Abstract
Abstract. In the first part of the paper we study the geometrical characteristics of the magnetospheric ions’ time series in the reconstructed phase space by using the SVD extended chaotic analysis, and we test the strong null hypothesis supposing that the ions’ time series is caused by a linear stochastic process perturbed by a static nonlinear distortion. The SVD reconstructed spectrum of the ions’ signal reveals a strong component of high dimensional, external coloured noise, as well as an internal low dimensional nonlinear deterministic component. Also, the stochastic Lorenz system produced by coloured noise perturbation of the deterministic Lorenz system was used as an archetype model in comparison with the dynamics of the magnetrospheric ions.Key words. Magnetospheric physics (energetic particles) – Radio science (nonlinear phenomena)
Highlights
Many theoretical and experimental studies support the hypothesis that the magnetosphere can be described as a low dimensional chaotic system
It follows from Eq (1) that when the power spectrum obeys a power law, the autocorrelation function decays as the lag time τ increases. These characteristics can be caused by linear-nonlinear stochastic dynamical systems or by low dimensional chaotic dynamical system
As we have shown elsewhere (Athanasiu and Pavlos, 2001), the white noise leaves invariant the correlation dimension passing from the original stochastic signal to its singular value decomposition (SVD) components
Summary
Many theoretical and experimental studies support the hypothesis that the magnetosphere can be described as a low dimensional chaotic system. In a recent series of papers, an extended chaotic analysis has been developed by Pavlos et al (1999a, b, c), Athanasiu and Pavlos (2001), in which convincing answers to the above criticism against the existence of internal low dimensional and chaotic magnetospheric dynamics have been given According to these papers the magnetospheric chaos hypothesis is strongly supported by studying the geometrical and dynamical characteristics of the magnetospheric time series and their corresponding nonlinear surrogate data. In the following we summarize the main points of the algorithm concerning the chaotic analysis of the experimental signals, which will be used in Sect. 3 for the analysis of the energetic particle signal
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