Fig. 4

Paths for hysteresis-loop bursting activity in the unfolding of the deg. TB singularity of focus type. This is a flat representation topologically equivalent to the bifurcation diagram shown in Fig. 3C. Different bifurcation curves are indicated with different colors, as indicated in the legend. The subscripts l, r, s, i (left, right, superior, inferior) refer to where, in the state space, the bifurcation occurs. For each region of the diagram, labeled with a Roman numeral from I to X, a schematic description of the phase portrait is proposed in gray, using solid/dashed circles to represent stable/unstable limit cycle, full/empty dots for stable/unstable foci and an empty dot with a line in the middle to represent saddles. A more detailed description of these ten regions is given in Fig. 5. There are two separate regions of bistability (in yellow): one, labeled LCb (limit cycle big), in the lower part of the unfolding, where the stable limit cycle is big enough to surround all the fixed points existing; the other, labeled LCs region, in the upper part, where the limit cycle does not surround all the fixed points. Paths for bursting activity are drawn as black arrows. The direction is chosen so that the path encounters first the offset and then the onset bifurcations. When building the model, this will be the direction along which the slow variable increases