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Generalized projective synchronization of two chaotic systems by using active control

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  • Li, Guo-Hui

Abstract

In this paper, an active control method is proposed to projective-synchronize two chaotic systems by constructing the response system no matter whether they are identical or not. The proposed technique is applied to achieve generalized projective synchronization for the Lorenz and Chen’s systems, where all state variables are in a proportional way. This property allows us to arbitrarily direct the scaling factor onto a desired value. Feasibility of the proposed control scheme is illustrated through the numerical examples.

Suggested Citation

  • Li, Guo-Hui, 2006. "Generalized projective synchronization of two chaotic systems by using active control," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 77-82.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:1:p:77-82
    DOI: 10.1016/j.chaos.2005.08.130
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    References listed on IDEAS

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    1. Yan, Jianping & Li, Changpin, 2005. "Generalized projective synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1119-1124.
    2. 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. Chang, Wei-Der, 2009. "PID control for chaotic synchronization using particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 910-917.
    2. Hu, Manfeng & Yang, Yongqing & Xu, Zhenyuan & Guo, Liuxiao, 2008. "Hybrid projective synchronization in a chaotic complex nonlinear system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 449-457.
    3. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2019. "Difference synchronization among three chaotic systems with exponential term and its chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 36-51.
    4. Elabbasy, E.M. & El-Dessoky, M.M., 2008. "Synchronization of van der Pol oscillator and Chen chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1425-1435.
    5. Huang, Yuehua & Wang, Yan-Wu & Xiao, Jiang-Wen, 2009. "Generalized lag-synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 766-770.
    6. Li, Jiayan & Cao, Jinde & Liu, Heng, 2022. "State observer-based fuzzy echo state network sliding mode control for uncertain strict-feedback chaotic systems without backstepping," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Grassi, Giuseppe, 2009. "Observer-based hyperchaos synchronization in cascaded discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1029-1039.
    8. Sharma, B.B. & Kar, I.N., 2011. "Stabilization and tracking controller for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 902-913.
    9. Sun, Yeong-Jeu, 2009. "Exponential synchronization between two classes of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2363-2368.
    10. El-Dessoky, M.M., 2009. "Synchronization and anti-synchronization of a hyperchaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1790-1797.
    11. Liu, Bin & Zhou, Yiming & Jiang, Min & Zhang, Zengke, 2009. "Synchronizing chaotic systems using control based on tridiagonal structure," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2274-2281.

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