Cheng Ly

*Coupling Regularizes Individual Units in Noisy Populations
*

**Abstract**

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
a simple linear stochastic process (Ornstein-Uhlenbeck) and find that
this can decrease the variance (i.e., regularize) of 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 apply asymptotic
theory that accurately explain these results. With our theory, we can
make concrete predictions about various phenomena. In particular, in a
network of neurons coupled electrically we predict the variance of the
spike times would be less compared to when coupling is abolished via
pharmacological drugs. The theory is general and can be applied to
other phenomena outside of Neuroscience; some of which are briefly
discussed. This talk will be accessible to a general mathematical audience.
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