Classification of bursting patterns: A tale of two ducks
Fig 6
Folded-node bursting in a nutshell.
The top row shows the essentials of folded-node bursting: (a) A fold-initiated bursting system (f1, f2, s1) (f1,2 are fast and s1 is slow) with (b) an added slow variable s2 creating a folded node and corresponding to the main parameter of the 3D burster organizing spike-adding transitions gives (c) a 2 slow variables/2 fast variables folded-node burster. The bottom row is an extension of the top panel (b) and shows the essentials of folded-node dynamics (whose typical time course is shown in the top panel (b)): A canard point (ε = 0) in the (f1, f2, s1) bursting system with s2 as parameter (left panel) becomes a folded node (black dot, center panel, ε = 0) when the slow dynamics put on s2 is evolving, for ε = 0 along the attracting and repelling parts of the critical manifold; for small ε > 0, this folded node creates small-amplitude oscillations nearby, organized by attracting and repelling slow manifold
(perturbations of
) and responsible for the quiescent oscillations of the folded-node burster in the resulting 4D system. See S1 Text for a glossary of labels and technical terms.