对“Hodgkin-Huxley和FitzHugh-Nagumo神经元网络中混沌的平均场描述和传播”的澄清和补充。

IF 2.3 4区医学 Q1 Neuroscience

Journal of Mathematical Neuroscience Pub Date : 2015-12-01 Epub Date: 2015-09-01 DOI:10.1186/s13408-015-0031-8

Mireille Bossy, Olivier Faugeras, Denis Talay

{"title":"对“Hodgkin-Huxley和FitzHugh-Nagumo神经元网络中混沌的平均场描述和传播”的澄清和补充。","authors":"Mireille Bossy, Olivier Faugeras, Denis Talay","doi":"10.1186/s13408-015-0031-8","DOIUrl":null,"url":null,"abstract":"In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-015-0031-8","citationCount":"9","resultStr":"{\"title\":\"Clarification and Complement to \\\"Mean-Field Description and Propagation of Chaos in Networks of Hodgkin-Huxley and FitzHugh-Nagumo Neurons\\\".\",\"authors\":\"Mireille Bossy, Olivier Faugeras, Denis Talay\",\"doi\":\"10.1186/s13408-015-0031-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters. \",\"PeriodicalId\":54271,\"journal\":{\"name\":\"Journal of Mathematical Neuroscience\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2015-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13408-015-0031-8\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Neuroscience\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://doi.org/10.1186/s13408-015-0031-8\",\"RegionNum\":4,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2015/9/1 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Neuroscience\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Neuroscience","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1186/s13408-015-0031-8","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2015/9/1 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Neuroscience","Score":null,"Total":0}

引用次数: 9

摘要

在本文中，我们澄清了Baladron等人在J. Math中提出的平均场n神经元模型的极限方程的适定性。神经科学。2:10,2012)，我们证明了混沌特性的相关传播。我们还在J. Math中完成了Baladron等人的建模问题。神经科学，2:10,2012)通过讨论控制离子通道行为和可用神经递质数量的随机微分方程的适定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Clarification and Complement to "Mean-Field Description and Propagation of Chaos in Networks of Hodgkin-Huxley and FitzHugh-Nagumo Neurons".

In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Mathematical Neuroscience Neuroscience-Neuroscience (miscellaneous)

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Journal of Mathematical Neuroscience (JMN) publishes research articles on the mathematical modeling and analysis of all areas of neuroscience, i.e., the study of the nervous system and its dysfunctions. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviours in neuroscience at all relevant scales, from the molecular world to that of cognition. The aim is to publish work that uses advanced mathematical techniques to illuminate these questions. It publishes full length original papers, rapid communications and review articles. Papers that combine theoretical results supported by convincing numerical experiments are especially encouraged. Papers that introduce and help develop those new pieces of mathematical theory which are likely to be relevant to future studies of the nervous system in general and the human brain in particular are also welcome.