Spike Patterns and Chaos in a Map-Based Neuron Model

被引：5
作者：
Bartlomiejczyk, Piotr [1 ]
Trujillo, Frank Llovera [2 ]
Signerska-Rynkowska, Justyna [1 ,3 ]
机构：
[1] Gdansk Univ Technol, Fac Appl Phys & Math, BioTechMed Ctr, G Narutowicza 11-12, PL-80233 Gdansk, Poland
[2] Gdansk Univ Technol, Doctoral Sch, G Narutowicza 11-12, PL-80233 Gdansk, Poland
[3] Polish Acad Sci, Inst Math, Dioscuri Ctr Topol Data Anal, Sniadeckich 8, PL-00656 Warsaw, Poland
来源：
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE | 2023年 / 33卷 / 03期
关键词：
neuronal dynamics; beta-transformations; Farey-Lorenz permutations; periodic spiking; chaos; DISCRETE MODEL; NETWORK;
D O I：
10.34768/amcs-2023-0028
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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 beta-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.
引用
收藏
页码：395 / 408
页数：14
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