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Parameter joint estimation of phase space reconstruction in chaotic time series based on radial basis function neural networks. (Chinese. English summary) Zbl 1274.93253

Summary: In this paper, we propose a joint estimation method of two parameters for phase space reconstruction in chaotic time series based on Radial Basis Function (RBF) neural networks. We obtain the best estimation values according to some objective standards. Furthermore, the single-step and multi-step RBF prediction model is used to estimate the best embedding dimension and delay time, and the Lorenz system is selected as an example. Finally, the estimation values are tested in the original model. The simulations show that we can obtain the best estimation values through the method, and the prediction accuracy is significantly improved.

MSC:

93E10 Estimation and detection in stochastic control theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93C15 Control/observation systems governed by ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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