Singularly perturbed phase response curves for relaxation oscillators

peer reviewedWe exploit a novel geometric method to construct the global isochrones of relaxation oscillators and the associated phase response curve. This method complements the classical infinitesimal (local) phase response curve approach by constructively predicting the finite phase response curve near the singular limit of infinite timescale separations between the oscillator variables. We illustrate the power of our construction on the FitzHugh-Nagumo model of neuronal spike generation. Because of its global and constructive nature, not requiring extensive numerical simulations, the proposed approach is particularly suited to control design applications