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Correlation analysis of chaotic trajectories from Chua’s system

Author

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  • Alvarez-Ramirez, Jose
  • Rodriguez, Eduardo
  • Echeverria, Juan Carlos
  • Puebla, Hector

Abstract

Chaotic systems exhibit an erratic behavior reflected by a strong divergence of trajectories with arbitrarily close initial condition. In this way, similar to trajectories from pseudorandom number generators, chaotic trajectories can be seen as noise with some degree of correlation. This work focuses on the study of some correlation properties (i.e., scaling) of chaotic trajectories from the Chua’s system. This is done by using detrended fluctuation analysis, which is a method designed for the detection of correlations in stochastic time series. It is found that, in general, Chua’s trajectories behave as a Brownian motion for small time scales, while they can display a white noise-like behavior or be dominated by harmonic oscillations for large time scales.

Suggested Citation

  • Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Echeverria, Juan Carlos & Puebla, Hector, 2008. "Correlation analysis of chaotic trajectories from Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1157-1169.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1157-1169
    DOI: 10.1016/j.chaos.2006.07.042
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    5. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
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    1. Vázquez-Medina, R. & Díaz-Méndez, A. & del Río-Correa, J.L. & López-Hernández, J., 2009. "Design of chaotic analog noise generators with logistic map and MOS QT circuits," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1779-1793.

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