【作者】 李军；

【导师】 程庆华；

【作者基本信息】 长江大学 ， 光学， 2012， 硕士

【摘要】 自然界中各种物理量的涨落通常用噪声来描述,依据噪声起源的不同,可将噪声分为内噪声和外噪声,内噪声由系统内部的统计性质所引起,外噪声则是由系统外部环境引起。研究表明,噪声及其关联形式对非线性系统的动力学行为有很大的影响,而双稳态系统作为典型的非线性系统,近年来成为人们广泛关注的热点。本论文采用数值模拟算法研究了关联噪声驱动的光学双稳态系统的统计特性,主要工作分为以下几个部分。(1)描述噪声的统计性质,并给出不同噪声间的互关联形式。研究了关联噪声驱动的双稳系统,并选取了一种较典型的情况,求出了其解析解,分析了其概率密度函数随噪声强度及噪声关联强度的变化规律。(2)推导了关联高斯白噪声驱动的朗之万方程的数值计算的常规积分算法,推导了福克—普朗克方程的二阶等价算法,与一阶常规积分算法比较,解决了求解福克—普朗克方程中处理非高斯交叉随机积分项的困难。计算机模拟实验表明,二阶等价算法具有更高的精确度和更好的稳定性。并将其模拟结果与第二章得到的解析解进行比较,验证了模拟算法的正确性。我们还进一步推导了关联色驱动的双稳系统的二阶算法。(3)选用了关联白噪声驱动的光学双稳系统,但用周期信号B cos Ωt对泵噪声进行了调制,用二阶等价算法对系统进行了计算机模拟计算,具体讨论了各个参量对其概率密度函数的影响。(4)选用了关联白噪声驱动的光学双稳系统,驱动系统的随机力选用周期力B cos Ωt用二阶等价算法对系统进行了计算机模拟计算,具体讨论了各个参量对其概率密度函数的影响。更多还原

【Abstract】 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.更多还原