Classification of bursting patterns: A tale of two ducks
Fig 11
Cyclic folded-node bursting cases.
We use polar coordinates in order to construct idealized models. The top panels show the slow-fast dissection for the amplitude variable r of the underlying bursting model, with 3 different torus canard scenarios (a), (b), and (c). Adding a slow dynamics on a parameter β controlling the slow nullcline then yields associated cyclic folded-node bursting scenarios for which we show both the slow-fast dissection in the (a, r) plane and the x time series: (a) initiated by a subcritical Hopf bifurcation; (b) terminated by a fold of cycles; (c) initiated by a fold of cycles. Equations and parameter values are given in S1 Text.