耦合哈密顿系统的时间序列分析

Time Series Analysis of Coupled Hamiltonian Systems

在研究许多物理模型问题中,人们对系统的具体结构知之甚少,甚至往往不知道其动力学规律,而只是测得与系统性质有关的某一变量随时间变化的数据,这就是所谓时间序列或信号。这被测得的变量可以是系统的状态变量之一,如细胞膜的内外电位差或振动系统沿某一方向的位移,但也可能并不是系统的状态变量而是与系统状态有关的某一变量,如医院里对人从体表测得的脉搏、心电图、脑电图、胃电图、心音和肺音都是如此。在这种情况下,如何由这种时间序列确定系统的运动性质和特征呢?人们用相空间重构和功率谱的方法来对系统的性质和特征进行分析判断。本文章用这两种方法对倾斜磁场下双势阱中粒子的运动模型做了进一步的分析。

In many physical model of the problem,people know little about the specific structure of the system,often do not even know the dynamic rules,but only one related to the nature of the system variables can be measured data changes over time,this is called time series or signal.This is measured variables can is one of the state variables of the system,such as inside and outside of the cell membrane potential difference along a certain direction of displacement or vibration system,but also may not be the state of the system but one related to the system state variables,such as the hospital from the surface to the person pulse,ecg,eeg,electrogastrogram,heart and lung sounds.In this case,how to determine the nature and characteristics of the system by this time series?The properties and characteristics of the system are analyzed and judged by means of phase space reconstruction and power spectrum.In this paper,the motion model of the particle in the two potential well in the tilted magnetic field is further analyzed.