Peron Thomas Kauê Dal'Maso, Rodrigues Francisco A
Instituto de Física de São Carlos, Universidade de São Paulo, Avenida Trabalhador São Carlense 400, Caixa Postal 369, CEP 13560-970, São Carlos, São Paulo, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016102. doi: 10.1103/PhysRevE.86.016102. Epub 2012 Jul 6.
This paper deals with the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees, and a time delay is included in the system. This assumption allows enhancing the explosive transition to reach a synchronous state. We provide an analytical treatment developed in a star graph, which reproduces results obtained in scale-free networks. Our findings have important implications in understanding the synchronization of complex networks since the time delay is present in most real-world complex systems due to the finite speed of the signal transmission over a distance.
本文通过考虑耦合相位振子的Kuramoto模型，研究了无标度网络中爆发性同步的出现。假设振子的固有频率与其度数相关，并在系统中引入了时间延迟。这一假设使得向同步状态的爆发性转变得以增强。我们给出了在星型图中展开的一种解析处理方法，该方法重现了在无标度网络中得到的结果。由于信号在远距离传输时具有有限速度，时间延迟在大多数现实世界的复杂系统中都存在，因此我们的研究结果对于理解复杂网络的同步具有重要意义。
