University of Pittsburgh
January 25, 2011
Coupling Regularizes Individual Units in Noisy Populations
(Joint work with Bard Ermentrout)
It is known that coupling in a population can lower the variability of the entire network making the collective activity more regular. We explore this question at the individual level of various noisy populations. We start by exploring the effects of coupling on Ornstein-Uhlenbeck (linear) processes and find that this can decrease the variance (i.e., regularize) the individuals. In addition, we find coupling can regularize the period, or spike times, of individual noisy (nonlinear) oscillators even when coupled to noisier ones.
Surprisingly, this effect is robust to different kinds of coupling. With a reduced model assuming weak forcing, we derive asymptotic formulas for the variance of the spike times that accurately explain these results. With our theory, we can make concrete predictions about various phenomena. In particular, in a network of inhibitory neurons coupled via gap junctions we predict the variance of the spike times would be less compared to when coupling is abolished via carbenoxolone & mefloquine.