The paper first describes the main bifurcation structure for a typical mode
l of an insulin producing pancreatic beta-cell. Considering a system of two
coupled identical and chaotically spiking beta-cells, the paper continues
to examine the bifurcations through which low periodic orbits embedded in t
he synchronized chaotic state lose their transverse stability and produce t
he characteristic picture of locally and globally riddled basins of attract
ion. We discuss the different types of riddled basins with the associated p
henomena of attractor bubbling and on-off intermittency.