Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model

Mixed mode oscillations (MMOs) are complex oscillatory waveforms 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, organising the dynamics along the Poincaré section. We examine the bifurcations of the return maps and demonstrate that the map formulation allows for an explanation of the different MMO patterns observed in the lactotroph model.