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

Abstract

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 prodiction, 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.