Before revision:  Here, the spiking statistics is derived for homoclinic conductance-based neuron models. Switching between rest and spiking is mainly determined along the downstroke of the action potential , a dynamical feature lacking in common neuron modelswith reset dynamics.
After revision:  Here, the spiking statistics is derived for homoclinic 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 lacking in common neuron modelswith reset dynamics.