{"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":1776008232988,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,5,27]],"date-time":"2020-05-27T00:00:00Z","timestamp":1590537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Ha\u2019il- Saudi Arabia","award":["RG-191307"],"award-info":[{"award-number":["RG-191307"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.<\/jats:p>","DOI":"10.3390\/sym12060879","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:16:27Z","timestamp":1590718587000},"page":"879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Bifurcations, Hidden Chaos and Control in Fractional Maps"],"prefix":"10.3390","volume":"12","author":[{"given":"Adel","family":"Ouannas","sequence":"first","affiliation":[{"name":"Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Othman Abdullah","family":"Almatroud","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, University of Hail, Hail 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":"Mohammad Mossa","family":"Alsawalha","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, University of Hail, Hail 81451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, 06530 Ankara, Turkey"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Institute of Space Sciences, 76900 Magurele-Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Van Van","family":"Huynh","sequence":"additional","affiliation":[{"name":"Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viet-Thanh","family":"Pham","sequence":"additional","affiliation":[{"name":"Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,27]]},"reference":[{"key":"ref_1","unstructured":"H\u00e9non, M. 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