The global attractive sets and synchronization of a fractional-order complex dynamical system

Minghung Lin; Yiyou Hou; Maryam A. Al-Towailb; Hassan Saberi-Nik; Minghung Lin; Yiyou Hou; Maryam A. Al-Towailb; Hassan Saberi-Nik

doi:10.3934/math.2023179

AIMS Mathematics

2023, Volume 8, Issue 2: 3523-3541. doi: 10.3934/math.2023179

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Research article

The global attractive sets and synchronization of a fractional-order complex dynamical system

1.
Department of Electrical Engineering, Cheng Shiu University, Kaohsiung 83301, Taiwan
2.
Department of Intelligent Commerce, National Kaohsiung University of Science and Technology, Kaohsiung 824004, Taiwan
3.
Department of Computer Science and Engineering, College of Applied Studies and Community Service, King Saud University, Riyadh, KSA
4.
Department of Mathematics and Statistics, University of Neyshabur, Neyshabur, Iran

Received: 07 October 2022 Revised: 07 November 2022 Accepted: 09 November 2022 Published: 22 November 2022
MSC : 34A08, 34C28, 34D06, 34H10

This paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boundedness. The global attractive sets (GASs) and positive invariant sets (PISs) for the fractional chaotic complex system are derived based on the Lyapunov stability theory and the Mittag-Leffler function. Furthermore, an effective control strategy is also designed to achieve the global synchronization of two fractional chaotic systems. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis.
- Mittag-Leffler GAS,
- fractional-order complex system,
- Lyapunov stability theory,
- globally synchronization
Citation: Minghung Lin, Yiyou Hou, Maryam A. Al-Towailb, Hassan Saberi-Nik. The global attractive sets and synchronization of a fractional-order complex dynamical system[J]. AIMS Mathematics, 2023, 8(2): 3523-3541. doi: 10.3934/math.2023179

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Abstract

This paper presents a chaotic complex system with a fractional-order derivative. The dynamical behaviors of the proposed system such as phase portraits, bifurcation diagrams, and the Lyapunov exponents are investigated. The main contribution of this effort is an implementation of Mittag-Leffler boundedness. The global attractive sets (GASs) and positive invariant sets (PISs) for the fractional chaotic complex system are derived based on the Lyapunov stability theory and the Mittag-Leffler function. Furthermore, an effective control strategy is also designed to achieve the global synchronization of two fractional chaotic systems. The corresponding boundedness is numerically verified to show the effectiveness of the theoretical analysis.

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