Phase reduction for FitzHugh-Nagumo neuron with large timescale separation.

Abstract

Phase reduction approach is a useful tool to reduce the dimension of limit-cycle oscillators. In this paper, it is applied to the FitzHugh-Nagumo neuron model with large timescale separation. To quantitate the response of the oscillator to the external perturbations, the asymptotic behaviors of the phase sensitivity functions for fast and slow variables are obtained. It is shown that in the relaxation limit, apart from the jump points which are the vertices of the cubic nullcline, the phase is insensitive to the perturbations on the fast variable. By using the phase sensitivity functions, two cases, namely, periodic pulse train perturbation and common noise perturbation, are investigated. Theoretical and numerical results suggest better performance for the synchronization behaviors of the perturbations on the slow variable for large timescale separation.