{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:04:38Z","timestamp":1760889878086,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,6]],"date-time":"2019-07-06T00:00:00Z","timestamp":1562371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61471158"],"award-info":[{"award-number":["61471158"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u03bc. 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 \u03bc is proposed and applied to a logistic system and to another chaotic system, which is equally effective.<\/jats:p>","DOI":"10.3390\/e21070663","type":"journal-article","created":{"date-parts":[[2019,7,8]],"date-time":"2019-07-08T03:01:31Z","timestamp":1562554891000},"page":"663","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8965-5470","authenticated-orcid":false,"given":"Chunyuan","family":"Liu","sequence":"first","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"},{"name":"Computer and Information Engineering College, Heilongjiang University of Science and Technology, Harbin 150027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lina","family":"Ding","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"},{"name":"Electrical Engineering College, Suihua University, Suihua 1520061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun","family":"Ding","sequence":"additional","affiliation":[{"name":"Electronic Engineering College, Heilongjiang University, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,6]]},"reference":[{"key":"ref_1","first-page":"2402","article-title":"A chaos synchronization secure communication system based on output control","volume":"31","author":"Huang","year":"2009","journal-title":"J. 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