Cheng Ly
Coupling Regularizes Individual Units in Noisy Populations

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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