The prevalence of synchronized neural spiking in the brain suggests a role in normal brain function. Neural synchronization can be modelled with coupled oscillators where the phase of each oscillator represents the timing of the neural spike. These models generate planar waves and spirals which resemble those observed in neural tissue. We recently characterized a new synchronization solution that we call ripple. Ripple is topologically distinct from waves and spirals and constitutes another possibility in neural synchronization.
Heitmann S, Ermentrout GB (2015) Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity. Biological Cybernetics 109:3.