Automated embedding and the creep phenomenon in chaotic time series by

Embedding techniques represent a powerful advance in the development of experimental chaos. However there seems no universal method to find the best set of parameters to use. In this paper we present a new approach, an automated embedding method, to estimate a near optimum embedding dimension and delay time based on the Γ-test [Stefánsson 1997]. A strange attractor can be regarded as the union of an infinite number of unstable periodic orbits. In order to extract these unstable periodic orbits from a set of embedding space vectors (used for reconstruction) we introduce a technique to estimate a suitable jump time. We also describe the ‘creep phenomenon’, discovered using these techniques, which may allow us to make more accurate longer term predictions.