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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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    References listed on IDEAS

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    1. Yanhui Liu & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1997. "Correlations in Economic Time Series," Papers cond-mat/9706021, arXiv.org.
    2. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
    3. Blesić, S. & Milošević, S. & Stratimirović, Dj. & Ljubisavljević, M., 1999. "Detrended fluctuation analysis of time series of a firing fusimotor neuron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 275-282.
    4. Malcolm P. Baker & E. Scott Mayfield & John E. Parsons, 1998. "Alternative Models of Uncertain Commodity Prices for Use with Modern Asset Pricing Methods," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 115-148.
    5. Bernabe, Araceli & Martina, Esteban & Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2004. "A multi-model approach for describing crude oil price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 567-584.
    6. 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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    Cited by:

    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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