Analysis of Chaotic Fluctuations Based on New Statistical Theory and Its Apphlications to Physical Systems

1.混沌波动的一个显著特征是它们与高斯噪声有很大的不同，反映了混沌的确定性。本文提出了一种利用大偏差理论分析这种高度非高斯时间序列的新方法，并将其应用于物理系统。在ⅰ型间歇跃迁点附近，我们成功地将爆发运动和层流运动分别分离出来，并发现了一种普通分析无法发现的新的异常统计行为。我们进一步提出了大偏差统计量的连分式展开。发现随着不稳定周期轨道周期的增大，近似变得更加合适。我们发现，一个空间分布的动力系统在经过长时间的随机初始运动过程后，表现出一种空间随机、时间周期性的新运动。这被称为“动态玻璃”。发现动态玻璃是在广泛的耗散耦合振子系统中观察到的一种独特现象，并阐明了动态玻璃出现的必要条件。进一步研究了玻璃态形成过程持续时间的分布，发现其具有多重分形性质。

1.One of eminent characteristics of chaotic fluctuations is that they are highly different from Gaussian noise, reflecting deterministic nature of chaos. In this study we developed a new method to analyze such highly non-Gaussian time series by employing the large deviation theory, and applied it to physical systems. Near the type-I intermittency transition pont we succeeded to single out burst and laminar motions separately, and found a new anomalous statistical behavior which cannot be found with an ordinary analysis. We further proposed a continued-fraction epansion for large deviation statistics. It is found that the approximation become more appropriate by increasing the period of the unstable periodic orbits.2.We found that a spatially distributed dynamical system exhibits a new type of motion which is spatially random and temporally periodic, observed after a long transient process for random initial candtion. This was called "dynamical glass". It was found that dynamical glass is a uniquituous phenomenon observed in a wide range of dissipative, coupled oscillator systems, and the necessity condition for the appearance of dynamical glass is clarified. We further studied the distribution of duration of formation process of glassy state, and found that multifractal property holds.