Diffusion approximation of neuronal models revisited

Cupera, Jakub

doi:10.3934/mbe.2014.11.11

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…In this section, we investigate how the dependence of the coefficients α, β, σ in the model (14) on the input rates given by Eqs. (16) and (20) affects the FPTs (and thus the ISIs) of the Jacobi neuronal model.…”

Section: A Firing Ratementioning

confidence: 99%

“…For all these reasons, the Jacobi neuronal model given by Eqs. (14), (16), and (20) constitutes a good compromise between the realistic description of a neuron and the mathematical tractability. Indeed, it is able to reproduce high degree of irregularity of the real neuronal firing.…”

Section: B Variability Of the Responsementioning

confidence: 99%

“…The studies in which both reversal potentials are considered are more rare, [13][14][15][16] and the present article is devoted to such a model. Here, the effect of multiplicative noise on the output of the Jacobi neuronal model with dependent parameters is examined in detail.…”

Section: Introductionmentioning

confidence: 99%

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The Jacobi diffusion process as a neuronal model

D’Onofrio

Tamborrino

Lánský

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein’s model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation.

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Section: A Firing Ratementioning

confidence: 99%

Section: B Variability Of the Responsementioning

confidence: 99%

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The Jacobi diffusion process as a neuronal model

D’Onofrio

Tamborrino

Lánský

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Well-known and often-studied modification in the direction of closer biological relevance is Stein's model with reversal potentials (Tuckwell 1979;Burkitt 2001;Di Crescenzo and Martinucci 2007;Jahn et al 2011). The frequently employed diffusion approximations of the Stein's model, in which the character of stochasticity changes to the Gaussian white noise (Ricciardi and Sacerdote 1979;Lansky 1984;Gerstner 2005, 2006;Benedetto and Sacerdote 2013;Cupera 2014;Giorno and Spina 2014), stem out from the Poissonian character of the input.…”

mentioning

confidence: 98%

Stein’s neuronal model with pooled renewal input

Rajdl

Lánský

2015

Biol Cybern

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The input of Stein's model of a single neuron is usually described by using a Poisson process, which is assumed to represent the behaviour of spikes pooled from a large number of presynaptic spike trains. However, such a description of the input is not always appropriate as the variability cannot be separated from the intensity. Therefore, we create and study Stein's model with a more general input, a sum of equilibrium renewal processes. The mean and variance of the membrane potential are derived for this model. Using these formulas and numerical simulations, the model is analyzed to study the influence of the input variability on the properties of the membrane potential and the output spike trains. The generalized Stein's model is compared with the original Stein's model with Poissonian input using the relative difference of variances of membrane potential at steady state and the integral square error of output interspike intervals. Both of the criteria show large differences between the models for input with high variability.

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Shot noise, weak convergence and diffusion approximations

Tamborrino

Lánský

2021

Physica D: Nonlinear Phenomena

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Diffusion approximation of neuronal models revisited

Cited by 3 publications

References 19 publications

The Jacobi diffusion process as a neuronal model

The Jacobi diffusion process as a neuronal model

Stein’s neuronal model with pooled renewal input

Shot noise, weak convergence and diffusion approximations

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