The exponential divergence or convergence of nearby trajectories (Lyapunov exponents) is conceptually the most basic indicator of deterministic chaos. We propose a new method to determine the spectrum of several Lyapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable. We have applied the method to various known model systems and also to the Rayleigh-Bénard experiment, and have elucidated the dependence of the Lyapunov exponents on the Rayleigh number.

• Received 26 February 1985

DOI:https://doi.org/10.1103/PhysRevLett.55.1082