*Article* **On Two-Dimensional Fractional Chaotic Maps with Symmetries**

**Fatima Hadjabi 1,\*, Adel Ouannas 2, Nabil Shawagfeh 1, Amina-Aicha Khennaoui 3 and Giuseppe Grassi 4**

1 Department of Mathematics, The University of Jordan, Amman 11942, Jordan; shawagnt@ju.edu.jo

2 Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa 12002, Algeria; ouannas.adel@univ-tebessa.dz


Received: 8 March 2020; Accepted: 8 April 2020; Published: 6 May 2020

**Abstract:** 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.

**Keywords:** discrete fractional systems; chaotic systems; closed curve fixed points; symmetry; 0–1 test; bifurcation diagram; Lyapunov exponents
