Potratzki Max, Bröhl Timo, Rings Thorsten, Lehnertz Klaus
Department of Epileptology, University of Bonn Medical Centre, Venusberg Campus 1, 53127 Bonn, Germany.
Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany.
Chaos. 2024 Apr 1;34(4). doi: 10.1063/5.0197930.
We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous natural frequencies. We employ the complex-valued order parameter-a widely used indicator for phase ordering-to assess the synchronization dynamics and observe the order parameter to exhibit either constant or periodic or non-periodic, possibly chaotic temporal evolutions for a given coupling strength but depending on initial conditions and the systems' disorder. Interestingly, both topological and spectral characteristics of the power grids point to a diminished capability of these networks to support a temporarily stable synchronization dynamics. We find non-trivial commonalities between the synchronization dynamics of oscillators on seemingly opposing topologies.
我们研究了欧洲和美国电网模型、典型网络模型的拓扑和频谱特性，以及它们对具有异质自然频率的相位振荡器同步动力学的影响。我们使用复值序参量——一种广泛用于相位排序的指标——来评估同步动力学，并观察到对于给定的耦合强度，序参量会呈现出恒定、周期性或非周期性的，甚至可能是混沌的时间演化，这取决于初始条件和系统的无序性。有趣的是，电网的拓扑和频谱特征都表明这些网络支持暂时稳定同步动力学的能力有所减弱。我们发现在看似相反拓扑结构上的振荡器同步动力学之间存在非平凡的共性。
