New dynamics in cerebellar Purkinje cells: torus canards

Details New dynamics in cerebellar Purkinje cells: torus canards New dynamics in cerebellar Purkinje cells: torus canards

2008-03-29

arxiv.org/abs/0803.4272v2

M. A. Kramer, R. D. Traub, and N. J. Kopell, Phys. Rev. Lett. 101, 068103 (2008)

Mathematics

Dynamical Systems

4 pages; 4 figures (low resolution); updated following peer-review: language and definitions updated, Figures 1 and 4 updated,

Scientific paper

10.1103/PhysRevLett.101.068103

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.

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