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

Abstract

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.