Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska-Rynkowska
{"title":"Spike Patterns and Chaos in a Map–Based Neuron Model","authors":"Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska-Rynkowska","doi":"10.34768/amcs-2023-0028","DOIUrl":null,"url":null,"abstract":"Abstract The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"43 1","pages":"395 - 408"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics and Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.34768/amcs-2023-0028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Abstract The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.
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