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New dynamics in cerebellar Purkinje cells: torus canards
Mark A Kramer1, Roger D Traub, Nancy J Kopell
1Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA.
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 temporarily follow 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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