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Fitting model equations to time series using chaos synchronization. (English) Zbl 1123.37325
Summary: We apply synchronization theory to model chaotic dynamical systems from the time series of the system’s output. This method estimates the coefficient differences based on the synchronization error, and adjusts the model coefficient until the synchronization error approaches zero. To evaluate the quality of the model, we investigate the effects of noise, sampling rate, and superfluous terms. Numerical simulation results show that applying chaos synchronization to the fitting of model equations may be superior to common modeling techniques, especially when the analyzed series are noisy and sampled at low frequencies.

MSC:
37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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