A six-dimensional nonlinear dynamics model is derived for the basic energy components of the night-side magnetotail coupled to the ionosphere by the region 1 currents. In the absence of solar wind driving and ionospheric dissipation the system is a 3 degree of freedom Hamiltonian system. The large ion gyroradius conductance of the quasi-neutral sheet produces the energization of the central plasma sheet (CPS), while the unloading is triggered when the net geotail current or current density exceeds a critical value. For a steady southward interplanetary magnetic field (IMF) the model predicts an irregular sequence of substorms with a mean recurrence period of about 1 hour as in the Klimas et al. [1992> Faraday loop model. Here we use the new model as a nonlinear prediction filter on the Bargatze et al. [1985> database. Starting with physics calculations of the 13 physical parameters of the model, we show that the average relative variance (ARV) is comparable to that obtained with data-based prediction filters. To obtain agreement between the predicted AL and the database AL it is essential to include the nonlinear increase of the ionospheric conductance with power deposited in the ionosphere. ¿ 1998 American Geophysical Union