PHASE-SPACE PREDICTION OF CHAOTIC TIME-SERIES

We report on improved phase-space prediction of chaotic time series. W e propose a new neighbour-searching strategy which corrects phase-spac e distortion arising from noise, finite sampling time and limited data length. We further establish a robust fitting algorithm which combine s phase-space transformation, weighted regression and singular value d ecomposition least squares to construct a local linear prediction func tion. The scaling laws of prediction error in the presence of noise wi th various parameters are discussed. The method provides a practical i terated prediction approach with relatively high prediction performanc e. The prediction algorithm is tested on maps (Logistic, Henon and Ike da), finite flows (Rossler and Lorenz) and a laser experimental time s eries, and is shown to give a prediction time zip to or longer than fi ve times the Lyapunov time. The improved algorithm also gives a reliab le prediction when using only a short training set and in the presence of small noise.