Abstract The influence of array geometry on synchronization properties of a 2-D oscillator array is investigated based on a comparison between a rectangular and a hexagonal grid. The Kuramoto model is solved for a nearest-neighbor case with periodic boundary conditions and for a small-scale, realistic coupling case with 1/ r 3 decay characteristic of spintronic oscillators. In both cases, it is found that the hexagonal grid choice leads to lower synchronization threshold and higher emission power than its rectangular counterpart, which results from increased connectivity, as well as, in the realistic-coupling case, from decreased contributions of the array edges. Additionally, a more general spin-torque oscillator model including both amplitude and phase as degrees of freedom is employed for reservoir computing simulations, showing that by using hexagonal grid one can increase the short-term memory capacity but not the parity-check capacity of the system.

中文翻译：

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六边形自旋电子振荡器阵列的同步特性和储层计算能力

摘要 基于矩形和六边形网格之间的比较，研究了阵列几何形状对二维振荡器阵列同步特性的影响。Kuramoto 模型针对具有周期性边界条件的最近邻情况和具有自旋电子振荡器的 1/ r 3 衰减特性的小规模、实际耦合情况求解。在这两种情况下，发现六边形网格选择比矩形网格导致更低的同步阈值和更高的发射功率，这是由于连通性增加，以及在现实耦合情况下，阵列边缘的贡献减少. 此外，更通用的自旋扭矩振荡器模型包括振幅和相位作为自由度，用于储层计算模拟，