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Bifurcations of Fibonacci generating functions

Author

Listed:
  • Özer, Mehmet
  • Čenys, Antanas
  • Polatoglu, Yasar
  • Hacibekiroglu, Gürsel
  • Akat, Ercument
  • Valaristos, A.
  • Anagnostopoulos, A.N.

Abstract

In this work the dynamic behaviour of the one-dimensional family of maps Fp,q(x)=1/(1−px−qx2) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean.

Suggested Citation

  • Özer, Mehmet & Čenys, Antanas & Polatoglu, Yasar & Hacibekiroglu, Gürsel & Akat, Ercument & Valaristos, A. & Anagnostopoulos, A.N., 2007. "Bifurcations of Fibonacci generating functions," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1240-1247.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:4:p:1240-1247
    DOI: 10.1016/j.chaos.2006.01.095
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    References listed on IDEAS

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    1. Mauriz, P.W. & Vasconcelos, M.S. & Albuquerque, E.L., 2003. "Specific heat properties of electrons in generalized Fibonacci quasicrystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 101-113.
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    Cited by:

    1. Louzzani, Noura & Boukabou, Abdelkrim & Bahi, Halima & Boussayoud, Ali, 2021. "A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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