Bifurcations of Fibonacci generating functions

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.