Chaotic appearance of the AE index

Abstract

A typical time sequence of AE shows no obvious regularities which suggests either that the magnetosphere is a random (stochastic) system or displays deterministic chaos. To find out whether the magnetosphere is random or chaotic, AE data have been studied by the embedding dimension method to find the correlation dimension of the magnetosphere. The autocorrelation ( AC ) time scale τ[ AC (τ) = ½ AC (0)] is about 50 minutes for all the cases we have investigated. This time scale may represent the time over which the magnetosphere adjusts to sudden changes. The frequency spectrum of the AE data is broadband with a universal form P (ω) ∼ ω −β , where β is about 2 for the frequencies, f = ω/2π between 0.04 mHz and 4 mHz. The correlation dimension for the AE data using a 1 minute delay to construct a time series of m dimensional vectors is between 3 and 4. With the proper time delay τ ⋍ 50min, which is the autocorrelation time, the correlation dimension is around 2.4. The variation of the correlation dimension with different time delays is shown. But because colored noise with β = 2 has a correlation dimension near 2.1, it is not yet possible to determine whether AE index is a signal resulting from colored noise or from deterministic chaos.