Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain.
School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom and The Alan Turing Institute, London, NW1 2DB, United Kingdom.
Phys Rev E. 2019 Feb;99(2-1):022307. doi: 10.1103/PhysRevE.99.022307.
Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We numerically test our analytical predictions on the recently introduced model of network geometry called complex network manifolds, which displays a tunable spectral dimension.
最近，人们对网络几何和拓扑结构产生了浓厚的兴趣。在这里，我们表明，谱维度在建立网络的拓扑和几何性质与其动力学之间的清晰关系方面起着根本性的作用。具体来说，我们探索了谱维度在确定 Kuramoto 模型同步性质中的作用。我们表明，只有在谱维度大于四的情况下，同步相位才能在热力学上稳定，并且只有在谱维度大于二的情况下，振荡器的相位同步才能被发现。我们在最近引入的称为复杂网络流形的网络几何模型上对我们的分析预测进行了数值测试，该模型显示出可调节的谱维度。
