The solar-wind driven magnetosphere-ionosphere system is a classic example
of a complex dynamical system (CDS). The defining properties of a CDS are (
1) sensitivity to initial conditions; (2) multiple space-time scales; (3) b
ifurcation sequences with hysteresis in transitions between attractors; and
(4) noncompositionality. Noncompositionality means that the behavior of th
e system as a whole is different from the dynamics of its subcomponents tak
en with passive or no couplings. In particular the dynamics of the geomagne
tic tail plasma depends on its coupling to the dissipative ionospheric plas
ma and on the nature of the solar-wind driving electric field over a suitab
ly long (many hours) previous time interval. These complex dynamical system
features are shown here in detail using the known WINDMI model for the sol
ar-wind driven magnetosphere-ionosphere (MI) system. Numerous features in t
he bifurcation sequence are identified with known substorm and storm charac
teristics. (C) 1999 American Institute of Physics. [S1070-664X(99)03111-0].