New dynamics in cerebellar Purkinje cells: torus canards

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Kramer, M. A.
Traub, R. D.
Kopell, N. J.
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Abstract
Description
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.
Comment: 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
Keywords
Mathematics - Dynamical Systems, Quantitative Biology - Neurons and Cognition, 37N25, 37G15
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