A stochastic complex model with random imaginary noise

In this paper, we study a stochastic complex beam-beam interaction model subjected to random imaginary noise. The general procedure is presented to obtain the Fokker-Planck-Kolmogorov equation (FPK) using stochastic averaging method in the case of a special example. The exact stationary probability of FPK is examined theoretically under certain conditions and then the first and second moments for the amplitude are expressed analytically. Finally, a numerical simulation is performed to verify the theoretical results of moments and excellent agreement can be observed between these two results.