Predicting Chaos with Lyapunov Exponents: Zero Plays no Role in Forecasting Chaotic Systems

We propose a novel 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 simula- tions of the Rössler, Lorenz and Chua attractors, we …nd that accuracy gains can be substantial. Also, we show that the candidate selection prob- lem identi…ed 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.