{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:42:45Z","timestamp":1774579365893,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"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 manuscript presents new fractional difference equations; we investigate their behaviors in-depth in commensurate and incommensurate order cases. The work exploits a range of numerical approaches involving bifurcation, the Maximum Lyapunov exponent (LEm), and the visualization of phase portraits and also uses the C0 complexity algorithm and the approximation entropy ApEn to evaluate the intricacy and verify the chaotic features. Thus, the outcomes indicate that the suggested fractional-order map can display a variety of hidden attractors and symmetry breaking if it has no fixed points. Additionally, nonlinear controllers are offered to stabilize the fractional difference equations. As a result, the study highlights how the map\u2019s sensitivity to the fractional derivative parameters produces different dynamics. Lastly, simulations using MATLAB R2024b are run to validate the results.<\/jats:p>","DOI":"10.3390\/sym17030352","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T06:15:33Z","timestamp":1740550533000},"page":"352","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Symmetry Breaking in Fractional Difference Chaotic Equations and Their Control"],"prefix":"10.3390","volume":"17","author":[{"given":"Louiza","family":"Diabi","sequence":"first","affiliation":[{"name":"Laboratory of Dynamical Systems and Control, Department of Mathematics and Computer Science, University of Oum El Bouaghi, Oum El Bouaghi 04000, Algeria"}]},{"given":"Adel","family":"Ouannas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]},{"given":"Giuseppe","family":"Grassi","sequence":"additional","affiliation":[{"name":"Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6326-8456","authenticated-orcid":false,"given":"Shaher","family":"Momani","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics Research Center, Ajman University, Ajman 346, United Arab Emirates"},{"name":"Department of Mathematics, The University of Jordan, Amman 11942, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hamadneh, T., Hioual, A., Alsayyed, O., Al-Khassawneh, Y.A., Al-Husban, A., and Ouannas, A. 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