A two-state neuronal model with alternating exponential excitation

Nikita Ratanov; Nikita Ratanov

doi:10.3934/mbe.2019171

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3411-3434. doi: 10.3934/mbe.2019171

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A two-state neuronal model with alternating exponential excitation

Nikita Ratanov ^,

Facultad de Economía, Universidad del Rosario, Calle 12c, No.4-69, Bogotá, D. C. Colombia

Received: 13 February 2019 Accepted: 04 April 2019 Published: 18 April 2019

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.
- jump-telegraph process,
- first passage time,
- neural activity,
- firing probability,
- asymptotical behaviour
Citation: Nikita Ratanov. A two-state neuronal model with alternating exponential excitation[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3411-3434. doi: 10.3934/mbe.2019171

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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.

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