{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:44:20Z","timestamp":1760229860980,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T00:00:00Z","timestamp":1656374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ideological and political Demonstration Courses in Yunnan Province in 2021 of China","award":["KYTZ201820"],"award-info":[{"award-number":["KYTZ201820"]}]},{"name":"Ideological and political Demonstration Courses in Dianchi College of Yunnan University in 2021 of China","award":["KYTZ201820"],"award-info":[{"award-number":["KYTZ201820"]}]},{"name":"Ideological and political education reform of undergraduate colleges and universities in Yunnan Province in 2022 of China","award":["KYTZ201820"],"award-info":[{"award-number":["KYTZ201820"]}]},{"name":"Scientific Research Fund of Chengdu University of Information Technology of China","award":["KYTZ201820"],"award-info":[{"award-number":["KYTZ201820"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, our aim is to study the following fuzzy system: xn+1=Axn\u22121xn\u22122+Bxn\u22123D+Cxn\u22124,\u2009n=0,1,2,\u22ef, where {xn} is a sequence of positive fuzzy numbers and the initial conditions x\u22124,x\u22123,x\u22122,x\u22121,x0 and the parameters A,B,C,D are positive fuzzy numbers. Firstly, the existence and uniqueness of positive fuzzy solutions of the fuzzy system are proved. Secondly, the dynamic behavior of the equilibrium points for the fuzzy system are studied by means of the fuzzy sets theory, linearization method and mathematical induction. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, and the numerical results not only show the dynamic behavior of the solutions for the fuzzy system, but also verify the effectiveness of the proposed results.<\/jats:p>","DOI":"10.3390\/sym14071337","type":"journal-article","created":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T03:26:37Z","timestamp":1656473197000},"page":"1337","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Dynamic Behavior of a Fractional-Type Fuzzy Difference System"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0164-2825","authenticated-orcid":false,"given":"Lili","family":"Jia","sequence":"first","affiliation":[{"name":"Dianchi College of Yunnan University, Kunming 650228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changyou","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China"},{"name":"College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaojuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Wei","sequence":"additional","affiliation":[{"name":"College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,28]]},"reference":[{"key":"ref_1","first-page":"7","article-title":"Dynamics of two-species harvesting model of almost periodic facultative mutualism with discrete and distributed delays","volume":"26","author":"Liao","year":"2018","journal-title":"Eng. 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