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

Abstract

We discuss issues concerning the reconstruction of attractors from experimental chaotic time-series data using Takens's method of delays [in Proceedings of the Warwick 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.