TY - JOUR

T1 - Explosive synchronization coexists with classical synchronization in the Kuramoto model

AU - Danziger, Michael M.

AU - Moskalenko, Olga I.

AU - Kurkin, Semen A.

AU - Zhang, Xiyun

AU - Havlin, Shlomo

AU - Boccaletti, Stefano

N1 - Publisher Copyright:
© 2016 Author(s).

PY - 2016/6/1

Y1 - 2016/6/1

N2 - Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model. We verify this theory with GPU-accelerated simulations on very large networks (N ~ 106) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.

AB - Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model. We verify this theory with GPU-accelerated simulations on very large networks (N ~ 106) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.

UR - http://www.scopus.com/inward/record.url?scp=84977662644&partnerID=8YFLogxK

U2 - 10.1063/1.4953345

DO - 10.1063/1.4953345

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C2 - 27369869

AN - SCOPUS:84977662644

SN - 1054-1500

VL - 26

SP - 065307

JO - Chaos

JF - Chaos

IS - 6

M1 - 065307

ER -