0960-0779(94)00286-X Chaos, Solirom & Fractals Vol. 6, pp. 411-415, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All tights tmmed 0960-0779/95 $9.50 + .ca Detecting Hidden Frequencies in Dynamical Time Series: A Numerical Report G. ORTEGA and L. ROMANELLI Departamento de Fisica, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires, Ciudad Universitaria, Capital Federal, Argentina zyxwvutsrqponmlkjihgfedcbaZYX Abstmct - Periodicities in a dynamical system are determined by using only one variable. Embedding the data in higher dimensional spaces allows us to find recurrence time associated with particular points in the attractor. The present analysis is useful for experimental time series where traditional tools (e.g., Fourier Transform) fail in detecting some intrinsic frequencies of the system. The most common tool for time series analysis is the Fourier (and related) Transforms of the data (1). It is a “linear” method to deal with potentially non-linear systems, although a great variety of methods exist to “smooth” discrepancies between theory and numerical implementations (2). Moreover, when we deal with time series generated by a non-linear dynamical system, the observations x(i) are projections of multivariate state space onto the one-dimensional axis of the x(i)‘s. Spectral analysis over this kind of time series may hide important frequencies intrinsic to the underlying system, since the processes leading to chaotic behavior are fundamentally multivariate (3). Thus, it is important to device a technique which provides access to the overall spectrum of frequencies inherent to the dynamical system by using only one variable. Recurrence plot (4) has been used over the past years to study stationarity of experimental and simulated time series but only a trend of mean value has been detected. A similar procedure (5,6,7) had been described to locate saddle periodic orbits in a chaotic strange attractor. In this report the recurrence plot is used a tool to detect frequencies inherent to the dynamical system under study, which can not be detected by means of standard methods. 411