<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>β</italic>-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.</p>
</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.

Spike Patterns and Chaos in a Map–Based Neuron Model

Doctoral School Gdańsk University of Technology

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Spike Patterns and Chaos in a Map\u2013Based Neuron Model"}

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...

Spike Patterns and Chaos in a Map–Based Neuron Model

Published Online: Sep 21, 2023

Page range: 395 - 408

Received: Oct 11, 2022

Accepted: Apr 13, 2023

DOI: https://doi.org/10.34768/amcs-2023-0028

Keywords
neuronal dynamics, -transformations, Farey–Lorenz permutations, periodic spiking, chaos

© 2023 Piotr Bartłomiejczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Spike Patterns and Chaos in a Map–Based Neuron Model

Published Online: Sep 21, 2023

Page range: 395 - 408

Received: Oct 11, 2022

Accepted: Apr 13, 2023

DOI: https://doi.org/10.34768/amcs-2023-0028

Keywordsneuronal dynamics, -transformations, Farey–Lorenz permutations, periodic spiking, chaos

© 2023 Piotr Bartłomiejczyk et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
neuronal dynamics, -transformations, Farey–Lorenz permutations, periodic spiking, chaos