M. Ciobanu, V.Babin, N.D.Nicolae, C. Radu C.Talianu, V.Mogaldea, M. Mogaldea, Chaotic behaviour of ideal four-level laser with periodic pump modulation, J. Optoelectron. Adv. Mater., 6/2 (2004) 399-404

Title: Chaotic behaviour of ideal four-level laser with periodic pump modulation

Abstract: In this paper we study the predictability of the ideal four-level laser for different pump modulation frequencies. Time series obtained from the well-known two ODE system are processed using the Grassberger-Procaccia algorithm in order to estimate the correlation dimension and the error-doubling time (computed via the Kolmogorov entropy). Results evidence windows of low predictability, which can be associated with chaotic behavior. The attractor dimension, approximated by the correlation dimension, varies between 1.61 and 2.56 for different pump modulation frequencies. However, these values were obtained in a somehow indefinite or undeterminated way. Supported by the large discrepancies in the results reported when chaotic dynamics is analyzed in other areas of physics (e.g. atmospheric physics), the rather vague character of the criteria used when setting some parameters on which the above-mentioned quantities crucially depend is emphasized.

Key words: predictability; correlation dimension; correlation function; Kolmogorov entropy; chaos