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, E1 4NS, London, United Kingdom.
Sci Rep. 2018 Jul 2;8(1):9910. doi: 10.1038/s41598-018-28236-w.
The dynamics of networks of neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular on their dimensionality. However, this phenomenon has been so far mostly unexplored from the theoretical point of view. Here we reveal the rich interplay between network geometry and synchronization of coupled oscillators in the context of a simplicial complex model of manifolds called Complex Network Manifold. The networks generated by this model combine small world properties (infinite Hausdorff dimension) and a high modular structure with finite and tunable spectral dimension. We show that the networks display frustrated synchronization for a wide range of the coupling strength of the oscillators, and that the synchronization properties are directly affected by the spectral dimension of the network.
神经元培养网络的动力学最近被证明强烈依赖于网络几何结构，特别是其维度。然而，到目前为止，从理论角度来看，这一现象还没有得到太多的探索。在这里，我们在一个被称为复杂网络流形的单纯复形模型的背景下，揭示了网络几何结构和耦合振子同步之间的丰富相互作用。该模型生成的网络结合了小世界特性（无穷大豪斯多夫维数）和具有有限且可调谐的谱维数的高模块结构。我们表明，对于振荡器耦合强度的广泛范围，网络显示出受挫同步，并且同步特性直接受到网络谱维数的影响。
