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Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy

1,2, 1,3 and 1,*
Electronic Engineering College, Heilongjiang University, Harbin 150080, China
Computer and Information Engineering College, Heilongjiang University of Science and Technology, Harbin 150027, China
Electrical Engineering College, Suihua University, Suihua 1520061, China
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 663;
Received: 12 April 2019 / Revised: 8 June 2019 / Accepted: 5 July 2019 / Published: 6 July 2019
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
PDF [8871 KB, uploaded 10 July 2019]


The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, a multi-scale entropy theory analysis and statistical analysis are carried out on the chaotic sequences produced by different parameters and different initial values of logistic systems. According to the simulation results, the complexity of the chaotic system represented by the logistic system is mainly decided by parameter μ. Not all characteristic parameters of the chaotic system depend on the initial values. It is possible to make a reasonable estimation and prediction of the chaotic system from a macroscopic level. A variance estimation method for the parameter μ is proposed and applied to a logistic system and to another chaotic system, which is equally effective. View Full-Text
Keywords: chaos; multi-scale entropy; the logistic system; variance chaos; multi-scale entropy; the logistic system; variance

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Liu, C.; Ding, L.; Ding, Q. Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy. Entropy 2019, 21, 663.

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