{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:46:00Z","timestamp":1760150760852,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018542","name":"Natural Science Foundation of Sichuan Province","doi-asserted-by":"publisher","award":["2023NSFSC0070","SUSE652B002"],"award-info":[{"award-number":["2023NSFSC0070","SUSE652B002"]}],"id":[{"id":"10.13039\/501100018542","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research and Innovation Team Program of Sichuan University of Science and Engineering","award":["2023NSFSC0070","SUSE652B002"],"award-info":[{"award-number":["2023NSFSC0070","SUSE652B002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper focuses on the relationship between a non-autonomous discrete dynamical system (NDDS) (H,f1,\u221e) and its induced set-valued discrete dynamical systems (K(H),f\u00af1,\u221e). Specifically, it explores the chaotic properties of these systems. The main finding is that f1,\u221e is Devaney chaotic if and only if f\u00af1,\u221e is Devaney chaotic in we-topology. The paper also provides similar conclusions for weak mixing, mixing, mild mixing, chain-transitivity, and chain-mixing in non-autonomous set-valued discrete dynamical systems (NSDDSs). Additionally, the paper proves that weak mixing implies sensitivity in NSDDSs.<\/jats:p>","DOI":"10.3390\/axioms13010020","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T05:43:15Z","timestamp":1703655795000},"page":"20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Chaotic Characteristics in Devaney\u2019s Framework for Set-Valued Discrete Dynamical Systems"],"prefix":"10.3390","volume":"13","author":[{"given":"Jie","family":"Zhou","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"},{"name":"South Sichuan Applied Mathematics Research Center, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-9656","authenticated-orcid":false,"given":"Tianxiu","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiazheng","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,27]]},"reference":[{"key":"ref_1","unstructured":"Robinson, R.C. 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