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Article

On Two-Dimensional Fractional Chaotic Maps with Symmetries

1
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2
Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria
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Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 4003, Algeria
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Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 756; https://doi.org/10.3390/sym12050756
Received: 8 March 2020 / Revised: 5 April 2020 / Accepted: 8 April 2020 / Published: 6 May 2020
(This article belongs to the Special Issue Bifurcation and Chaos in Fractional-Order Systems)
In this paper, we propose two new two-dimensional chaotic maps with closed curve fixed points. The chaotic behavior of the two maps is analyzed by the 0–1 test, and explored numerically using Lyapunov exponents and bifurcation diagrams. It has been found that chaos exists in both fractional maps. In addition, result shows that the proposed fractional maps shows the property of coexisting attractors. View Full-Text
Keywords: discrete fractional systems; chaotic systems; closed curve fixed points; symmetry; 0–1 test; bifurcation diagram; Lyapunov exponents discrete fractional systems; chaotic systems; closed curve fixed points; symmetry; 0–1 test; bifurcation diagram; Lyapunov exponents
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MDPI and ACS Style

Hadjabi, F.; Ouannas, A.; Shawagfeh, N.; Khennaoui, A.-A.; Grassi, G. On Two-Dimensional Fractional Chaotic Maps with Symmetries. Symmetry 2020, 12, 756. https://doi.org/10.3390/sym12050756

AMA Style

Hadjabi F, Ouannas A, Shawagfeh N, Khennaoui A-A, Grassi G. On Two-Dimensional Fractional Chaotic Maps with Symmetries. Symmetry. 2020; 12(5):756. https://doi.org/10.3390/sym12050756

Chicago/Turabian Style

Hadjabi, Fatima, Adel Ouannas, Nabil Shawagfeh, Amina-Aicha Khennaoui, and Giuseppe Grassi. 2020. "On Two-Dimensional Fractional Chaotic Maps with Symmetries" Symmetry 12, no. 5: 756. https://doi.org/10.3390/sym12050756

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