New dynamics in cerebellar Purkinje cells: torus canards

A showcase of torus canards in neuronal bursters

Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In computational models of neuronal systems, the transition from spiking to bursting often exhibits complex bifurcation structure. One type of transition involves the torus canard, which was originally observed in a simple biophysical model of a Purkinje cell. In this article, we expand on that original result by showing that torus canards arise in a broad array of well-known computational neuronal models with three diffe…