Consider two neurons, A and B, which reciprocally inhibit each other. If both of the neurons receive input at the same time, it seems to me that no oscillation will occur between the two. Such would occur only if one of the two is initially "favored" over the other. So what I'm wondering is, how does that happen? Is it essentially random?
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Noise will ensure that there will not be perfect symmetry and therefore that one has an advantage to fire first. Whichever one fires first will inhibit the other and ensure that the first one to fire will stay on for however long the dynamics of the pattern generator allow.