Suppression of Multimodality in Inter-Spike Interval Distribution: Role of External Damped Oscillatory Input

A theoretical model based on the generalized neuronal model with distributed delay (GNMDD) is proposed to generate multimodal/bimodal inter-spike interval (ISI) distribution. The distributed delay is assumed to be general in the sense that it is a linear combination of gamma distributed weak and strong memory kernels. It is found that the expected membrane potential in the subthreshold regime exhibits damped oscillatory behavior. This causes the ISI pattern to become bimodal/multimodal. Furthermore, the effect of external damped oscillatory current in the GNMDD model is investigated. Based on extensive simulation study of a set of coupled stochastic differential equations in the presence of a threshold, a vast amount of spiking data are generated. Using the non-parametric modeling approach, the optimal bin width of the histogram is obtained by using the Freedman-Diaconis rule. It is to be noted that, with the increasing amplitude of the damped oscillatory current, the multimodal ISI distribution changes to unimodal ISI distribution when the magnitude of external current reaches a critical value. It is found that the entropy also shows a sudden transition around the critical point. This phenomenon is akin to a phase transition.