A coupled-map model of the magnetotail is used to study the dynamics of the magnetosphere. Using different types of colored noise as an input to the model, it is shown that the high-frequency part of the behavior is intrinsic to the model, while the low-frequency part reflects the dynamics of the input time series. It is also shown that the relation of the power spectra of the magnetospheric input (vBS) and output (AE) time series is very similar to the relation of the power spectra of the model input and output. It is then argued that the magnetosphere acts, similarly to the model, as a low-pass filter. It is also suggested that the power law distributions of the AE data may be partly due to the power law distribution of polarity changes in the interplanetary magnetic field BZ. ¿ 2000 American Geophysical Union