Abstract
AbstractChaotic 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. Wolff (1992) introduced local Lyapunov exponents and used them to obtain two diagnostic plots for differentiating between stochastic and deterministic time series. We extend the definition of the local Lyapunov exponent and the diagnostic plots to accommodate time series that arise from bivariate maps and investigate the behaviour of the local Lyapunov exponents and the corresponding diagnostic plots for some dynamical systems and stochastic time series. We consider the application of these diagnostic plots to some heart rate variability data.
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