Research on the Phase Space Reconstruction Method of Chaotic Time Series

2010 ◽  
Vol 26-28 ◽  
pp. 236-240
Author(s):  
Yun Fei Ma ◽  
Pei Feng Niu ◽  
Xiao Fei Ma
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaotic Dynamics ◽  
Original System ◽  
Chaotic Signal ◽  
Phase Space Reconstruction ◽  
Reconstruction Method ◽  
Numerical Verification ◽  
Signal Recognition

The puzzle over the recognition of the quality of the Chaotic Dynamics based on single variable time series brings forward the new method of phase space reconstruction—identify the embedding dimension with the FNN after delay time is fixed through the method of autocorrelation function. By means of the numerical verification of a few typical examples of chaotic dynamic system, the result shows that this method can be able to efficiently reconstruct the phase space of the original system out of the time series and relatively completely reduce the dynamic characteristics of the original system and thus the validity of the method is testified on chaotic signal recognition.

scholarly journals Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tai-fu Li ◽  
Wei Jia ◽  
Wei Zhou ◽  
Ji-ke Ge ◽  
Yu-cheng Liu ◽  
...  
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Phase Space ◽  
Adaptive Evolution ◽  
Kalman Filtering ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Reconstruction Method ◽  
Extended Kalman Filtering ◽  
Subspace Approximation

The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF) is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

scholarly journals Prediction in Chaotic Environments Based on Weak Quadratic Classifiers

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1630
Author(s):  
Alexander Musaev ◽  
Ekaterina Borovinskaya
Keyword(s):  
Time Series ◽  
Electric Potential ◽  
Chaotic Dynamics ◽  
System Component ◽  
Retrospective Data ◽  
Stationary Noise ◽  
Periodic Processes ◽  
Flow Processes

The problem of prediction in chaotic environments based on identifying analog situations in arrays of retrospective data are considered. Traditional recognition schemes are ineffective and form weak classifiers in cases where the system component of the observed process is represented by a non-periodic oscillatory time series (realization of chaotic dynamics). The objective is to develop a system of such classifiers, which allows for improvements in the quality of forecasts for non-stationary dynamics in flow processes. The introduced technique can be applied for the prediction of oscillatory non-periodic processes with non-stationary noise, i.e., dependence of different relay frequencies, external electric potential and microchannel width in an electrokinetic micromixer.

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