On the continuous differentiability of inter-spike intervals of synaptically connected cortical spiking neurons in a neuronal network

Gautam Kumar, Mayuresh V. Kothare

Research output: Contribution to journalArticlepeer-review

Abstract

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous singleneuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

Original languageEnglish (US)
Pages (from-to)3183-3206
Number of pages24
JournalNeural Computation
Volume25
Issue number12
DOIs
StatePublished - 2013
Externally publishedYes

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Arts and Humanities (miscellaneous)

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