Chaos and the Limits of Predictability for the solar-wind-driven Magnetosphere-ionosphere
W. Horton and R. S. Weigel
Department of Physics and Institute for Fusion Studies, The University
of Texas, Austin, Texas 78712
J. C. Sprott
Department of Physics, University
of Wisconsin, Madison, Wisconsin 53706
(Received 2 August 2000; accepted 20 March 2001)
The solar-wind-driven magnetosphere-ionosphere exhibits a variety of dynamical
states including low-level steady plasma convection, episodic releases
of geotail stored plasma energy into the ionospheric known broadly as substorms,
and states of continuous strong unloading. The WINDMI model [J. P.
Smith et al., J. Geophys. Res. 105, 12 983 (2000)] is a six-dimensional
substorm model that uses a set of ordinary differential equations to describe
the energy flow through the solar wind-magnetosphere-ionosphere system.
This model has six major energy components, with conservation of energy
and charge described by the coupling coefficients. The six-dimensional
model is investigated by introducing reductions to derive a new minimal
three-dimensional model for deterministic chaos. The reduced model
is of the class of chaotic equations studied earlier [J. C. Sprott, Am.
J. Phys. 68, 758 (2000)]. The bifurcation diagram remains
similar, and the limited prediction time, which is in the range of three
to five hours, occurs in the chaotic regime for both models. Determining
all three Lyapunov exponents for the three-dimensional model allows one
to determine the dimension of the chaotic attractor for the system.
Ref: W. Horton, R. S. Weigel, and J. C. Sprott,
Phys. Plasmas 8, 2946-2952 (2001)
The complete paper is available in PDF format.
Return to Sprott's Books and Publications.