Entropy Map Might Be Chaotic

Abstract

Chaos is a phenomenon observable in many areas. Chaotic behaviours can be visualized in chaotic maps, which are deterministic iterative functions and sensitive to initial conditions. As a result, they are wildly adopted in random number generator, image encryption, etc. In this paper, two new chaotic maps inspired by information entropy are proposed. Through bifurcation diagram and Lyapunov exponent analysis, period doubling bifurcations are observed and chaos is suggested. Furthermore, these maps lead to a special case of the FrobeniusPerron operator in their distributions and are extended to the complex plane to obtain the Julia set.