Sahoo Samir, Gupte Neelima
Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400088, India.
Department of Physics, Indian Institute of Technology, Madras, Chennai 600036, India.
Entropy (Basel). 2025 Feb 24;27(3):233. doi: 10.3390/e27030233.
The analysis of the synchronization of oscillator systems based on simplicial complexes presents some interesting features. The transition to synchronization can be abrupt or smooth depending on the substrate, the frequency distribution of the oscillators and the initial distribution of the phase angles. Both partial and complete synchronization can be seen as quantified by the order parameter. The addition of interactions of a higher order than the usual pairwise ones can modify these features further, especially when the interactions tend to have the opposite signs. Cluster synchronization is seen on sparse lattices and depends on the spectral dimension and whether the networks are mixed, sparse or compact. Topological effects and the geometry of shared faces are important and affect the synchronization patterns. We identify and analyze factors, such as frustration, that lead to these effects. We note that these features can be observed in realistic systems such as nanomaterials and the brain connectome.
基于单纯复形的振荡器系统同步分析呈现出一些有趣的特征。向同步的转变可以是突然的或平滑的，这取决于基质、振荡器的频率分布以及相角的初始分布。部分同步和完全同步都可以通过序参量来量化。添加比通常的成对相互作用更高阶的相互作用可以进一步改变这些特征，特别是当相互作用倾向于具有相反符号时。在稀疏晶格上可以看到簇同步，它取决于谱维以及网络是混合的、稀疏的还是紧凑的。拓扑效应和共享面的几何形状很重要，并影响同步模式。我们识别并分析导致这些效应的因素，如挫折感。我们注意到这些特征可以在诸如纳米材料和脑连接组等现实系统中观察到。
