First entrance time distribution multimodality in a model neuron

A simple jump-diffusion neuronal model accounting for the spatial geometry of the cell is considered and the probability density function of the interspike interval distribution is studied to find out the conditions under which it becomes multimodal. An approximate formula for such density is obtained in the case where the underlying diffusion is a Wiener process with drift and the jumps are Poisson time distributed. This formula holds when the Poisson events are rare but correspond to jumps of relevant amplitude and it results to be valid in some neuronal modeling instance. Some examples are shown that illustrate its range of application.