The Numerical Simulation Algorithm Of The Optical Bistable System Driven By Correlated Noises

The fluctuations of various physical quantities in nature are usually described by the noise. According to the different origin, noise could be divided into internal noise and external noise. Usually, the internal noises are caused by the statistical properties of the system, while the external noises are produced by the external environment of the system. The research results show that the noise and its cross-correlation form have great influence on the dynamic behaviors of the nonlinear system. The bistable system is a typical nonlinear system, the study of dynamic behavior for such a system has attracted researcher’s extensive attention in recent years. In this paper, using numerical simulation algorithm, we have investigated the statistical properties of the optical bistable system driven by correlated noises, and the main work as follows:Firstly, the statistical characteristics of white and colored noises are described respectively, and the cross-correlated froms between different noises are presented. Researching the bistable system driven by correlated noises, we have selected a typical case, its analytical solution is solved, and the stationary probability distribution with different noise intensities and noise cross-correlation intensities are analyzed.Secondly, the numerical algorithms for generalized Langevin equation with cross-correlated Gaussian white noises are developed. Computer simulation experiments show that the second order stochastic equivalent method (SOS) is more accurate and stable than the first order conventional approach (FOC), The SOS algorithm from the point of view of Fokker-Planck dynamics avoids the difficulty with cross integrals of stochastic terms encountered in the FOC method. Further more, the second-order numerical algorithm for the case of cross-correlated O-U noises is derived. The cross-integral of different noise terms are dealt with the concept of mean values. The simulation results with the second chapter get the analytical solution of the comparison, verify the correctness of the simulation algorithm.Thirdly, making use of periodic signals B cos Qt to modulate pump noise and using numerical algorithm simulation calculation to research the bistable system driven by correlated white noises, the influences of the various parameters on the probability density function are discussed. The case of the optical bistable system is driven by the white cross-correlation noise and periodic force be introduced into the system, we adopt the numerical algorithm simulation calculation, and investigate the influence of the various parameter on the probability density function.