Synchronization in time-varying networks

Vivek Kohar, Peng Ji, Anshul Choudhary, Sudeshna Sinha, and Jüergen Kurths
Phys. Rev. E 90, 022812 – Published 25 August 2014

Abstract

We study the stability of the synchronized state in time-varying complex networks using the concept of basin stability, which is a nonlocal and nonlinear measure of stability that can be easily applied to high-dimensional systems [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Phys. 9, 89 (2013)]. The time-varying character is included by stochastically rewiring each link with the average frequency f. We find that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks. Further we uncover that small-world networks are much more sensitive to link changes than random ones, with the time-varying character of the network having a significant effect at much lower rewiring frequencies. At very high rewiring frequencies, random networks perform better than small-world networks and the synchronized state is stable over a much wider window of coupling strengths. Lastly we show that the stability range of the synchronized state may be quite different for small and large perturbations, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability.

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  • Received 6 April 2014
  • Revised 27 June 2014

DOI:https://doi.org/10.1103/PhysRevE.90.022812

©2014 American Physical Society

Authors & Affiliations

Vivek Kohar1,2,*, Peng Ji1,3, Anshul Choudhary2, Sudeshna Sinha2, and Jüergen Kurths1,3,4,5

  • 1Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany
  • 2Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli PO 140 306, Punjab, India
  • 3Department of Physics, Humboldt University, 12489 Berlin, Germany
  • 4Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
  • 5Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia

  • *Corresponding author: vivek.kohar@gmail.com

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Vol. 90, Iss. 2 — August 2014

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