Ódor Géza, Deng Shengfeng, Kelling Jeffrey
Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary.
School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
Entropy (Basel). 2024 Dec 9;26(12):1074. doi: 10.3390/e26121074.
We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular 405 and 1004 lattice results with those of 12,0002 lattice substrates with power-law decaying long links (ll). The latter heterogeneous network exhibits ds>4 spectral dimensions. We show strong corrections to scaling and mean-field type of criticality at d=5, with logarithmic corrections at d=4 Euclidean dimensions. Contrarily, the ll model exhibits a non-mean-field smeared transition, with oscillating corrections at similarly high spectral dimensions. This suggests that the network heterogeneity is relevant, causing frustrated synchronization akin to Griffiths effects.
我们展示了在极大图上局部耦合Kuramoto模型的同步转变研究。我们将规则的405和1004晶格结果与具有幂律衰减长链接（ll）的12,0002晶格基底的结果进行比较。后一种异质网络表现出大于4的谱维度。我们表明在d = 5时对标度和平均场类型的临界性有强烈修正，在d = 4欧几里得维度时有对数修正。相反，ll模型表现出非平均场的模糊转变，在类似的高谱维度时有振荡修正。这表明网络异质性是相关的，导致类似于格里菲斯效应的受挫同步。
