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

Firing statistics in the bistable regime of neurons with homoclinic spike generation