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1,1

Global wavelet analysis of impure chaotic dynamics

doi: 10.6062/jcis.2016.07.01.0105

(Free PDF)

Authors

Paulo G. F. Zeferino, A. Zanandrea and M. W. Beims

Abstract

In this paper we introduce the spectral complex index in order to characterize the variability pattern of different chaotic dynamics. This index is obtained from the global wavelet analysis (GWA) of a chaotic signal with impurities (a stochastic noise component). The parameter is defined as the absolute distance between the powers with and without impurity (following the same principle of the KL divergence but not in the full entropic definition). The results suggest that, due to the Global Wavelet Spectrum logarithmic properties, this new spectral method provides a high sensitive measure for characterization of at least three different properties of the underlying dynamical process such as (i) the intrinsic noise level, (ii) the nature of the nonlinear deterministic rule (discrete or continuous) and (iii) the presence or not of spatial correlation.

Keywords

Large scale structures; Observational cosmology; Model comparison; Computational astronomy.

References

[1] Packard, N. H., J. P. Crutchfield, J. D. Farmer, R. S. Shaw, Phys. Rev. Lett. 45: 712-716, 1980.

[2] Kants, H., T. Schereiber. Nonlinear time series analysis, Cambridge University Press, UK, 1999.

[3] Ge, T., Cui, Y., Lin, W., Kurths, J., Liu, C., New J. of Physics 14: 2-11, 2012.

[4] Chian, A. C. -L., Rempel, E. L., Macau, E. E., Rosa, R. R., and Christiansen, F. Phys. Rev. E 65: 035203 (R), 2002.

[5] Beims, M. W., Rech, P. C., Gallas, J. A. C., Physica A 295: 276-279, 2001

[6] Osborne, A. R., A. Provenzale. Physica D 35: 357-381, 1989.

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