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Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter

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  • Park, Ju H.

Abstract

An adaptive modified projective synchronization (AMPS) is proposed to acquire a general kind of proportional relationship between the drive and response systems. Based on the Lyapunov stability theory, a nonlinear control scheme for the synchronization has been presented. The control performances are verified by numerical simulations.

Suggested Citation

  • Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1552-1559
    DOI: 10.1016/j.chaos.2006.04.047
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "Chaos synchronization between two different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 549-554.
    2. Park, Ju H., 2005. "Stability criterion for synchronization of linearly coupled unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1319-1325.
    3. Wang, Yan-Wu & Guan, Zhi-Hong, 2006. "Generalized synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 97-101.
    4. Park, Ju H., 2005. "Adaptive synchronization of hyperchaotic Chen system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 959-964.
    5. Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
    6. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    7. Park, Ju H., 2005. "GCS of a class of chaotic dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1429-1435.
    8. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    9. Park, Ju H., 2005. "Adaptive synchronization of Rossler system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 333-338.
    10. Park, Ju H., 2006. "Chaos synchronization of nonlinear Bloch equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 357-361.
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    Citations

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    Cited by:

    1. Dadras, Sara & Momeni, Hamid Reza, 2009. "Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3140-3146.
    2. 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.
    3. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.
    4. Jin, Yunguo & Zhong, Shouming, 2015. "Function projective synchronization in complex networks with switching topology and stochastic effects," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 730-740.
    5. Qin, Xiaoli & Wang, Cong & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Ye, Lu, 2018. "Finite-time modified projective synchronization of memristor-based neural network with multi-links and leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 302-315.
    6. Gu, Yajuan & Wang, Hu & Yu, Yongguang, 2020. "Synchronization for fractional-order discrete-time neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. Du, Hongyue & Zeng, Qingshuang & Wang, Changhong, 2009. "Modified function projective synchronization of chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2399-2404.
    8. Shen, Liqun & Liu, Wanyu & Ma, Jianwei, 2009. "Robust function projective synchronization of a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1292-1296.
    9. Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    10. Yao, Qijia & Alsaade, Fawaz W. & Al-zahrani, Mohammed S. & Jahanshahi, Hadi, 2023. "Fixed-time neural control for output-constrained synchronization of second-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Gao, Shigen & Wang, Yubing & Dong, Hairong & Ning, Bin & Wang, Hongwei, 2017. "Controlling uncertain Genesio–Tesi chaotic system using adaptive dynamic surface and nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 180-188.

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