Research on the entropy of logistic chaos

Abstract

As a simple one-dimensional chaotic system, logistic map has some important applications in many fields. The stable entropy characteristic of logistic function is proposed in this paper. A series of logistic sequence entropy, calculated under different initial values and values of parameter μ, is found to have some special distributions. A great number of numerical simulations prove that the entropy is determined by parameter μ, and it is irrelevant with initial value. The logistic sequence becomes a uniform distribution, and its entropy is close to a maximum, when μ is increased to 4. Thereby the stationary quality of logistic chaos can be speculated to some extent.