New dynamics in cerebellar Purkinje cells: torus canards

TL;DR

This paper introduces the concept of torus canards, a new dynamical phenomenon observed in a mathematical model of cerebellar Purkinje cells, explaining a transition from bursting to rapid spiking.

Contribution

The study identifies and characterizes torus canards as a novel dynamical behavior in biophysical neuron models, expanding understanding of neuronal firing patterns.

Findings

Discovery of torus canards in Purkinje cell models

Analysis of bifurcation leading to bursting to spiking transition

Identification of repelling limit cycle branches as key dynamics

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.