Bifurcations of Fibonacci generating functions

ÖZER M., Cenys A., Polatoglu Y., Hacibekiroglu G., Akat E., Valaristos A., ...More

CHAOS SOLITONS & FRACTALS, vol.33, no.4, pp.1240-1247, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1016/j.chaos.2006.01.095
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1240-1247
  • Istanbul Kültür University Affiliated: Yes

Abstract

In this work the dynamic behaviour of the one-dimensional family of maps F-p,F-q(x) = 1/(1 - px - qx(2)) 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. (c) 2006 Elsevier Ltd. All rights reserved.