Voltage interval mappings for an elliptic bursting model

Abstract

We employed Poincaré 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 Poincaré mappings, for the neuronal models and for similar (electro)chemical systems.

References in corpus (1)

• New dynamics in cerebellar Purkinje cells: torus canards

Cited by in corpus (4)

• Bottom-up approach to torus bifurcation in neuron models
• Slow passage through a Hopf-like bifurcation in piecewise linear systems: application to elliptic bursting
• A showcase of torus canards in neuronal bursters
• Canonical models for torus canards in elliptic bursters