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Chaos synchronization of the fractional Lü system

Author

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  • Deng, W.H.
  • Li, C.P.

Abstract

Chaos synchronization of the fractional Lü system is theoretically and numerically studied by two methods. The suitable conditions for achieving synchronization of this fractional differential system are derived by using the Laplace transform theory. Numerical simulations coincide with the theoretical analysis.

Suggested Citation

  • Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
    • Handle: RePEc:eee:phsmap:v:353:y:2005:i:c:p:61-72
    DOI: 10.1016/j.physa.2005.01.021
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    Citations

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    Cited by:

    1. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    2. Deshpande, Amey S. & Daftardar-Gejji, Varsha, 2017. "On disappearance of chaos in fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 119-126.
    3. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    4. Li, Changpin & Yan, Jianping, 2007. "The synchronization of three fractional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 751-757.
    5. A.G., Soriano–Sánchez & C., Posadas–Castillo & M.A., Platas–Garza & A., Arellano–Delgado, 2018. "Synchronization and FPGA realization of complex networks with fractional–order Liu chaotic oscillators," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 250-262.
    6. Taher S. Hassan & Ismoil Odinaev & Rasool Shah & Wajaree Weera, 2022. "Dynamical Analysis of Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    7. Zhou, Shuang & Wang, Xingyuan, 2021. "Simple estimation method for the largest Lyapunov exponent of continuous fractional-order differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    8. Shi, Tian & Qin, Yi & Yang, Qi & Ma, Zhongjun & Li, Kezan, 2023. "Synchronization of directed uniform hypergraphs via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    9. Petráš, Ivo, 2008. "A note on the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 140-147.
    10. Abdelfattah Mustafa & Reda S. Salama & Mokhtar Mohamed, 2023. "Analysis of Generalized Nonlinear Quadrature for Novel Fractional-Order Chaotic Systems Using Sinc Shape Function," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    11. Zhang, Weiwei & Zhou, Shangbo & Li, Hua & Zhu, Hao, 2009. "Chaos in a fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1684-1691.
    12. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    13. Huang, Chengdai & Cao, Jinde, 2017. "Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 262-275.
    14. Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    15. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    16. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    17. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    18. Chen, Liping & Pan, Wei & Wang, Kunpeng & Wu, Ranchao & Machado, J. A. Tenreiro & Lopes, António M., 2017. "Generation of a family of fractional order hyper-chaotic multi-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 244-255.
    19. Cruz-Victoria, Juan C. & Martínez-Guerra, Rafael & Pérez-Pinacho, Claudia A. & Gómez-Cortés, Gian Carlo, 2015. "Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 224-231.
    20. Liang Chen & Chengdai Huang & Haidong Liu & Yonghui Xia, 2019. "Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    21. Zhu, Hao & Zhou, Shangbo & Zhang, Jun, 2009. "Chaos and synchronization of the fractional-order Chua’s system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1595-1603.
    22. Zhu, Hao & Zhou, Shangbo & He, Zhongshi, 2009. "Chaos synchronization of the fractional-order Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2733-2740.
    23. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    24. Ouannas, Adel & Khennaoui, Amina-Aicha & Odibat, Zaid & Pham, Viet-Thanh & Grassi, Giuseppe, 2019. "On the dynamics, control and synchronization of fractional-order Ikeda map," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 108-115.

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