Spike patterns and chaos in a map-based neuron model - Bartłomiejczyk, Piotr; Llovera Trujillo, Frank; Signerska-Rynkowska, Justyna (Zielona Góra: Uniwersytet Zielonogórski)
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 ß-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; ß-transformations; Farey-Lorenz permutations; periodic spiking; chaos