In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decompo...In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.展开更多
The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium point...The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium points. Finally, the impacts of the superlattice parameter changes on the characteristics of the output chaotic signal are analyzed. The experimental results show that parameter changes of the superlattice will affect the eigenstructure around the equilibrium points in the output phase space, and DLEs are sensitive to these changes.展开更多
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
In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise ad...In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.展开更多
A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space...A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.展开更多
Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through di...Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF （MMCF） that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.展开更多
基金supported by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2010J01210 and T0750008)
文摘In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.
文摘The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium points. Finally, the impacts of the superlattice parameter changes on the characteristics of the output chaotic signal are analyzed. The experimental results show that parameter changes of the superlattice will affect the eigenstructure around the equilibrium points in the output phase space, and DLEs are sensitive to these changes.
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supported partly by the National Natural Science Foundation of China(60573065)the Natural Science Foundation of Shandong Province,China(Y2007G33)the Key Subject Research Foundation of Shandong Province,China(XTD0708).
文摘In the reconstructed phase space, based on the Karhunen-Loeve transformation （KLT）, the new local linear prediction method is proposed to predict chaotic time series. ＆ noise-free chaotic time series and a noise added chaotic time series are analyzed. The simulation results show that the KLT-based local linear prediction method can effectively make one-step and multi-step prediction for chaotic time series, and the one-step and multi-step prediction accuracies of the KLT-based local linear prediction method are superior to that of the traditional local linear prediction.
基金Project(51374035)supported by the National Natural Science Foundation of ChinaProject(2012BAB08B02)supported by the National“Twelfth Five”Science and Technology,ChinaProject(NCET-13-0669)supported by New Century Excellent Talents in University of Ministry of Education of China
文摘A laboratory leaching experiment with samples of different grades was carried out, and an analytical method of concentration of leaching solution was put forward. For each sample, respectively, by applying phase space reconstruction for time series of monitoring data, the saturated embedding dimension and the correlation dimension were obtained, and the evolution laws between neighboring points in the reconstructed phase space were revealed. With BP neural network, a prediction model of concentration of leaching solution was set up and the maximum error of which was less than 2%. The results show that there exist chaotic characteristics in leaching system, and samples of different grades have different nonlinear dynamic features; the higher the grade of sample, the smaller the correlation dimension; furthermore, the maximum Lyapunov index, energy dissipation and chaotic extent of the leaching system increase with grade of the sample; by phase space reconstruction, the subtle change features of concentration of leaching solution can be magnified and the inherent laws can be fully demonstrated. According to the laws, a prediction model of leaching cycle period has been established to provide a theoretical foundation for solution mining.
基金the National Natural Science Foundation of China (60673071)
文摘Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF （MMCF） that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.
