The method of Klimas et al. [1997] for constructing dynamical analogue
s of physical input-output systems is generalized. Higher-order analog
ues with sensitivity to more features of the input data are derived. S
olar wind VBs parameter data are used for input and Dst index data are
used for output to construct analogues of the magnetospheric dynamics
responsible for Dst storms. A detailed study of the dynamics involved
in a single storm is presented. It is shown that the relationship bet
ween VBs input and Dst output for this storm can be described in the c
ontext of the model of Burton et al. [1975] but with variable decay ti
me and strength of coupling to the solar wind VBs parameter. During th
e storm recovery it is found that the decay time varies from approxima
te to 4 hours at the storm maximum to approximate to 20 hours midway i
n the recovery and then back to approximate to 10 hours. There appears
to be nothing in the simultaneous solar wind data to explain this rev
ersal in the evolution of the decay time. It is shown that the strengt
h of coupling to the solar wind VBs parameter varies considerably. The
coupling strength peaks strongly at the time of the storm maximum and
decays to low values during the storm recovery. Solar wind VBs input
during the storm recovery does not affect the recovery rate. Using thi
s storm data, empirical nonlinear analogues are constructed, These ana
logues are tested out of sample for their prediction effectiveness. Co
mparisons with the predictions of the model due to Burton et al. are g
iven. It is shown that these analogues are promising prediction tools,
but their lack of sensitivity to solar wind dynamic pressure must be
corrected.