Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

doi:10.1088/1674-1056/ab820d

中国物理B ›› 2020, Vol. 29 ›› Issue (5): 50504-050504.doi: 10.1088/1674-1056/ab820d

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali

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

收稿日期:2020-01-26 修回日期:2020-03-12 出版日期:2020-05-05 发布日期:2020-05-05
通讯作者: Viet-Thanh Pham E-mail:phamvietthanh@tdtu.edu.vn
基金资助:
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.

Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

Adel Ouannas^1,2, Amina Aicha Khennaoui³, Shaher Momani^2,4, 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

Received:2020-01-26 Revised:2020-03-12 Online:2020-05-05 Published:2020-05-05
Contact: Viet-Thanh Pham E-mail:phamvietthanh@tdtu.edu.vn
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: discrete chaos, discrete fractional calculus, hidden attractor

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.

Key words: discrete chaos, discrete fractional calculus, hidden attractor

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Ac (Low-dimensional chaos) 05.45.Gg (Control of chaos, applications of chaos) 05.30.Pr (Fractional statistics systems)

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[J]. 中国物理B, 2020, 29(5): 50504-050504.

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Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

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