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Chapitre D'ouvrage Année : 2011

Predicting chaos with Lyapunov exponents: zero plays no role in forecasting chaotic systems

Justin Leroux
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Résumé

We propose a nouvel methodology for forecasting chaotic systems which uses information on local Lyapunov exponents (LLEs) to improve upon existing predictors by correcting for their inevitable bias. Using simulations of the Rössler, Lorenz and Chua attractors, we find that accuracy gains can be substantial. Also, we show that the candidate selection problem identified in Guégan and Leroux (2009a,b) can be solved irrespective of the value of LLEs. An important corrolary follows : the focal value of zero, which traditionally distinguishes order from chaos, plays no role whatsoever when forecasting deterministic systems.
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Dates et versions

halshs-00644500 , version 1 (24-11-2011)

Identifiants

  • HAL Id : halshs-00644500 , version 1

Citer

Dominique Guegan, Justin Leroux. Predicting chaos with Lyapunov exponents: zero plays no role in forecasting chaotic systems. E. Tielo-Cuantle. Chaotic Systems, InTech Publishers, 25-38 (chapitre 2), 2011. ⟨halshs-00644500⟩
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