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A two-state neuronal model with alternating exponential excitation

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

Special Issues: Advances in Stochastic processes and Applications

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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Keywords jump-telegraph process; first passage time; neural activity; firing probability; asymptotical behaviour

Citation: Nikita Ratanov. A two-state neuronal model with alternating exponential excitation. Mathematical Biosciences and Engineering, 2019, 16(5): 3411-3434. doi: 10.3934/mbe.2019171


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This article has been cited by

  • 1. Nikita Ratanov, Ornstein-Uhlenbeck Processes of Bounded Variation, Methodology and Computing in Applied Probability, 2020, 10.1007/s11009-020-09794-x
  • 2. Nikita Ratanov, Mean-reverting neuronal model based on two alternating patterns, Biosystems, 2020, 196, 104190, 10.1016/j.biosystems.2020.104190

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