  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.
