Danziger Michael M, Moskalenko Olga I, Kurkin Semen A, Zhang Xiyun, Havlin Shlomo, Boccaletti Stefano
Department of Physics, Bar-Ilan University, Ramat Gan, Israel.
Faculty of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, Saratov 410012, Russia.
Chaos. 2016 Jun;26(6):065307. doi: 10.1063/1.4953345.
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(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.
最近有报道称，在自适应耦合的Kuramoto振子系统中出现了爆发性同步现象，且对节点的频率或度数没有任何条件限制。在此，我们发现，实际上，爆发相与Kuramoto振子的标准相共存。我们通过将具有完全耦合的自适应耦合振子的平均场理论扩展到部分耦合分数为f的情况来确定这一点。该分析表明，对于所有f > 0的有限值，都存在一个亚稳区域，因此，对于添加到标准Kuramoto模型中的自适应耦合的任何微扰，都预期会出现爆发性同步。我们在非常大的网络（N ∼ 10(6)）上通过GPU加速模拟验证了这一理论，并且发现，实际上，对于所有有限耦合都观察到了具有滞后现象的爆发性转变。通过证明在f → 0的极限情况下爆发性转变与标准转变共存，我们表明这种行为比之前认为的更有可能自然发生。
