Fig. 19

Existence and complexity of classes. A The letters from A to F refer to the stages of topological equivalence identified in Fig. 15 for increasing R. Some of the classes that were found for small R disappeared far from the codim-3 singularity, while new classes appeared when exploring the codim-4 unfolding. The figure shows the lifespan of each class as a function of R (gray indicates the existence of a class). For each class we report the smallest codimension of the local singularity in which unfolding the class first appears. This can be used as a measure of complexity. We identified hysteresis-loop bursters of complexity 2, 3 and 4 (green, orange and red). For the classes with a question mark, further investigation is needed to establish their complexity in terms of codimension. As an additional element to understand the complexity of a class, we report the minimum number of bifurcation curves that the path for that class here identified has to cross, which may also affect whether an arc of great circle can be used as a path (last column, ‘y’ (yes) if the great circle ‘g.c.’ can be used, ‘n’ (no) otherwise). B The table summarizes the hysteresis-loop bursting classes present in our model, considering also changes in R. The letters ‘s’ and ‘b’ indicate whether the silent state is, respectively, outside or inside the limit cycle of the active phase