Explosive synchronization coexists with classical synchronization in the Kuramoto model
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2016
- Source ID
- 10.1063/1.4953345
Entities
People
- Michael M Danziger
- Olga I. Moskalenko
- Semen A Kurkin
- Shlomo Havlin
- Stefano Boccaletti
- Xiyun Zhang
Organizations
- Azrieli Foundation
- Bar-Ilan University
- Defense Threat Reduction Agency
- East China Normal University
- European Commission
- Israel Science Foundation
- Office of Naval Research Global
- Russian Center for Science Information
- Saratov State Technical University
- Saratov State University