Reconstructing Attractors from Scalar Time Series: a Comparison of Singular System and Redundancy Criteria

A delay-vector phase space reconstruction in which the delay time satisfies a minimum redundan~ criterion is compared with a reconstruction obtained using a singular system approach, Minimum redundancy produces the better reconstruction. The reconstructions are compared using a distortion functional .~ which measures how well the location of a point in the original phase space can be determ~i~ed on the basis of its image under the reconstruction process. The superiority of the redundancy analysis over the singular system analysis ~s found to arise from the former's foundation on the notion of general independence as opposed to the latter's foundation on the notion of linear independence.