Colloquium

It is known that coupling in a population can lower the variability of the entire network making the collective activity more regular. In addition, we find that coupled nonlinear noisy oscillators can regularize the spike times of the individual which can have significant implications in cellular networks when a small fraction play a prominent role. Surprisingly, this effect is robust to different kinds of coupling. With a reduced model of two coupled noisy oscillators and assuming weak forcing, we derive asymptotic formulas for the variance of the spike times that accurately explain these results. We also consider a network of recurrently coupled noisy oscillators. The behavior can vary depending on the phase-resetting curve (PRC) and type of coupling. The PDEs describing the system are not amenable to standard linear stability analysis. This is overcome by a method utilizing asymptotic theory to obtain analytic descriptions of the system.