[1] In this paper we report the evidence of a low-dimensional chaos in a set of data observed outside laboratories. The dynamic behavior of the time series of the fluctuations of the total electron content (TEC) measured at Goose Bay, which is a high-latitude station, is analyzed in detail using the tools of nonlinear dynamics. The low-dimensional character of the dynamics is evident from the estimated value of the fraction of false neighbors for various dimensions and the correlation dimension. The deterministic nature of the dynamics is investigated using recurrence plots and spatiotemporal entropy. The chaotic nature of the underlying dynamics of the fluctuations of TEC is shown by the power spectrum indicating exponential decay and the calculated positive value of Lyapunov exponent. This is also supported by the results of the comparison of the chaotic characteristics of the time series of variations of TEC with the pseudochaotic characteristic of the colored noise time series. The results of the tests based on the prediction error and the time reversal asymmetry statistic reject the hypothesis that TEC belongs to the family of linear stochastic signals. The nonlinear non-Gaussian nature of the oscillations of variations of TEC is further investigated by the surrogate data test based on several geometrical and dynamical characteristics of the variations of TEC such as mutual information, the fraction of the false nearest neighbours, the local slopes of the correlation sums, the curves giving Lyapunov exponents, and finally, the value of Lyapunov exponents. The results of this analysis show that low-dimensional chaotic dynamics could be a possible and fruitful concept which can be utilized to study the disturbance in the ionosphere as in the case of magnetospheric dynamics. We feel that the dynamical invariants like Lyapunov exponents and correlation dimension can describe the disturbance in the variations of TEC and thus the disturbance in the ionosphere. Hence the techniques of nonlinear and chaos theory and the measure of the dynamical invariants could be used for the characterization and thus for the modeling of variations of the total electron content.

Abstract.A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2 • N; 77.5 • E; mag: dip 3.5 • N) has been carried out to investigate the dynamical behaviour of the fluctuations of H . The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H , using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.

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