A New Property of Logistic Map with Scalable Precision

Abstract

In this paper, iteration method of logistic map with low positions is introduced in order to investigate property of logistic map. Basic structure of logistic map is proposed, which consists of common gene positions (CGPs) and individual gene positions (IGPs). CGPs have the same value of corresponding positions which transferred from previous numerical solutions. The ergodicity and long-term unpredictability of logistic map are largely dependent on IGPs. CGPs and IGPs can help us to deeply understand the property of chaos.