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Shape synchronization control for three-dimensional chaotic systems

Author

Listed:
  • Huang, Yuanyuan
  • Wang, Yinhe
  • Chen, Haoguang
  • Zhang, Siying

Abstract

This paper aims to the three-dimensional continuous chaotic system and shape of the chaotic attractor by utilizing the basic theory of plane curves in classical differential geometry, the continuous controller is synthesized for the master–slave synchronization in shape. This means that the slave system can possess the same shape of state trajectory with the master system via the continuous controller. The continuous controller is composed of three sub-controllers, which respectively correspond to the master–slave synchronization in shape for the three projective curves of the chaotic attractor onto the three coordinate planes. Moreover, the proposed shape synchronization technique as well as application of control scheme to secure communication is also demonstrated in this paper, where numerical simulation results show the proposed control method works well.

Suggested Citation

  • Huang, Yuanyuan & Wang, Yinhe & Chen, Haoguang & Zhang, Siying, 2016. "Shape synchronization control for three-dimensional chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 136-145.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:136-145
    DOI: 10.1016/j.chaos.2016.03.025
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    References listed on IDEAS

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    1. Chang, Jen-Fuh & Hung, Meei-Ling & Yang, Yi-Sung & Liao, Teh-Lu & Yan, Jun-Juh, 2008. "Controlling chaos of the family of Rössler systems using sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 609-622.
    2. Martínez-Guerra, Rafael & Mata-Machuca, Juan L., 2014. "Generalized synchronization via the differential primitive element," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 848-857.
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    Cited by:

    1. Huang, Yuanyuan & Huang, Huijun & Huang, Yunchang & Wang, Yinhe & Yu, Fei & Yu, Beier & Liu, Chenghao, 2024. "Asymptotic shape synchronization in three-dimensional chaotic systems and its application in color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Fei Yu & Li Liu & Binyong He & Yuanyuan Huang & Changqiong Shi & Shuo Cai & Yun Song & Sichun Du & Qiuzhen Wan, 2019. "Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four-Wing Memristive System, Active Control Synchronization, and Secure Communication Application," Complexity, Hindawi, vol. 2019, pages 1-18, November.

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