A unified and automated approach to attractor reconstruction

Abstract

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.

arXiv comment37 pages, 12 figures

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• Averaged Recurrence Quantification Analysis -- Method omitting the recurrence threshold choice
• Sampling rate-corrected analysis of irregularly sampled time series
• Ordinal Poincaré Sections: Reconstructing the First Return Map from an Ordinal Segmentation of Time Series
• Recurrence flow measure of nonlinear dependence
• ComplexityMeasures.jl: scalable software to unify and accelerate entropy and complexity timeseries analysis