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Robustness to noise and independence from a prior state are phenomena often believed to be determined by the overall topology of a network. We show that these features can instead be present at the level of a single limit cycle, representing the activity of a small group of neurons inside a cortical column. In particular, we find a bifurcation where this limit cycle changes from being susceptible to noise to being remarkably robust to noise, such that any history of input is erased over a single oscillation. We then show how this property leads to spatially patterned synchronization and pattern expression when many such limit cycles are coupled in a large-scale model of the superficial layers of the visual cortex

Noise robustness and spatially patterned synchronization of cortical oscillators