Analyzing Nonlinear Dynamical Systems with Nonparametric Regression

Henning U. Voss

Chapter Chapter 17 in Nonlinear Dynamics and Statistics, 2001, pp 413-434 from Springer

Abstract: Abstract The analysis of dynamical systems data often can be considerably simplified using some knowledge of the system’s structure rather than performing a general phase space reconstruction. For the common case when the evolution equations are given by a sum of functions of measurements, the statistical problem of model estimation is reduced from a multidimensional density estimation problem to several two-dimensional problems, connected by an in general nonlinear relationship. To recover this relationship, we use the statistical approach of nonparametric nonlinear regression analysis. This allows (a) for the analysis of systems with high-dimensional dynamics, like spatially extended and time-delayed feedback systems, and (b) for the further investigation of the resulting models. To illustrate these points, we review the application of nonparametric regression analysis to two physical experiments and numerical examples of nonlinear dynamics.

Keywords: Nonlinear Dynamical System; Nonparametric Regression; Maximal Correlation; Amplitude Equation; Optimal Transformation (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0177-9_17

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DOI: 10.1007/978-1-4612-0177-9_17

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