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Chaos synchronization of a new chaotic system via nonlinear control

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  • Zhang, Qunjiao
  • Lu, Jun-an

Abstract

This paper investigates chaos synchronization of a new chaotic system [Lü J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507–37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons & Fractals 2005;25:579–84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method.

Suggested Citation

  • Zhang, Qunjiao & Lu, Jun-an, 2008. "Chaos synchronization of a new chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 175-179.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:175-179
    DOI: 10.1016/j.chaos.2006.08.036
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    References listed on IDEAS

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    1. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    2. Zhou, Jin & Lu, Jun-an & Wu, Xiaoqun, 2007. "Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 230-235.
    3. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
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    2. Lam, H.K., 2009. "Output-feedback synchronization of chaotic systems based on sum-of-squares approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2624-2629.
    3. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "On anti-synchronization of chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 170-179.
    4. J. Humberto Pérez-Cruz, 2018. "Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control," Complexity, Hindawi, vol. 2018, pages 1-19, December.
    5. J. Humberto Pérez-Cruz & Pedro A. Tamayo-Meza & Maricela Figueroa & Ramón Silva-Ortigoza & Mario Ponce-Silva & R. Rivera-Blas & Mario Aldape-Pérez, 2019. "Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-10, July.
    6. 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.
    7. Santos Coelho, Leandro dos & de Andrade Bernert, Diego Luis, 2009. "An improved harmony search algorithm for synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2526-2532.
    8. 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.
    9. Farivar, Faezeh & Aliyari Shoorehdeli, Mahdi & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2012. "Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 80-97.
    10. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
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