论文标题
通过广义比对指数（GALI）方法调查混乱
Investigating Chaos by the Generalized Alignment Index (GALI) Method
论文作者
论文摘要
动态系统研究中的基本任务之一是歧视常规行为和混乱行为。多年来，已经开发了几种混乱检测方法。其中一些，例如系统的庞加莱部分的构建，适用于低维系统。但是，高维系统描述了大量的现实问题。因此，现代的数值方法（例如较小（SALI）和广义（GALI）对齐指数也可以用于较低维系统，适用于在高维系统中调查常规和混乱的运动。在这项工作中，我们从数值上研究了盛大的稳定周期性轨道的行为。特别是，我们研究了晚会的值如何取决于稳定岛的宽度和系统的能量。我们发现，当研究的常规轨道更靠近稳定岛的边缘以获得固定能量，而这些指数随着系统的能量的增加而降低时，渐近的gali值会增加。我们还研究了晚会对用于计算的偏差向量坐标的初始分布的依赖性以及这些向量之间的相应角度。在这种情况下，我们表明，盛大的最终常数值与其计算所需的初始偏差向量的选择无关。
One of the fundamental tasks in the study of dynamical systems is the discrimination between regular and chaotic behavior. Over the years several methods of chaos detection have been developed. Some of them, such as the construction of the system's Poincaré Surface of Section, are appropriate for low-dimensional systems. However, an enormous number of real-world problems are described by high-dimensional systems. Thus, modern numerical methods like the Smaller (SALI) and the Generalized (GALI) Alignment Index, which can also be used for lower-dimensional systems, are appropriate for investigating regular and chaotic motion in high-dimensional systems. In this work, we numerically investigate the behavior of the GALIs in the neighborhood of simple stable periodic orbits of the well-known Fermi-Pasta-Ulam-Tsingou lattice model. In particular, we study how the values of the GALIs depend on the width of the stability island and the system's energy. We find that the asymptotic GALI values increase when the studied regular orbits move closer to the edge of the stability island for fixed energy, while these indices decrease as the system's energy increases. We also investigate the dependence of the GALIs on the initial distribution of the coordinates of the deviation vectors used for their computation and the corresponding angles between these vectors. In this case, we show that the final constant values of the GALIs are independent of the choice of the initial deviation vectors needed for their computation.
