Summary
Phase resetting investigates oscillatory systems by quantifying the phase shift between a point on a stable periodic orbit and its return position following a perturbation. While this approach is applicable to numerical simulations of mathematical models, computing phase resets with high precision poses challenges. We employ a recently developed high-precision computational method based on the numerical continuation of a multi-segment boundary value problem to compute phase resets. We focus on phase reset resulting from fixed perturbation amplitude applied at a fixed phase, while the perturbation angle varies. We call the graph of the map that relates the perturbation angle with the new phase the dircetional transition curve and show how characteristics of this map and curve changes as the perturbation amplitude increases. We illustrate our findings with the FitzHugh-Nagumo system.
