Neural mechanism for a cognitive timer

To examine a possible biological mechanism for a cognitive timer, the stochastic dynamics of a network of neurons possessing two stable, states (on and off states) is studied. The fraction of on neurons existing at t = 0 remains large for an extended interval, and then abruptly falls. The distribution of the lengths of the interval is scale invariant in the following sense: The ratio (k)root mu ((k))/m, with m and mu ((k)) being the mean and the kth central moment, respectively, is invariant under scale transformations of m and mu ((k)). In the special case k = 2, this gives Weber's law, a hallmark of cognitive timing.