Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes

A class of differential equations that model electrical activity in pancreatic beta cells is considered. It is demonstrated that these equations must give rise to both bursting solutions and, for different values of the parameters, continuous spiking. We also consider how the number of spikes per burst changes as parameters in the equations are varied. This transition may be continuous, in which case the period of the bursting solution increases significantly and then decreases. Hence, small perturbations may cause macroscopic changes in the bursting solution. This transition may also give rise to chaotic dynamics due to the existence of a Smale horseshoe.