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Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters

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  • Zhou, Xiaobing
  • Wu, Yue
  • Li, Yi
  • Xue, Hongquan

Abstract

This paper addresses problems of control and synchronization for a new modified hyperchaotic Lü system with uncertain parameters. This new modified uncertain hyperchaotic Lü system is stabilized to its unique unstable equilibrium by using adaptive control. Furthermore, an adaptive control law and a parameter estimation update law are derived to synchronize two identical modified hyperchaotic Lü systems with uncertain parameters. Numerical examples are proposed to demonstrate and verify the theoretical analysis.

Suggested Citation

  • Zhou, Xiaobing & Wu, Yue & Li, Yi & Xue, Hongquan, 2009. "Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2477-2483.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2477-2483
    DOI: 10.1016/j.chaos.2007.07.017
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    References listed on IDEAS

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    1. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    2. Zhang, Hao & Ma, Xi-kui & Li, Ming & Zou, Jian-long, 2005. "Controlling and tracking hyperchaotic Rössler system via active backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 353-361.
    3. Wang, Guangyi & Zhang, Xun & Zheng, Yan & Li, Yuxia, 2006. "A new modified hyperchaotic Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 260-272.
    4. Nikolov, Svetoslav & Clodong, Sébastien, 2006. "Hyperchaos–chaos–hyperchaos transition in modified Rössler systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 252-263.
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    Cited by:

    1. Wang, Huanqing & Ai, Yingdong, 2022. "Adaptive fixed-time control and synchronization for hyperchaotic Lü systems," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    2. Lorı´a, Antonio, 2011. "Cascades-based synchronization of hyperchaotic systems: Application to Chen systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 702-709.

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