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Applications of bivariate and univariate local lyapunov exponents
Author(s) -
Seifu Yodit,
Reid N.
Publication year - 1997
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315348
Subject(s) - lyapunov exponent , bivariate analysis , univariate , mathematics , chaotic , dynamical systems theory , series (stratigraphy) , divergence (linguistics) , lyapunov function , statistical physics , multivariate statistics , statistics , nonlinear system , computer science , physics , paleontology , linguistics , philosophy , artificial intelligence , biology , quantum mechanics
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. 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.