Type
Journal Article
Abstract
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for
the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase
oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly,
an extremely low instantaneous connectivity. We show that with strong coupling and sufficiently fast rewiring the network
reaches partial synchronization even in the vanishing connectivity limit. In particular, we provide an approximate analytical
argument, based on the comparison between the different characteristic timescales of our system in the low connectivity
regime, which is able to predict the transition to synchronization threshold with satisfactory precision beyond the formal fast
rewiring limit. We interpret our results as a qualitative mechanism for emergence of consensus in social communities. In
particular, our result suggest that groups of individuals are capable of aligning their opinions under extremely sparse exchanges
of views, which is reminiscent of fast communications that take place in the modern social media. Our results may also be
relevant to characterize the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities
the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase
oscillators in which the links mediating the interactions are constantly rearranged with a characteristic timescale and, possibly,
an extremely low instantaneous connectivity. We show that with strong coupling and sufficiently fast rewiring the network
reaches partial synchronization even in the vanishing connectivity limit. In particular, we provide an approximate analytical
argument, based on the comparison between the different characteristic timescales of our system in the low connectivity
regime, which is able to predict the transition to synchronization threshold with satisfactory precision beyond the formal fast
rewiring limit. We interpret our results as a qualitative mechanism for emergence of consensus in social communities. In
particular, our result suggest that groups of individuals are capable of aligning their opinions under extremely sparse exchanges
of views, which is reminiscent of fast communications that take place in the modern social media. Our results may also be
relevant to characterize the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities
Date Issued
2019-07-15
Date Acceptance
2019-06-20
Citation
Scientific Reports, 2019, 9 (10207), pp.1-11
ISSN
2045-2322
Publisher
Nature Publishing Group
Start Page
1
End Page
11
Journal / Book Title
Scientific Reports
Volume
9
Issue
10207
Copyright Statement
© The Author(s) 2019. This article is licensed under a Creative Commons Attribution 4.0 International
License, which permits use, sharing, adaptation, distribution and reproduction in any medium or
format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Te images or other third party material in this
article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
License, which permits use, sharing, adaptation, distribution and reproduction in any medium or
format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Te images or other third party material in this
article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the
copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://www.nature.com/articles/s41598-019-46345-y
Publication Status
Published
Date Publish Online
2019-07-15