# American Institute of Mathematical Sciences

2014, 11(2): 217-231. doi: 10.3934/mbe.2014.11.217

## On a spike train probability model with interacting neural units

 1 Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy, Italy 2 Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126 Napoli, Italy

Received  October 2012 Revised  April 2013 Published  October 2013

We investigate an extension of the spike train stochastic model based on the conditional intensity, in which the recovery function includes an interaction between several excitatory neural units. Such function is proposed as depending both on the time elapsed since the last spike and on the last spiking unit. Our approach, being somewhat related to the competing risks model, allows to obtain the general form of the interspike distribution and of the probability of consecutive spikes from the same unit. Various results are finally presented in the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.
Citation: Antonio Di Crescenzo, Maria Longobardi, Barbara Martinucci. On a spike train probability model with interacting neural units. Mathematical Biosciences & Engineering, 2014, 11 (2) : 217-231. doi: 10.3934/mbe.2014.11.217
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