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Power law periodicity in the tangent bifurcations of the logistic map

Author

Listed:
  • de S. Cavalcante, Hugo L.D
  • Vasconcelos, Giovani L
  • Rios Leite, José R

Abstract

Numerical studies were carried out for the average of the logistic map on the tangent bifurcations from chaos into periodic windows. A critical exponent of 12 is found on the average amplitude as one approaches the transition. Additionally, the averages oscillate with a period that decreases with the same exponent. This Power Law Periodicity is related to the reinjection mechanism of the map. The undulations appear at control parameter values much earlier than the values where the critical exponent of the bifurcation shows significant changes in the average amplitude.

Suggested Citation

  • de S. Cavalcante, Hugo L.D & Vasconcelos, Giovani L & Rios Leite, José R, 2001. "Power law periodicity in the tangent bifurcations of the logistic map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 291-296.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:1:p:291-296
    DOI: 10.1016/S0378-4371(01)00090-5
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    Cited by:

    1. Ide, Kayo & Sornette, Didier, 2002. "Oscillatory finite-time singularities in finance, population and rupture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(1), pages 63-106.
    2. de S. Cavalcante, Hugo L.D. & Leite, J.R.Rios, 2004. "Fine structure in the scaling of type-I intermittency bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 356-362.
    3. 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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