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Paper details
Number 3 - September 2023
Volume 33 - 2023
Spike patterns and chaos in a map-based neuron model
Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska-Rynkowska
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.
Keywords
neuronal dynamics, β-transformations, Farey–Lorenz permutations, periodic spiking, chaos