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To overcome the inevitable degradation of the logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the logistic map over ring [Formula: see text] from the perspective of its associated functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the logistic map over various domains. <\/jats:p>","DOI":"10.1142\/s0218127423500633","type":"journal-article","created":{"date-parts":[[2023,4,28]],"date-time":"2023-04-28T09:06:31Z","timestamp":1682672791000},"source":"Crossref","is-referenced-by-count":30,"title":["Periodicity Analysis of the Logistic Map Over Ring \u21243n"],"prefix":"10.1142","volume":"33","author":[{"given":"Xiaoxiong","family":"Lu","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric Yong","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Computer Science, Xiangtan University, Xiangtan 411105, Hunan, P. R. 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