The Jacobi diffusion process as a neuronal model

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985823%3A_____%2F18%3A00498575" target="_blank" >RIV/67985823:_____/18:00498575 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1063/1.5051494" target="_blank" >http://dx.doi.org/10.1063/1.5051494</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.5051494" target="_blank" >10.1063/1.5051494</a>

Result language

angličtina

Original language name

The Jacobi diffusion process as a neuronal model

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10103 - Statistics and probability

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Chaos

ISSN

1054-1500

e-ISSN

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Volume of the periodical

28

Issue of the periodical within the volume

10

Country of publishing house

US - UNITED STATES

Number of pages

10

Pages from-to

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UT code for WoS article

000448974600023

EID of the result in the Scopus database

2-s2.0-85055636852