  The stochastic Hodgkin-Huxley neurons considered in this paper replace
time-constant deterministic input $a dt$ of the classical deterministic model
by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is
Ornstein-Uhlenbeck with volatility $\sigma>0$ and backdriving force $\tau>0$,
and we call $\vartheta>0$ the signal. We have ergodicity and strong laws of
large numbers for various functionals of the process, and characterize 'quiet
behaviour' and 'regular spiking' as events whose probability depends on the
parameters $(\tau,\sigma)$ and on the signal $\vartheta$. The notions of quiet
behaviour and regular spiking allow for a construction of circuits of
interacting stochastic Hodgkin-Huxley neurons, combining excitation with
inhibition according to a bloc structure along the circuit, on which
self-organized rhythmic oscillations can be observed.
