Role of low-pass filtering in the process of attractor reconstruction from experimental chaotic time series

• Published in: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Vol. 47; no. 4; pp. 2520 - 2535
• Main Authors: Lawkins, WF, Daw, CS, Downing, DJ, Clapp, Jr, NE
• Format: Journal Article
• Language: English
• Published: United States 01-04-1993
• Subjects: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DATA ACQUISITION; FILTERS; MATHEMATICS 661000 > General Physics > (1992-); NONLINEAR PROBLEMS; TIME-SERIES ANALYSIS
• ISSN: 1063-651X; 1095-3787
• DOI: 10.1103/PhysRevE.47.2520

We discuss issues concerning the reconstruction of attractors from experimental chaotic time-series data using Takens's method of delays [in [ital Proceedings] [ital of] [ital the] [ital Warwick] [ital Symposium], 1981, edited by D. A. Rand and L. S. Young (Springer, New York, 1981)]. The focus of this paper is on the selection of appropriate lag-time and embedding-dimension values with an emphasis on the relationship between those parameters and data-measurement considerations. We are particularly interested in the effect that low-pass filtering has on the appearance and measured properties of reconstructed attractors. Empirical results are presented using data measured from a laboratory fluidized bed and from data generated by integrating the Lorenz [J. Atmospheric Sci. 20, 130 (1963)] and Franceschini [Physica 6D, 285 (1983)] models of chaotic dynamic systems.