Interaction of Canard and Singular Hopf Mechanisms in a Neural Model

We consider an ordinary differential equation model for neural competition, presented previously in the study of binocular rivalry, which features two adapting populations of neurons interacting through mutual inhibition. This model is known to exhibit a variety of dynamic regimes, including mixed-mode oscillations (MMOs) featuring alternating small and large amplitude oscillations, depending on the value of an input parameter. In this work, we use geometric dynamical systems techniques to study the structure of the model in the singular limit as well as the emergence of MMOs in the perturbed system. In particular, exploiting a normal form calculation allows us to numerically compute a way-in/way-out function, which we use to elucidate the interaction of canard and singular Hopf mechanisms for small amplitude oscillations that occurs as the input parameter approaches a critical value. keywords: neural competition; inhibition; mixed-mode oscillations; canards; singular Hopf bifurcation MSC2010: 34E17, 92C20, 34A26, 34D15, 37G05