FAST AND SLOW SUBSYSTEMS FOR A CONTINUUM MODEL OF BURSTING ACTIVITY IN THE PANCREATIC-ISLET

A simple model for the bursting electrical activity of individual panc reatic beta-cells is introduced. Using the model, a continuum model fo r collections (islets) of large numbers of such cells is then analyzed , using asymptotic methods, linear stability techniques, and monotone methods. When the coupling strength D is large, fast and slow subsyste ms for the continuum model are shown to be the same as those for the s ingle cell if the slow variables are replaced by their spatial average . It is demonstrated that fast variables can synchronize while the slo w variables simultaneously exhibit nonsynchronous behavior. Last, spat ial inhomogeneities in slow subsystem parameters are shown to inactiva te the islet. It is demonstrated that if a sufficient fraction of cell s are inactive, the average value of the slow variables can be decreas ed significantly.