Predicting chaos with Lyapunov exponents: zero plays no role in forecasting chaotic systems
Book section: 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.
Author(s)
Dominique Guegan, Justin Leroux
Publisher(s)
- InTech Publishers
Scientific editor(s)
- E. Tielo-Cuantle
Title of the work
- Chaotic Systems
Date of publication
- 2011
Keywords
- Chaos theory
- Forecasting
- Lyapunov exponent
- Lorenz attractor
- Rössler attractor
- Chua attractor
- Monte Carlo simulations
Pages
- 25-38 (chapitre 2)
URL of the HAL notice
Version
- 1