Nonlinear Modeling and Prediction with Time Series Data

该提案计划对磁层中的非线性、耗散和非平衡系统进行检查。最近的研究表明，具有复杂行为的系统可能具有简单的动力学描述，并且实验数据可以用于重建系统动力学，从而独立于特定的建模假设而深入了解复杂非线性系统的物理。利用这些技术，单个动态变量的时间序列数据可以得到分形维数、李雅普诺夫指数等。如果系统是低维的，因而自由度较少，则其动力学可以用几个常微分方程的非线性耦合集来描述，这些常微分方程可以由时间序列数据构造而成。然后，这些方程可以用于预测，然而，由于混沌行为，这将受到限制，并且可以通过比较预测和观测数据来定义可预测的时间尺度。利用地磁数据分析磁层活动显示出低维混沌行为，因此可以构造其动力学方程。我们建议利用相空间重建技术建立太阳风-磁层耦合和恒星变率的非线性动力学模型。这种非线性动力学技术对天体物理和空间物理现象研究的影响是所提出的研究的主要焦点。

The proposal plans an examination of nonlinear, dissipative and non-equilibrium systems in the magnetosphere. Recently studies have shown that a system with complex behavior may have a simply dynamical description and that experimental data can be used to reconstruct the system dynamics, thus gaining insight into the physics of complex nonlinear systems, independently of particular modeling assumptions. Using these techniques, the time series data of a single dynamical variable can be used to obtain the fractal dimension, Lyapunov exponents, etc. If the system is low dimensional and thus has a small number of degrees of freedom, its dynamics may be described by a nonlinearly coupled set of a few ordinary differential equations, which can be constructed from time series data. These equations can then be used for prediction, which however would be limited because of the chaotic behavior, and a predictability time scale can be defined by a comparison of the predicted and observational data. Analysis of magnetospheric activity using geomagnetic data has shown a low-dimensional chaotic behavior, and thus its dynamical equations can be constructed. We propose to develop nonlinear dynamical models using the phase space reconstruction techniques in the solar wind--magnetosphere coupling and stellar variability. The implications of such nonlinear dynamical techniques for the study of astrophysical and space physical phenomena is the prime focus of the proposed research.