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 of (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.