Electroencephalographic (EEG) potentials are analysed by the Lyapunov spectrum in order to evaluate the orbital instability peculiar to deterministic chaos quantitatively. First, the Lyapunov spectra are estimated to confirm the existence of chaotic behavior in EEG data by the optimal approximation of Jacobian matrix in the reconstructed statespace. Second, the same method is applied to a neural network model with chaotic dynamics, the macroscopic average activity of which is analysed as a simple model of EEG data. The first analysis shows that the largest Lyapunov exponent is actually positive in the EEG data. On the other hand, the second analysis on the chaotic neural network shows that the positive largest Lyapunov exponent can be obtained by observing only the macroscopic average activity. Thus, these results indicate the possibility that one can know the existence of chaotic dynamics in the brain by analysing the Lyapunov spectrum of the macroscopic EEG data.

The long spikes have been often recorded at the multiples of the electron cyclotron frequency in the ionograms of the topside sounders observed in low latitudes. There has not been sufficient explanation for the physical cause for occourrence of the long spike so far. Here, by interpreting this phenomenon as receiving the trapped cyclotron harmonic wave, some analyses for the length of spike are done not only from the viewpoint of the sweeping property of the frequency spectrum of the transmitted pulse but also from that of the mutual positional relation between the propagation path and the orbit of the sounder. The cause of forming a single spike and a graphical calculation method for the long spike are proposed, respectively. Thus, the cause and the fine structure of long spike consisting of superposed spikes are clarified.