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Numerical study of the oscillatory convergence to the attractor at the edge of chaos

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  • R. Tonelli
  • M. Coraddu

Abstract

This paper compares three different types of “onset of chaos” in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three window; the transition to chaos in the generalized logistic with inflection 1/2 (x n+1 =1-μx n 1/2 ), in which the main bifurcation cascade, as well as the bifurcations generated by the periodic windows in the chaotic region, collapse in a single point. The occupation number and the Tsallis entropy are studied. The different regimes of convergence to the attractor, starting from two kinds of far-from-equilibrium initial conditions, are distinguished by the presence or absence of log-log oscillations, by different power-law scalings and by a gap in the saturation levels. We show that the escort distribution implicit in the Tsallis entropy may tune the log-log oscillations or the crossover times. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • R. Tonelli & M. Coraddu, 2006. "Numerical study of the oscillatory convergence to the attractor at the edge of chaos," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 355-359, March.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:1:p:355-359
    DOI: 10.1140/epjb/e2006-00064-6
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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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