Classification of bursting Mappings

When a system’s activity alternates between a resting state (e.g. a stable equilibrium) and an active state (e.g. a stable periodic orbit), the system is said to exhibit bursting behavior. We use bifurcation theory to identify three distinct topological types of bursting in one-dimensional mappings and 20 topological types in two-dimensional mappings having one fast and one slow variable. We show that different bursters can interact, synchronize, and process information differently. Our study suggests that bursting mappings do not occur only in a few isolated examples, rather they are robust nonlinear phenomena.