Open AccessA two-state neuronal model with alternating exponential excitation
Author(s) -
Nikita Ratanov
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019171
Subject(s) - excitatory postsynaptic potential , depolarization , scaling , amplitude , laplace transform , exponential function , statistical physics , excitation , point process , physics , stimulus (psychology) , mathematics , control theory (sociology) , neuroscience , computer science , mathematical analysis , statistics , artificial intelligence , quantum mechanics , medicine , psychology , inhibitory postsynaptic potential , psychotherapist , biology , endocrinology , geometry , control (management)
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.