School of Physics and Materials Science, Anhui University, Hefei 230039, People's Republic of China.
Chaos. 2013 Sep;23(3):033124. doi: 10.1063/1.4818543.
It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.
最近有报道称，在相位振荡器[Gómez-Gardeñes 等人，物理评论快报 106,128701(2011)]和混沌振荡器[Leyva 等人，物理评论快报 108,168702(2012)]网络中可能发生爆炸式同步转变。在这里，我们研究了耦合 FitzHugh-Nagumo 振荡器的动力学和相互作用拓扑之间的微观相关性对 Barabási-Albert(BA)无标度网络和 Erdös-Rényi(ER)随机网络中相位同步转变的影响。我们表明，如果振荡的自然频率与节点度呈正相关，并且频率分布的宽度大于一个阈值，则 BA 网络的同步图中会出现强滞后环，表明存在朝向弛豫振荡器系统同步的爆炸式转变的证据。与 BA 网络的结果相反，在更均匀的 ER 网络中，无论频率分布的宽度如何，同步转变始终是连续的。此外，我们考虑了度混合模式对同步转变性质的影响，并发现度配价不利于这种爆炸式转变的发生。
