College of Liberal Arts & Sciences
Math Biology Seminar
Abstract:
Mixed mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in a coupled Morris-Lecar model neurons with three distinct timescales. We show how features and mechanisms of MMOs vary with respect to several key model parameters. Moreover, we give conditions under which two separate mechanisms of MMOs in two-timescale context, canard and delayed Andronov-Hopf bifurcation, can interact in a three-timescale setting and produce more robust MMOs.