Eur. Phys. J. D 19, 111-117 (2002)
https://doi.org/10.1140/epjd/e20020062

Colored noise in a two-dimensional nonlinear system

China Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China and Department of Physics (mailing address) , College of Sciences, Suzhou University, Suzhou, Jiangsu 215006, P.R. China

Corresponding author: ^a szhu@suda.edu.cn

Received: 20 August 2001
Revised: 4 December 2001
Published online: 15 April 2002

Abstract

A two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser systems, the mean, variance, and effective eigenvalue of laser intensity are calculated. Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. It is seen that the increase of noise correlation time can reduce the fluctuations in the laser system. It is also shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light when the theory is applied to a single mode dye laser.