"Green" noise in quasistationary stochastic systems.

We consider the behavior of stochastic systems driven by noise with a zero value of spectral density at zero frequency ("green" noise). For this purpose we propose the version of the Krylov-Bogoliubov averaging method to study the systems which are not stationary in the case of an external white noise. We use the ergodicity of a nonlinear random function in the method, and obtain equations for any approximation of the theory. In particular, it is shown in the first approximation that there is an effective potential to describe the averaged motion of the system. We consider a phase-locked loop as an example and show that metastable states are possible. The lifetime of these states essentially increases if the form of a green noise spectrum becomes sharper in the low-frequency region. The high stability of the system driven by green noise is confirmed by numerical simulation. It is important that the theoretical result obtained by the averaging method and the one obtained in the simulation coincide with sufficient accuracy. In conclusion, we discuss some of the unsolved green noise problems. (c) 2001 American Institute of Physics.