On a stochastic neuronal model integrating correlated inputs

Giacomo Ascione; Enrica Pirozzi; Giacomo Ascione; Enrica Pirozzi

doi:10.3934/mbe.2019260

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5206-5225. doi: 10.3934/mbe.2019260

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On a stochastic neuronal model integrating correlated inputs

Giacomo Ascione ,
Enrica Pirozzi ^,

Dipartimento di Matematica e Applicazioni ”Renato Caccioppoli”, Università degli studi di Napoli Federico II, Via Cintia, Monte S.Angelo Napoli, 80126, Italy

Received: 30 December 2018 Accepted: 17 May 2019 Published: 06 June 2019

A modified LIF-type stochastic model is considered with a non-delta correlated stochastic process in place of the traditional white noise. Two different mechanisms of reset are specified with the aim to model endogenous and exogenous correlated input stimuli. Ornstein-Uhlenbeck processes are used to model the two different cases. An equivalence between different ways to include currents in the model is also shown. The theory of integrated stochastic processes is evoked and the main features of involved processes are obtained, such as mean and covariance functions. Finally, a simulation algorithm of the proposed model is described; simulations are performed to provide estimations of firing densities and related comparisons are given.
- LIF neuronal model,
- colored noise,
- Ornstein-Uhlenbeck process,
- simulation,
- random Euler scheme
Citation: Giacomo Ascione, Enrica Pirozzi. On a stochastic neuronal model integrating correlated inputs[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5206-5225. doi: 10.3934/mbe.2019260

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Abstract

A modified LIF-type stochastic model is considered with a non-delta correlated stochastic process in place of the traditional white noise. Two different mechanisms of reset are specified with the aim to model endogenous and exogenous correlated input stimuli. Ornstein-Uhlenbeck processes are used to model the two different cases. An equivalence between different ways to include currents in the model is also shown. The theory of integrated stochastic processes is evoked and the main features of involved processes are obtained, such as mean and covariance functions. Finally, a simulation algorithm of the proposed model is described; simulations are performed to provide estimations of firing densities and related comparisons are given.

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