Abstract
Phase space reconstruction is the first step of recognizing the chaotic time series. On the basis of differential entropy ratio method, the embedding dimension m opt and time delay τ 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 τ, 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.
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Supported by the Key Program of National Natural Science Foundation of China (Nos. 61077071, 51075349) and Program of National Natural Science Foundation of Hebei Province (Nos. F2011203207, F2010001312).
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Zhang, S., Hu, Y., Bao, H. et al. Parameters determination method of phase-space reconstruction based on differential entropy ratio and RBF neural network. J. Electron.(China) 31, 61–67 (2014). https://doi.org/10.1007/s11767-014-3125-7
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DOI: https://doi.org/10.1007/s11767-014-3125-7
Key words
- Phase-space reconstruction
- Chaotic time series
- Differential entropy ratio
- Embedding dimension
- Time delay
- Radial Basis Function (RBF) neural network