Identification and prediction of nonlinear dynamics

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Title: Identification and prediction of nonlinear dynamics
Author: Dick, Andrew
Abstract: Chaos theory and associated analyses are being applied to a growing number of disciplines. Studies of biological and ecological systems have shown the widest application of chaotic analyses thus far. When studying these systems, it is often only possible to measure a subset of the system's many variables. To effectively perform a number of the analyses required to study a chaotic system, it is necessary to identify a complete strange attractor for the system. Consequently, it is necessary to reconstruct the system's strange attractor from the available data. Many different methods exist for reconstructing strange attractors, but the effectiveness of each of these methods has not been studied and compared. This investigation examines the effectiveness of various reconstruction methods used to preserve the fractal structure of the attractor and the exponential divergence of nearby trajectories in an effort to determine the optimal method for reconstructing strange attractors. With an optimal method to reconstruct strange attractors for chaotic physical systems, engineers and scientists can more successfully characterize a nonlinear system and apply methods to predict its future behavior.
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Date: 2003-10

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