Applications of Bivariate and Univariate Local Lyapunov Exponents

Abstract

Chaotic systems are characterized by sensitivity to initial conditions, and this property can be measured by global Lyapunov exponents, which are measures of the average divergence rate of initially close trajectories. Woll (1992) introduced local Lyapunov exponents and used them to obtain two diagnostic plots for diierentiating between stochastic and deterministic time series. We extend the deenition of the local Lya-punov exponent and the diagnostic plots to accommodate time series that arise from bivariate maps and investigate the behavior of the local Lyapunov exponents and the corresponding diagnostic plots for some dynamical systems and stochastic time series. We consider the application of this diagnostic plots to some heart rate variability data. Council of Canada. We are very much obliged to R. Hughson and Y. Yamamoto for permission to use their data. We are also grateful to Colleen Cutler and John Kolassa for helpful discussions and to the reviewers for very useful comments on an earlier draft.

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