  Neuronal voltage dynamics of regularly firing neurons typically has one
stable attractor: either a fixed point (like in the subthreshold regime) or a
limit cycle that defines the tonic firing of action potentials (in the
suprathreshold regime). In two of the three spike onset bifurcation sequences
that are known to give rise to all-or-none type action potentials, however, the
resting-state fixpoint and limit cycle spiking can coexist in an intermediate
regime, resulting in bistable dynamics. Here, noise can induce switches between
the attractors, i.e., between rest and spiking, and thus increase the
variability of the spike train compared to neurons with only one stable
attractor. Qualitative features of the resulting spike statistics depend on the
spike onset bifurcations. This study focuses on the creation of the spiking
limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives
interspike interval (ISI) densities for a conductance-based neuron model in the
bistable regime. The ISI densities of bistable homoclinic neurons are found to
be unimodal yet distinct from the inverse Gaussian distribution associated with
the saddle-node-on-invariant-cycle (SNIC) bifurcation. It is demonstrated that
for the HOM bifurcation the transition between rest and spiking is mainly
determined along the downstroke of the action potential -- a dynamical feature
that is not captured by the commonly used reset neuron models. The deduced
spike statistics can help to identify HOM dynamics in experimental data.
