Phase reduction of stochastic limit cycle oscillators

We point out that for an oscillator subjected to noise the conventional phase equation is not a proper approximation even for weak noise. We present a phase reduction method valid for an oscillator subjected to weak white Gaussian noise. Numerical evidence demonstrates that the phase equation properly approximates dynamics of the original oscillator. Moreover, we show that, in general, noise causes a shift of the oscillator frequency and discuss its effects on entrainment.