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Chaotic spikes arising from a model of bursting in excitable membranes. (English) Zbl 0754.58026
Modified author’s abstract: 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. The author also considers 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.
Reviewer: F.Neuman (Brno)

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92C99 Physiological, cellular and medical topics
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