Fig. 11

Transitions among classes. Transitions between bursting classes can be obtained through an ultra-slow modulation of the starting and ending points of the path followed by the fast subsystem in the unfolding. We here report two examples. A Simulated timeseries for the fast variable x and the slow one z. Dotted vertical lines mark the separation between different bursting classes. B The path followed in the unfolding is displayed in red. In the example portrayed, bursting activity moves from the LCs region (SN/SN, supH/supH, supH/SH, SN/SH) in the upper part of the unfolding, through a region with only oscillatory behavior, to the LCb region (SN/SH, SN/FLC, subH/FLC) in the lower part of the unfolding. The ultra-slow modulation pushes \(\mathbf{A}_{1}\) and \(\mathbf{B}_{1}\) downwards along arcs of great circles joining them with \(\mathbf{A}_{2}\) and \(\mathbf {B}_{2}\) respectively. C In this second example class SN/supH (c3s) switches to supH/SH (c10s). We show the timeseries and a zoom of the LCs region of the unfolding where the bursting takes place, with the path followed by the fast subsystem in red