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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 495-507. doi: 10.3934/mbe.2016003
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Successive spike times predicted by a stochastic neuronal model with a variable input signal

  • 1.
    Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126
  • 2.
    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : Primary: 60G20, 60J70; Secondary: 65C30.

  • Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided.

    Citation: Giuseppe D'Onofrio, Enrica Pirozzi. Successive spike times predicted by a stochastic neuronal model with a variable input signal[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 495-507. doi: 10.3934/mbe.2016003

    Related Papers:

  • Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous Ornstein-Uhlenbeck process and its first passage time through a constant threshold is used to model the first spike time after the signal onset. The second process is a Gauss-Markov process identified by a particular mean function dependent on the first passage time of the first process. It is shown that the second process is also of a diffusion type. The probability density function of the maximum between the first passage time of the first and the second process is considered to approximate the distribution of the second spike time. Results obtained by simulations are compared with those following the numerical and asymptotic approximations. A general equation to model successive spike times is given. Finally, examples with specific input signals are provided.


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  • This article has been cited by:

    1. G. D'Onofrio, P. Lansky, E. Pirozzi, On two diffusion neuronal models with multiplicative noise: The mean first-passage time properties, 2018, 28, 1054-1500, 043103, 10.1063/1.5009574
    2. Mario Abundo, Enrica Pirozzi, On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes, 2019, 7, 2227-7390, 991, 10.3390/math7100991
    3. Giuseppe D’Onofrio, Enrica Pirozzi, Marcelo O. Magnasco, 2015, Chapter 22, 978-3-319-27339-6, 166, 10.1007/978-3-319-27340-2_22
    4. Mario Abundo, Enrica Pirozzi, Integrated stationary Ornstein–Uhlenbeck process, and double integral processes, 2018, 494, 03784371, 265, 10.1016/j.physa.2017.12.043
    5. Giacomo Ascione, Enrica Pirozzi, 2018, Chapter 1, 978-3-319-74726-2, 3, 10.1007/978-3-319-74727-9_1
    6. Aniello Buonocore, Amelia G. Nobile, Enrica Pirozzi, Carlo Cattani, Simulation of sample paths for Gauss-Markov processes in the presence of a reflecting boundary, 2017, 4, 2331-1835, 1354469, 10.1080/23311835.2017.1354469
    7. A. Buonocore, A.G. Nobile, E. Pirozzi, Generating random variates from PDF of Gauss–Markov processes with a reflecting boundary, 2018, 118, 01679473, 40, 10.1016/j.csda.2017.08.008
    8. G. D’Onofrio, E. Pirozzi, Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes, 2019, 21, 1387-5841, 735, 10.1007/s11009-018-9617-4
    9. Giuseppe D’Onofrio, Claudio Macci, Enrica Pirozzi, Asymptotic Results for First-Passage Times of Some Exponential Processes, 2018, 20, 1387-5841, 1453, 10.1007/s11009-018-9659-7
    10. Virginia Giorno, Amelia G. Nobile, On the Construction of a Special Class of Time-Inhomogeneous Diffusion Processes, 2019, 177, 0022-4715, 299, 10.1007/s10955-019-02369-2
    11. Giuseppe D’Onofrio, Enrica Pirozzi, Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics, 2017, 74, 0303-6812, 1511, 10.1007/s00285-016-1061-x
    12. Pengfei Xu, Yanfei Jin, Mean first-passage time in a delayed tristable system driven by correlated multiplicative and additive white noises, 2018, 112, 09600779, 75, 10.1016/j.chaos.2018.04.040
    13. Angelo Pirozzi, Enrica Pirozzi, 2019, Chapter 100665-1, 978-1-4614-7320-6, 1, 10.1007/978-1-4614-7320-6_100665-1
    14. Olha Shchur, Alexander Vidybida, First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback, 2020, 19, 0219-4775, 2050005, 10.1142/S0219477520500054
    15. Enrica Pirozzi, Colored noise and a stochastic fractional model for correlated inputs and adaptation in neuronal firing, 2018, 112, 0340-1200, 25, 10.1007/s00422-017-0731-0
    16. Alexander Vidybida, Olha Shchur, Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback, 2018, 17, 0219-4775, 1850005, 10.1142/S0219477518500050
    17. Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi, Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications, 2021, 23, 1387-5841, 53, 10.1007/s11009-019-09748-y
    18. Angelo Pirozzi, Enrica Pirozzi, 2022, Chapter 100665, 978-1-0716-1004-6, 1674, 10.1007/978-1-0716-1006-0_100665
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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