{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:23:44Z","timestamp":1768991024713,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map\u2019s states in commensurate and incommensurate cases.<\/jats:p>","DOI":"10.3390\/sym16070840","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T11:35:57Z","timestamp":1720006557000},"page":"840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On New Symmetric Fractional Discrete-Time Systems: Chaos, Complexity, and Control"],"prefix":"10.3390","volume":"16","author":[{"given":"Ma\u2019mon Abu","family":"Hammad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Louiza","family":"Diabi","sequence":"additional","affiliation":[{"name":"Laboratory of Dynamical Systems and Control, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]},{"given":"Amer","family":"Dababneh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Amjed","family":"Zraiqat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Shaher","family":"Momani","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates"},{"name":"Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan"}]},{"given":"Adel","family":"Ouannas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6944-1689","authenticated-orcid":false,"given":"Amel","family":"Hioual","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1364\/AO.511890","article-title":"Adaptive phase retrieval algorithm for local highlight area based on a piecewise sine function","volume":"63","author":"Zou","year":"2024","journal-title":"Appl. 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