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Bursting is a phenomenon found in a variety of physical and biologicalsystems. For example, in neuroscience, bursting is believed to play a key rolein the way information is transferred in the nervous system. In this work, wepropose a model that, appropriately tuned, can display several types ofbursting behaviors. The model contains two subsystems acting at differenttimescales. For the fast subsystem we use the planar unfolding of a highcodimension singularity. In its bifurcation diagram, we locate paths thatunderly the right sequence of bifurcations necessary for bursting. The slowsubsystem steers the fast one back and forth along these paths leading tobursting behavior. The model is able to produce almost all the classes ofbursting predicted for systems with a planar fast subsystems. Transitionsbetween classes can be obtained through an ultra-slow modulation of the model'sparameters. A detailed exploration of the parameter space allows predictingpossible transitions. This provides a single framework to understand thecoexistence of diverse bursting patterns in physical and biological systems orin models.

Fast-slow bursters in the unfolding of a high codimension singularity and the ultra-slow transitions of classes