{"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":"<p><p>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. </p>","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}
引用次数: 9
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.
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.
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