  We consider a model describing a neuron and the input it receives from its
dendritic tree when this input is a random perturbation of a periodic
deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron
itself is modeled by a variant of the classical Hodgkin-Huxley model. Using the
existence of an accessible point where the weak Hoermander condition holds and
the fact that the coefficients of the system are analytic, we show that the
system is non-degenerate. The existence of a Lyapunov function allows to deduce
the existence of (at most a finite number of) extremal invariant measures for
the process. As a consequence, the complexity of the system is drastically
reduced in comparison with the deterministic system.
