Explosive synchronization coexists with classical synchronization in the Kuramoto model
- Department of Physics, Bar-Ilan University, Ramat Gan (Israel)
- Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, Saratov 410012 (Russian Federation)
- Department of Physics, East China Normal University, Shanghai 200062 (China)
- CNR-Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence (Italy)
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 ∼ 10{sup 6}) 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.
- OSTI ID:
- 22596640
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 26, Issue 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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