Spike patterns and chaos in a map-based neuron model
Piotr Bartłomiejczyk, Frank Llovera Trujillo, Justyna Signerska‐Rynkowska · International Journal of Applied Mathematics and Computer Science · 2023
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.