MULTIPLE BIFURCATIONS IN A POLYNOMIAL MODEL OF BURSTING OSCILLATIONS

Bursting oscillations are commonly seen to be the primary mode of elec trical behaviour in a variety of nerve and endocrine cells, and have a lso been observed in some biochemical and chemical systems. There are many models of bursting. This paper addresses the issue of being able to predict the type of bursting oscillation that can be produced by a model. A simplified model capable of exhibiting a wide variety of burs ting oscillations is examined. By considering the codimension-2 bifurc ations associated with Hopf, homoclinic, and saddle-node of periodics bifurcations, a bifurcation map in two-dimensional parameter space is coated. Each region on the map is characterized by a qualitatively dis tinct bifurcation diagram and, hence, represents one type of bursting oscillation. The map elucidates the relationship between the various t ypes of bursting oscillations. In addition, the map provides a differe nt and broader view of the current classification scheme of bursting o scillations.