Synchronization in time-varying random networks with vanishing connectivity

Marco Faggian, Francesco Ginelli, Fernando Rosas, Zoran Levnajic (Corresponding Author)

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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, provided strong coupling and fast enough rewiring are considered, the network is able to reach partial synchronization even in the vanishing connectivity limit. We also provide an intuitive 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. In the formal fast switching limit, finally, we argue that the onset of collective synchronization is captured by the time-averaged connectivity network. Our results may be relevant to qualitatively describe the emergence of consensus in social communities with time-varying interactions and to study the onset of collective behavior in engineered systems of mobile units with limited wireless capabilities.
Original languageEnglish
Article number10207
JournalScientific Reports
Publication statusPublished - 15 Jul 2019

Bibliographical note

We wish to thank D. Fanelli and M. Lucas for fruitful discussions. This work has been supported by H2020-MSCAITN-2015 Project COSMOS No. 642563. ZL also acknowledges support from ”Slovenian research agency” via P1-0383 and J5-8236”. FR acknowledges support from H2020 MSCA grant agreement No. 702981.


  • applied mathematics
  • statistical physics
  • thermodyamics
  • nonlinear dynamics


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