{"title":"受随机刺激的渗漏整合发射神经元的柯尔莫哥洛夫正向方程的弱噪声近似值","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":"{\"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}","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}
Weak noise approximation for the Kolmogorov forward equation for a leaky integrate-and-fire neuron subject to stochastic stimulation
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.