Comment on "Phase Reduction of Stochastic Limit Cycle Oscillators"

This is a comment on a recent paper by Yoshimura and Arai [Phys. Rev. Lett. 101, 154101 (2008)] on phase reduction of noisy limit-cycle oscillators, in which the authors claimed that the conventional phase stochastic differential equation used in previous studies does not give a proper approximation and proposed a modified phase equation. Here we point out that both phase equations are valid depending on the situation. We argue that the relative size of amplitude relaxation time and noise correlation time determines which of the two equations is appropriate in the white-noise limit. The conventional phase equation is also a proper approximation to noisy limit cycles with sufficiently fast amplitude relaxation, which can be used as a starting point for further analysis.