Nonlinear Modeling and Prediction with Time Series Data

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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.