{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:23:26Z","timestamp":1771673006235,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T00:00:00Z","timestamp":1614124800000},"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 investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.<\/jats:p>","DOI":"10.3390\/e23030261","type":"journal-article","created":{"date-parts":[[2021,2,24]],"date-time":"2021-02-24T20:53:21Z","timestamp":1614200001000},"page":"261","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems"],"prefix":"10.3390","volume":"23","author":[{"given":"Nadjette","family":"Debbouche","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Larbi Ben M\u2019hidi, Oum El Bouaghi 04000, Algeria"}]},{"given":"Shaher","family":"Momani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan"},{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates"}]},{"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"},{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates"}]},{"given":"\u2019Mohd Taib\u2019","family":"Shatnawi","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Al-Huson University College, Al-Balqa Applied University, Irbid 21510, Jordan"}]},{"given":"Giuseppe","family":"Grassi","sequence":"additional","affiliation":[{"name":"Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy"}]},{"given":"Zohir","family":"Dibi","sequence":"additional","affiliation":[{"name":"Department of Electronics, University of Batna 2, Batna 05000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8443-8848","authenticated-orcid":false,"given":"Iqbal M.","family":"Batiha","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates"},{"name":"Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.chaos.2017.10.032","article-title":"Generation of a family of fractional order hyper-chaotic multi-scroll attractors","volume":"105","author":"Chen","year":"2017","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"034101","DOI":"10.1103\/PhysRevLett.91.034101","article-title":"Chaotic dynamics of the fractional lorenz system","volume":"91","author":"Grigorenko","year":"2003","journal-title":"Phys. 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