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Generalized projective synchronization between Lorenz system and Chen’s system

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  • Li, Guo-Hui

Abstract

On the basis of active backstepping design, this paper presents the generalized projective synchronization between two different chaotic systems: Lorenz system and Chen’s system. The proposed method combines backstepping methods and active control without having to calculate the Lyapunov exponents and the eigenvalues of the Jacobian matrix, which makes it simple and convenient. Numerical simulations show that this method works very well.

Suggested Citation

  • Li, Guo-Hui, 2007. "Generalized projective synchronization between Lorenz system and Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1454-1458.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1454-1458
    DOI: 10.1016/j.chaos.2005.11.073
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    References listed on IDEAS

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    1. 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.
    2. Yan, Jianping & Li, Changpin, 2005. "Generalized projective synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1119-1124.
    3. Wen, Guilin & Xu, Daolin, 2005. "Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 71-77.
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    Cited by:

    1. Runzi, Luo & Zhengmin, Wei, 2009. "Adaptive function projective synchronization of unified chaotic systems with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1266-1272.
    2. Xu, Yuhua & Zhou, Wuneng & Fang, Jian-an, 2009. "Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lü chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1305-1315.
    3. Remus-Daniel Ene & Camelia Pop & Camelia Petrişor, 2020. "Systematic Review of Geometrical Approaches and Analytical Integration for Chen’s System," Mathematics, MDPI, vol. 8(9), pages 1-14, September.
    4. Mahmoud, Emad E., 2013. "Modified projective phase synchronization of chaotic complex nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 69-85.
    5. Du, Hongyue & Zeng, Qingshuang & Wang, Changhong, 2009. "Modified function projective synchronization of chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2399-2404.
    6. Sun, Junwei & Guo, Jinchao & Yang, Cunxiang & Zheng, Anping & Zhang, Xuncai, 2015. "Adaptive generalized hybrid function projective dislocated synchronization of new four-dimensional uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 304-314.
    7. Mahmoud, Gamal M. & Mahmoud, Emad E., 2010. "Synchronization and control of hyperchaotic complex Lorenz system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2286-2296.

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