New dynamics in cerebellar Purkinje cells: torus canards
Dynamical Systems
2009-11-13 v2 Neurons and Cognition
Abstract
We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that -- after a saddle node bifurcation of limit cycles -- the full model dynamics follow temporarily a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.
Keywords
Cite
@article{arxiv.0803.4272,
title = {New dynamics in cerebellar Purkinje cells: torus canards},
author = {M. A. Kramer and R. D. Traub and N. J. Kopell},
journal= {arXiv preprint arXiv:0803.4272},
year = {2009}
}
Comments
4 pages; 4 figures (low resolution); updated following peer-review: language and definitions updated, Figures 1 and 4 updated, typos corrected, references added and removed