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

Abstract

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.Chaos theory, forecasting, Lyapunov exponent, Lorenz attractor, Rössler attractor, Chua attractor, Monte Carlo simulations.