Bifurcations of Canard-Induced Mixed Mode Oscillations in a Pituitary Lactotroph Model

Theodore Vo, Richard Bertram, Martin Wechselberger

Mixed mode oscillations (MMOs) are complex oscillatory wave-forms that naturally occur in physiologically relevant dynamical processes. MMOs were studied in a model of electrical bursting in a pituitary lactotroph [34] where geometric singular perturbation theory and bifurcation analysis were combined to demonstrate that the MMOs arise from canard dynamics. In this work, we extend the analysis done in [34] and consider bifurcations of canard solutions under variations of key parameters. To do this, a global return map induced by the flow of the equations is constructed and a qualitative analysis given. The canard solutions act as separatrices in the return maps, organ- ising the dynamics along the Poincare section. We examine the bifurcations of the return maps and demonstrate that the map formulation allows for an explanation of the dithe lactotroph model.