A two-state neuronal model with alternating exponential excitation

Nikita Ratanov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We develop a stochastic neural model based on point excitatory inputs. The nerve cell depolarisation is determined by a two-state point process corresponding the two states of the cell. The model presumes state-dependent excitatory stimuli amplitudes and decay rates of membrane potential. The state switches at each stimulus time. We analyse the neural firing time distribution and the mean firing time. The limit of the firing time at a definitive scaling condition is also obtained. The results are based on an analysis of the first crossing time of the depolarisation process through the firing threshold. The Laplace transform technique is widely used.

Original languageEnglish (US)
Pages (from-to)3411-3434
Number of pages24
JournalMathematical Biosciences and Engineering
Volume16
Issue number5
DOIs
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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