Volume 109, Number 6, March 2015
|Number of page(s)||6|
|Published online||25 May 2015|
Onset and suffusing transitions towards synchronization in complex networks
1 Potsdam Institute for Climate Impact Research (PIK) - 14473 Potsdam, Germany
2 Department of Physics, Humboldt University - 12489 Berlin, Germany
3 Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University Shanghai, PRC
4 Department of Computer Science, The University of Warwick - Coventry CV4 7AL, UK
5 Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen AB24 3UE, UK
Received: 27 November 2014
Accepted: 19 March 2015
Based on the basin of attraction, the basin stability is quantified to measure a system's ability to regain an equilibrium state subjected to even large perturbations. In this letter, we demonstrate a novel phenomenon uncovered by the basin stability that in complex networks of second-order Kuramoto models successively undergoes two first-order transitions: an onset transition from an unstable to a locally stable synchronous state, and a suffusing transition from a locally stable to a globally stable synchronous state; we call this sequence onset-suffusing transitions. We provide an analytical treatment of basin stability by a mean-field analysis. Our findings are in good agreement with simulations and fundamentally deepen the understanding of stability of microscopic mechanisms towards synchronization.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Xt – Synchronization; coupled oscillators
© EPLA, 2015
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