Logistic map as a Fourier’s series expansion: numerical analysis

Abstract

Abstract Logistic map is one of the simplest, and at the same time the most commonly used dynamic system, which is characterized by chaos. The article presents approximations of the logistic map through its extension into the Fourier’s series. Obtained in such way dynamical systems were analyzed, among others for the Lyapunov exponent and bifurcation diagrams. Furthermore the issue of the density of the iterated variable and some applications in chaos based cryptography were commented.