Chaos and the limits of predictability for the solar-wind-driven magnetosphere-ionosphere system

The solar-wind-driven magnetosphere-ionosphere exhibits a variety of dynami cal states including low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionospheric known broadly as subst orms, and states of continuous strong unloading. The WINDMI model [J. P. Sm ith , J. Geophys. Res. 105, 12 983 (2000)] is a six-dimensional substorm mo del that uses a set of ordinary differential equations to describe the ener gy flow through the solar wind-magnetosphere-ionosphere system. This model has six major energy components, with conservation of energy and charge des cribed by the coupling coefficients. The six-dimensional model is investiga ted by introducing reductions to derive a new minimal three-dimensional mod el for deterministic chaos. The reduced model is of the class of chaotic eq uations studied earlier [J. C. Sprott, Am. J. Phys. 68, 758 (2000)]. The bi furcation diagram remains similar, and the limited prediction time, which i s in the range of three to five hours, occurs in the chaotic regime for bot h models. Determining all three Lyapunov exponents for the three-dimensiona l model allows one to determine the dimension of the chaotic attractor for the system. (C) 2001 American Institute of Physics.