{"title":"Weak noise approximation for the Kolmogorov forward equation for a leaky integrate-and-fire neuron subject to stochastic stimulation","authors":"","doi":"10.1016/j.padiff.2024.100834","DOIUrl":null,"url":null,"abstract":"<div><p>We develop a weak noise approximation for the Kolmogorov forward equation governing the dynamics of a leaky integrate-and-fire neuron subject to white noise. Although being very simple, our approximation provides accurate results as far the magnitude of noise-induced fluctuations <span><math><mi>Δ</mi></math></span> remains much smaller than the distance <span><math><mi>A</mi></math></span> between the mean potential (center of mass) and the excitation threshold. The error for the firing rate is <span><math><mrow><mo><</mo><mn>3</mn><mtext>%</mtext></mrow></math></span> if <span><math><mrow><mi>A</mi><mo>/</mo><mi>Δ</mi><mo>></mo><mn>3</mn></mrow></math></span> for the stationary stimuli and if <span><math><mrow><mi>A</mi><mo>/</mo><mi>Δ</mi><mo>></mo><mn>5</mn></mrow></math></span> for time-varying stimuli.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124002201/pdfft?md5=ee8775cda04de2e4fcc8aeaaaa076757&pid=1-s2.0-S2666818124002201-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818124002201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We develop a weak noise approximation for the Kolmogorov forward equation governing the dynamics of a leaky integrate-and-fire neuron subject to white noise. Although being very simple, our approximation provides accurate results as far the magnitude of noise-induced fluctuations remains much smaller than the distance between the mean potential (center of mass) and the excitation threshold. The error for the firing rate is if for the stationary stimuli and if for time-varying stimuli.