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Chin. Phys. B, 2020, Vol. 29(5): 050504    DOI: 10.1088/1674-1056/ab820d
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Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

Adel Ouannas1,2, Amina Aicha Khennaoui3, Shaher Momani2,4, Viet-Thanh Pham5, Reyad El-Khazali6
1 Laboratory of Mathematics, Informatics and Systems(LAMIS), University of Laarbi Tebessi, Tebessa, 12002, Algeria;
2 College of Humanities and Sciences, Ajman University, Ajman, UAE;
3 Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El Bouaghi, Algeria;
4 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan;
5 Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
6 ECCE Department, Khalifa University, Abu-Dhabi 127788, United Arab Emirates
Abstract  This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator. This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium. Through phase portrait, bifurcation diagrams, and largest Lyapunov exponents, it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors. Also, different tests are used to confirm the existence of chaos, such as 0-1 test and C0 complexity. In addition, the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique. Furthermore, based on the fractional linearization method, a one-dimensional controller to stabilize the new system is proposed. Numerical results are presented to validate the findings of the paper.
Keywords:  discrete chaos      discrete fractional calculus      hidden attractor  
Received:  26 January 2020      Revised:  12 March 2020      Published:  05 May 2020
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Ac (Low-dimensional chaos)  
  05.45.Gg (Control of chaos, applications of chaos)  
  05.30.Pr (Fractional statistics systems)  
Fund: The author Adel Ouannas was supported by the Directorate General for Scientific Research and Technological Development of Algeria. The author Shaher Momani was supported by Ajman University in UAE.
Corresponding Authors:  Viet-Thanh Pham     E-mail:  phamvietthanh@tdtu.edu.vn

Cite this article: 

Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control 2020 Chin. Phys. B 29 050504

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