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Lyapunov exponent of magnetospheric activity from AL time series
Author(s) -
Vassiliadis D.,
Sharma A. S.,
Papadopoulos K.
Publication year - 1991
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/91gl01378
Subject(s) - lyapunov exponent , correlation dimension , magnetosphere , chaotic , physics , exponent , exponential function , statistical physics , nonlinear system , sensitivity (control systems) , series (stratigraphy) , dimension (graph theory) , mathematical analysis , mathematics , fractal dimension , quantum mechanics , magnetic field , fractal , computer science , paleontology , linguistics , philosophy , artificial intelligence , electronic engineering , pure mathematics , biology , engineering
A correlation dimension analysis of the AE index indicates that the magnetosphere behaves as a low‐dimensional chaotic system with a dimension close to 4. Similar techniques are used to determine if the system's behavior is due to an intrinsic sensitivity to initial conditions and thus is truly chaotic. The quantity used to measure the sensitivity to initial conditions is the Lyapunov exponent. Its calculation for AL shows that it is nonzero (0.11±0.05 min −1 ). This gives the exponential rate at which initially similar configurations of the magnetosphere evolve into completely different states. Also predictions of deterministic nonlinear models are expected to deviate from the observed behavior at the same rate.