An Investigation of the Ability of Nonlinear Methods to Infer Dynamics from Observables

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In this study analysis of data whose character was kept secret was performed by employing a variety of nonlinear approaches. The idea was to test the ability of approaches stemming from the theory of nonlinear dynamical systems to infer the true properties hidden in the data. The approaches employed include dimension estimation, nonlinear prediction, Lyapunov exponent estimation, and false nearest neighbors. It is concluded that even though the methods have problems and occasionally may be inconclusive, when correctly applied they are effective in delineating the dynamics underlying the data.

*Department of Geosciences, University of Wisconsin—Milwaukee, Milwaukee, Wisconsin.

+Department of Meteorology, The Florida State University, Tallahassee, Florida.

**Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, Virginia.

Corresponding author address: A. A. Tsonis, Department of Geosciences, University of Wisconsin—Milwaukee, Lapham Hall, P. O. Box 413, Milwaukee, WI 53201.

In this study analysis of data whose character was kept secret was performed by employing a variety of nonlinear approaches. The idea was to test the ability of approaches stemming from the theory of nonlinear dynamical systems to infer the true properties hidden in the data. The approaches employed include dimension estimation, nonlinear prediction, Lyapunov exponent estimation, and false nearest neighbors. It is concluded that even though the methods have problems and occasionally may be inconclusive, when correctly applied they are effective in delineating the dynamics underlying the data.

*Department of Geosciences, University of Wisconsin—Milwaukee, Milwaukee, Wisconsin.

+Department of Meteorology, The Florida State University, Tallahassee, Florida.

**Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, Virginia.

Corresponding author address: A. A. Tsonis, Department of Geosciences, University of Wisconsin—Milwaukee, Lapham Hall, P. O. Box 413, Milwaukee, WI 53201.
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