Peron Thomas Kauê Dal'maso, Rodrigues Francisco A
Instituto de Física de São Carlos, Universidade de São Paulo, Av. Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970, São Carlos, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056108. doi: 10.1103/PhysRevE.86.056108. Epub 2012 Nov 12.
An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.
当Kuramoto振子的固有频率等于其连接数时，在无标度网络中可以观察到爆发性同步。本文报道了用于确定这种爆发性同步临界耦合的平均场近似。已经验证，所得到的临界耦合方程与网络平均度呈反比关系。该表达式不同于那些频率分布为单峰且均匀的表达式。在这种情况下，临界耦合取决于度分布的一阶和二阶统计矩之间的比率。还进行了数值模拟以验证我们的分析结果。
