Various physiological systems display bursting electrical activity (BEA).
There exist numerous three variable models to describe this behavior. 
However, four variables may be required to explain some qualitative features of the BEA. 


In this dissertation a model with two slow and two fast variables
is presented. For some parameter values the system has stable equilibria while
for other values there exist bursting solutions. A singular construction of the
latter solutions corresponds to the existence of a fixed point of a one
dimensional map. The map is the composition of two maps derived from the
slow-subsystem and the averaged fast-subsystem. In a degenerate case this fixed
point is determined. For non-degenerate cases numerical methods for calculating
these maps will be presented.