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Predicting chaotic time series with wavelet networks. (English) Zbl 0888.93005
Summary: A new technique, wavelet network, is introduced to predict chaotic time series. By using this technique, firstly, we make accurate short-term predictions of the time series from chaotic attractors. Secondly, we make accurate predictions of the values and bifurcation structures of the time series from dynamical systems whose parameter values are changing with time. Finally we predict chaotic attractors by making long-term predictions based on remarkably few data points, where the correlation dimensions of predicted attractors are calculated and are found to be almost identical to those of actual attractors.

MSC:
93A30 Mathematical modelling of systems (MSC2010)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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