Phase space reconstruction using input-output time series data

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Abstract
In this paper we suggest that an extension of a procedure recently proposed by Wayland et al. [Phys. Rev. Lett. 70, 580 (1993)] for recognizing determinism in an autonomous time series can also be used as a diagnostic for determining an appropriate embedding dimension for driven (“input-output”) systems. We compare the results of this extension to the results produced by the extensions to the method of false nearest neighbors put forward by Rhodes and Morari [Proceedings of the American Control Conference, Seattle, edited by The American Automatic Control Council (IEEE, Piscataway, 1995)] and the method of averaged false nearest neighbors by Cao et al. [Int. J. Bifurcation Chaos 8, 1491 (1998)].