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Global synchronization criterion and adaptive synchronization for new chaotic system

Author

Listed:
  • Elabbasy, E.M.
  • Agiza, H.N.
  • El-Dessoky, M.M.

Abstract

This paper proposes two schemes of synchronization of two four-scorll chaotic attractor, a simple global synchronization and adaptive synchronization in the presence of unknown system parameters. Based on Lyapunov stability theory and matrix measure, a simple generic criterion is derived for global synchronization of four-scorll chaotic attractor system with a unidirectional linear error feedback coupling. This methods are applicable to a large class of chaotic systems where only a few algebraic inequalities are involved. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization method.

Suggested Citation

  • Elabbasy, E.M. & Agiza, H.N. & El-Dessoky, M.M., 2005. "Global synchronization criterion and adaptive synchronization for new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1299-1309.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:4:p:1299-1309
    DOI: 10.1016/j.chaos.2004.06.068
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    Cited by:

    1. Li, Guo-Hui & Xiong, Chu-An & Sun, Xiao-Nan, 2007. "Projective synchronization based on suitable separation," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 561-565.
    2. Wu, Xiaofeng & Cai, Jianping & Wang, Muhong, 2008. "Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 121-128.
    3. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
    4. Yu, Yongguang, 2007. "The synchronization for time-delay of linearly bidirectional coupled chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1197-1203.
    5. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Huang, De-Xian & Tang, Fang, 2007. "Control and synchronization of chaotic systems by differential evolution algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 412-419.
    6. Chen, Heng-Hui, 2009. "Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 466-473.
    7. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    8. Zhang, Fuchen & Shu, Yonglu & Yang, Hongliang & Li, Xiaowu, 2011. "Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 137-144.
    9. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Tang, Fang & Huang, De-Xian, 2006. "Directing orbits of chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 454-461.
    10. Li, Damei & Wang, Pei & Lu, Jun-an, 2009. "Some synchronization strategies for a four-scroll chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2553-2559.
    11. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    12. Li, Guo-Hui, 2009. "Generalized synchronization of chaos based on suitable separation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2056-2062.
    13. He, Qie & Wang, Ling & Liu, Bo, 2007. "Parameter estimation for chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 654-661.
    14. Peng, Bo & Liu, Bo & Zhang, Fu-Yi & Wang, Ling, 2009. "Differential evolution algorithm-based parameter estimation for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2110-2118.
    15. Sun, Yeong-Jeu, 2009. "Exponential synchronization between two classes of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2363-2368.

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