On a system of hyperstable frequency locking persistence under white noise

This paper studies a special system of N-coupled oscillators under white no ise. It is shown that we can get a positive recurrent diffusion process by winding the solution of this system on a cylinder along a special direction . Thus defining the rotation number as the limit of the frequency of the os cillator, we can prove that the rotation number exists and the frequency lo cking is successful no matter how large the white noise is.