{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T01:05:13Z","timestamp":1767834313562,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T00:00:00Z","timestamp":1730332800000},"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>According to recent research, discrete-time fractional-order models have greater potential to investigate behaviors, and chaotic maps with fractional derivative values exhibit rich dynamics. This manuscript studies the dynamics of a new fractional chaotic map-based three functions. We analyze the behaviors in commensurate and incommensurate orders, revealing their impact on dynamics. Through the maximum Lyapunov exponent (LEmax), phase portraits, and bifurcation charts. In addition, we assess the complexity and confirm the chaotic features in the map using the approximation entropy ApEn and C0 complexity. Studies show that the commensurate and incommensurate derivative values influence the fractional chaotic map-based three functions, which exhibit a variety of dynamical behaviors, such as hidden attractors, asymmetry, and symmetry. Moreover, the new system\u2019s stabilizing employing a 3D nonlinear controller is introduced. Finally, our study validates the research results using the simulation MATLAB R2024a.<\/jats:p>","DOI":"10.3390\/sym16111447","type":"journal-article","created":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T12:31:32Z","timestamp":1730377892000},"page":"1447","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Asymmetry and Symmetry in New Three-Dimensional Chaotic Map with Commensurate and Incommensurate Fractional Orders"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7644-9937","authenticated-orcid":false,"given":"Hussein","family":"Al-Taani","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan"}]},{"given":"Ma\u2019mon","family":"Abu Hammad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan"}]},{"given":"Mohammad","family":"Abudayah","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Information Technology, German Jordanian University, Amman 11180, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3734-3679","authenticated-orcid":false,"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":"Adel","family":"Ouannas","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":[[2024,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/1742-6596\/1255\/1\/012023","article-title":"Analysis of Backpropagation Method with Sigmoid Bipolar and Linear Function in Prediction of Population Growth","volume":"1255","author":"Siregar","year":"2019","journal-title":"J. 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