ON THE STRUCTURE OF THE BURSTING REGION FOR A NEURONAL MODEL

We examine the question of whether the bursting region of a neuronal m odel is simply or multiply connected in the parameter space. Taking in to account that the presence of slow oscillations of intracellular cal cium concentration is a necessary condition for a bursting mode, we an alyze the subysystem responsible for the slow component of bursting. E xplicit parametric form of the Hopf bifurcation is given. It enables u s to reduce the problem to determining the number of the bifurcation c urves by finding the number of discontinuities of the expressions givi ng the bifurcation parameter values. The results obtained suggest that the bursting region is simply connected over the physiologically poss ible parameter range.