New dynamics in cerebellar Purkinje cells: torus canards

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.

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

References in corpus (2)

• Subthreshold oscillations in a map-based neuron model
• On transition to bursting via deterministic chaos

Cited by in corpus (14)

• Coexisting attractors and chaotic canard explosions in a slow-fast optomechanical system
• Bottom-up approach to torus bifurcation in neuron models
• Voltage interval mappings for an elliptic bursting model
• Generic Torus Canards
• Spatio-temporal canards in neural field equations
• From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation
• Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons
• Tunable Oscillations in the Purkinje Neuron
• Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems
• Towards a new classification of bursting patterns: review & extensions
• Canonical models for torus canards in elliptic bursters
• Collective canard explosions of globally-coupled rotators with adaptive coupling
• On the Existence of and Relationship between Canards and Torus Canards in Forced Slow/Fast Systems
• A showcase of torus canards in neuronal bursters