Mixed-mode oscillations and bifurcation analysis in a pituitary model

Bursting is an intrinsically electrical activity in excitable cells such as endocrine cells and many types of neurons. Our purpose is to recognize the pituitary model from a new perspective and provide guidance for its further improvement by exploring the mechanism of bursting generation and its dynamic behavior. The technique of slow–fast dynamics analysis is very helpful when analyzing two subsystems that vary significantly in time scale. Based on the original model, A-type potassium channels and BK-type potassium channels are added simultaneously to the system. And its dynamical property differs from merely adding a fast potassium ion channel (A-type or BK-type). We acquire a deeper understanding for the novel bursting pattern (pseudo-plateau) from discussing the original system to considering bifurcation analysis to the whole system. We mainly explore the existence of mixed-mode oscillations (MMOs) in the improved pituitary model and its bifurcation behaviors via using geometric singular perturbation theory and slow–fast dynamics analysis, respectively. The result we obtained is very helpful in explaining mathematical mechanisms and improving the pituitary model.