{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T15:37:12Z","timestamp":1776008232475,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T00:00:00Z","timestamp":1606435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0\u20131 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.<\/jats:p>","DOI":"10.3390\/e22121344","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T09:16:49Z","timestamp":1606468609000},"page":"1344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control"],"prefix":"10.3390","volume":"22","author":[{"given":"A. Othman","family":"Almatroud","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amina-Aicha","family":"Khennaoui","sequence":"additional","affiliation":[{"name":"Laboratory of Dynamical Systems and Control, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Grassi","sequence":"additional","affiliation":[{"name":"Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Mossa","family":"Al-sawalha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Ha\u2019il, Ha\u2019il 81451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahlem","family":"Gasri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Larbi Tebessi, Tebessa 12002, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic nonperiodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. 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