Voltage interval mappings for an elliptic bursting model
Chaotic Dynamics
2013-10-22 v1
Abstract
We employed Poincar\'e return mappings for a parameter interval to an exemplary elliptic bursting model, the FitzHugh-Nagumo-Rinzel model. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally, mixed-mode oscillations and quiescence in the FitzHugh-Nagumo-Rinzel model. We illustrate the wealth of information, qualitative and quantitative, that was derived from the Poincar\'e mappings, for the neuronal models and for similar (electro)chemical systems.
Cite
@article{arxiv.1310.5232,
title = {Voltage interval mappings for an elliptic bursting model},
author = {Jeremy Wojcik and Andrey Shilnikov},
journal= {arXiv preprint arXiv:1310.5232},
year = {2013}
}