Extreme value distributions in chaotic dynamics |
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| Authors: | V. Balakrishnan C. Nicolis G. Nicolis |
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| Affiliation: | (1) Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, C.P. 231, 1050 Brussels, Belgium;(2) Department of Physics, Indian Institute of Technology, 600 036 Madras, India;(3) Institut Royal Météorologique de Belgique, 1180 Bruxelles, Belgium |
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| Abstract: | A theory of extremes is developed for chaotic dynamical systems and illustrated on representative models of fully developed chaos and intermitent chaos. The cumulative distribution and its associated density for the largest value occurring in a data set, for monotonically increasing (or decreasing) sequences, and for local maxima are evaluated both analytically and numerically. Substantial differences from the classical statistical theory of extremes are found, arising from the deterministic origin of the underlying dynamics. |
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| Keywords: | Extreme value theory local maxima statistics fully developed chaos intermittent chaos |
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