Classification of bursting patterns: A tale of two ducks
Fig 4
Rinzel classification of bursting patterns.
Square-wave bursting, here in the Hindmarsh–Rose model [40] (panels (a1)-(b1)); elliptic bursting, here in the FitzHugh–Rinzel model [6,41] (panels (a2)-(b2)); parabolic bursting, here in Plant’s model [42] (panels (a3)-(b3)). In each case, we show a phase-space projection of the bursting solution of the full system (orange) together with the bifurcation diagram of the fast subsystem (left panel) and the time course of membrane potential V (orange, right panel). Labels for bifurcations are as follows: Ho for homoclinic, HB for Hopf bifurcation, LP for saddle-node (limit point) bifurcation of equilibria, and SNP for saddle-node of periodic orbits. (a3) The critical manifold S0 (green) is the S-shaped (not fully rendered) surface of equilibria of the fast subsystem; this surface is folded along the fold curve . Equations and parameter values are given in S1 Text.