New Discrete Chaotic Multiplicative Maps Based on the Logistic Map

Abstract

Chaos is a phenomenon which cannot be predicted if it manifests itself in a nonlinear system. Simple deterministic models, such as the logistic map [Formula: see text], are constructed to capture the essence of processes observed in nature. They are interesting also from a mathematical point of view: nonlinear models can behave in chaotic and complicated ways. The logistic map is the simplest mathematical model exhibiting chaotic behavior. Therefore, its dynamical properties, stable points and stable cycles are well known and widely described. In this paper, the properties of multiplicative calculus were employed to transform the classical logistic map into multiplicative ones. The multiplicative logistic maps were tested for chaotic behavior. The Lyapunov exponents together with the bifurcation diagrams are given.