Mixed mode oscillations as a mechanism for pseudo-plateau bursting

We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called pseudo-plateau bursting. Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic beta-cells.