A novel fractional-order hyperchaotic complex system and its synchronization

doi:10.1088/1674-1056/acc0f6

中国物理B ›› 2023, Vol. 32 ›› Issue (6): 60501-060501.doi: 10.1088/1674-1056/acc0f6

A novel fractional-order hyperchaotic complex system and its synchronization

Mengxin Jin(金孟鑫), Kehui Sun(孙克辉)^†, and Shaobo He(贺少波)

School of Physics and Electronics, Central South University, Changsha 410083, China

收稿日期:2022-12-08 修回日期:2023-02-21 接受日期:2023-03-03 出版日期:2023-05-17 发布日期:2023-06-07
通讯作者: Kehui Sun E-mail:kehui@csu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 62071496, 61901530, and 62061008) and the Innovation Project of Graduate of Central South University (Grant No. 2022zzts0681).

A novel fractional-order hyperchaotic complex system and its synchronization

Mengxin Jin(金孟鑫), Kehui Sun(孙克辉)^†, and Shaobo He(贺少波)

School of Physics and Electronics, Central South University, Changsha 410083, China

Received:2022-12-08 Revised:2023-02-21 Accepted:2023-03-03 Online:2023-05-17 Published:2023-06-07
Contact: Kehui Sun E-mail:kehui@csu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 62071496, 61901530, and 62061008) and the Innovation Project of Graduate of Central South University (Grant No. 2022zzts0681).

摘要/Abstract

摘要： A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.

关键词: fractional calculus, complex hyperchaos, simplified Lorenz system, complex generalized projective synchronization

Abstract: A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.

Key words: fractional calculus, complex hyperchaos, simplified Lorenz system, complex generalized projective synchronization

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Pq (Numerical simulations of chaotic systems) 05.45.Xt (Synchronization; coupled oscillators)

Mengxin Jin(金孟鑫), Kehui Sun(孙克辉), and Shaobo He(贺少波). A novel fractional-order hyperchaotic complex system and its synchronization[J]. 中国物理B, 2023, 32(6): 60501-060501.

Mengxin Jin(金孟鑫), Kehui Sun(孙克辉), and Shaobo He(贺少波). A novel fractional-order hyperchaotic complex system and its synchronization[J]. Chin. Phys. B, 2023, 32(6): 60501-060501.

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A novel fractional-order hyperchaotic complex system and its synchronization

A novel fractional-order hyperchaotic complex system and its synchronization

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