Dynamic System Properties and Long Time Series

Abstract

The Correlation integral function method has often been used to analyse the dynamical systems governing turbulent processes in fluid dynamics (Brandstater et al., 1983; Guckenheimer and Buzyna, 1983; Malraison et al., 1983 [74, 201, 322]), series of volcanic eruptions (Sornette et al., 1991; Dubois and Cheminée, 1993 [481, 137]) and climatological time series (Nicolis and Nicolis, 1984 ; Essex et al., 1987 ; Tsonis and Eisner, 1988 [381, 142, 511]). The method is presented in Dubois and Gvishiani (1998) (section 9.2) [134]. The method was recently applied (Beauvais et al., 1998; Aubert et al., 1999; Aubert, 2000 [47, 19, 18]) to daily time series of the Oubangui river discharge. The geometrical organization of the original non-filtered time series in a 2-dimension pseudo-phase space only shows the annual cycle of rising, high, and falling regimes that cannot really account for the underlying dynamical system. Instead, the results obtained on the filtered time series, i.e. free of the annual cycle, indicate that the system is governed by ~ 10 degrees of freedom which may correspond to climatic variables such as the mean annual rainfall, and the intensity, magnitude and duration of rainstorms. The filtered time series is also described by an attractor exhibiting a relatively clear geometrical organization.