Bifurcations of Fibonacci generating functions

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

Chaos, Solitons & Fractals, 2007, vol. 33, issue 4, 1240-1247

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:33:y:2007:i:4:p:1240-1247

DOI: 10.1016/j.chaos.2006.01.095

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