%0 Journal Article
%T Voltage interval mappings for an elliptic bursting model
%A Jeremy Wojcik
%A Andrey Shilnikov
%J Physics
%D 2013
%I arXiv
%R 10.1016/j.physd.2011.04.003
%X 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.
%U http://arxiv.org/abs/1310.5232v1