DETECTION THRESHOLD OF THE CONTROL PARAMETERS MODULATION IN A NOISY CHAOTIC MAP

Abstract

The least squares procedure is suggested to reveal weak modulation of the control parameters in a noisy chaotic map in the presence of both dynamical and observational noise. For a map of a known dynamical structure, which is supposed to depend linearly on modulated control parameters, the procedure allows to detect both harmonic and pulse modulation, reducing the problem of modulation extraction from noisy empirical time series to the classical scheme of signal detection in noisy data. As an example, detection of harmonic modulation in a logistic map is studied. It is shown that threshold amplitude is subjected to the influence of the noise enhancement phenomenon in chaotic systems. Despite noise enhancement, the method suggested is shown to be superior to direct spectral analysis of chaotic time series due to wideband noise-like spectrum of the chaotic map, which masks the weak control parameters modulation.