Open AccessUniversal phase transitions to synchronization in Kuramoto-like models with heterogeneous coupling
Author(s) -
Can Xu,
Stefano Boccaletti,
Zhigang Zheng,
Shuguang Guan
Publication year - 2019
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ab4f59
Subject(s) - kuramoto model , physics , metastability , synchronization (alternating current) , coupling (piping) , statistical physics , phase synchronization , phase transition , phase (matter) , manifold (fluid mechanics) , explosive material , topology (electrical circuits) , quantum mechanics , mechanical engineering , mathematics , combinatorics , engineering , chemistry , organic chemistry
We reveal a class of universal phase transitions to synchronization in Kuramoto-like models with both in- and out-coupling heterogeneity. By analogy with metastable states, an oscillatory state occurs as a high-order coherent phase accompanying explosive synchronization in the system. The critical points of synchronization transition and the stationary solutions are obtained analytically, by the use of mean-field theory. In particular, the stable conditions for the emergence of phase-locked states are determined analytically, consistently with the analysis based on the Ott–Antonsen manifold. We demonstrate that the in- or out-coupling heterogeneity have influence on both the dynamical properties (eigen’spectrum) and the synchronizability of the system.