Phase-space prediction of chaotic time series

Dejin Yu, Weiping Lu, Robert G. Harrison

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We report on improved phase-space prediction of chaotic time series. We propose a new neighbour-searching strategy which corrects phase-space distortion arising from noise, finite sampling time and limited data length. We further establish a robust fitting algorithm which combines phase-space transformation, weighted regression and singular value decomposition least squares to construct a local linear prediction function. The scaling laws of prediction error in the presence of noise with various parameters are discussed. The method provides a practical iterated prediction approach with relatively high prediction performance. The prediction algorithm is tested on maps (Logistic, Hénon and Ikeda), finite flows (Rössler and Lorenz) and a laser experimental time series, and is shown to give a prediction time up to or longer than five times the Lyapunov time. The improved algorithm also gives a reliable prediction when using only a short training set and in the presence of small noise.

Original languageEnglish
Pages (from-to)219-236
Number of pages18
JournalDynamics and Stability of Systems
Volume13
Issue number3
Publication statusPublished - 1998

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