Dynamics in noise-driven ensembles of globally coupled excitable systems: from noisy subthreshold oscillations to spiking

We study the stochastic dynamics of an ensemble of globally coupled
excitable elements. Each element is modeled by a FitzHugh-Nagumo
oscillator and is disturbed by Gaussian noise. In simulations of the
Langevin dynamics we observe that under the increase of noise the mean
field proceeds from a steady equilibrium to global oscillations and then,
for sufficiently strong noise, back to the equilibrium. In the course of
thesetransitions diverse regimes of collective dynamics ranging from periodic
subthreshold oscillations to large-amplitude oscillations and chaos are
observed.Details and mechanisms of these noise-induced phenomena are explained in
termsof the bifurcations in the deterministic dynamical system which governs,
in the thermodynamic limit, the behavior of the cumulants.