Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reco...Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.展开更多
Phase space reconstruction is the first step to recognizing the chaos from observed time series.On the basis of differential entropy,this paper introduces an efficient method to estimate the embedding dimension and th...Phase space reconstruction is the first step to recognizing the chaos from observed time series.On the basis of differential entropy,this paper introduces an efficient method to estimate the embedding dimension and the time delay simultaneously.The differential entropy is used to characterize the disorder degree of the reconstructed attractor.The minimum value of the differential entropy corresponds to the optimum set of the reconstructed parameters.Simulated experiments show that the original phase space can be effectively reconstructed from time series,and the accuracy of the invariants in phase space reconstruction is greatly improved.It provides a new method for the identification of chaotic signals from time series.展开更多
基金Supported by the Key Program of National Natural Science Foundation of China(Nos.61077071,51075349)Program of National Natural Science Foundation of Hebei Province(Nos.F2011203207,F2010001312)
文摘Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.50775198 and 60102002)
文摘Phase space reconstruction is the first step to recognizing the chaos from observed time series.On the basis of differential entropy,this paper introduces an efficient method to estimate the embedding dimension and the time delay simultaneously.The differential entropy is used to characterize the disorder degree of the reconstructed attractor.The minimum value of the differential entropy corresponds to the optimum set of the reconstructed parameters.Simulated experiments show that the original phase space can be effectively reconstructed from time series,and the accuracy of the invariants in phase space reconstruction is greatly improved.It provides a new method for the identification of chaotic signals from time series.
