## Abstract

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 Δ, and denoted as f_{sv} (Δ). For a given value of k, it gives the fractional power in the first k singular values. We seek to choose Δ so that folding of the attractor is minimised, but the attractor volume is maximised, and we thus choose Δ to be at the first minimum of f_{sv}. Equivalently we use a window of size Δ_{w}, where Δ_{w} is apprximately the first major maximum of f_{sv}. It is shown that this method compares favourably with some other extant methods.

Original language | English |
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Pages (from-to) | 72-80 |

Number of pages | 9 |

Journal | Physics Letters A |

Volume | 179 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2 Aug 1993 |

Externally published | Yes |