A CORRELATION-FUNCTION FOR CHOOSING TIME DELAYS IN-PHASE PORTRAIT RECONSTRUCTIONS

A new method is proposed for the selection of the time delay used in creating phase portrait reconstructions of dynamical systems. Using the singular values computed from a singular value decomposition (SVD) of the embedded flow, we compute a quantity which we term the singular value fraction (SVF) as a function of the chosen lag time DELTA, and denoted as f(sv) (DELTA). For a given value of k, it gives the fractional power in the first k singular values. We seek to choose DELTA so that folding of the attractor is minimised, but the attractor volume is maximised, and we thus choose DELTA to be at the first minimum of f(sv). Equivalently we use a window of size DELTA(w), where DELTA(w) is approximately the first major maximum of f(sv). It is shown that this method compares favourably with some other extant methods.