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Synchronization and control of hyperchaotic complex Lorenz system

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  • Mahmoud, Gamal M.
  • Mahmoud, Emad E.

Abstract

The aim of this paper is to investigate the phenomenon of projective synchronization (PS) and modified projective synchronization (MPS) of hyperchaotic attractors of hyperchaotic complex Lorenz system which has been introduced recently in our work. The control problem of these attractors is also studied. Our system is a 6-dimensional continuous real autonomous hyperchaotic system. The active control method based on Lyapunov function is used to study PS and MPS of this system. The problem of hyperchaos control is treated by adding the complex periodic forcing. The control performances are verified by calculating Lyapunov exponents. Numerical simulations are implemented to verify the results of these investigations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:12:p:2286-2296
    DOI: 10.1016/j.matcom.2010.03.012
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    References listed on IDEAS

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    1. Li, Guo-Hui, 2007. "Generalized projective synchronization between Lorenz system and Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1454-1458.
    2. GAMAL M. MAHMOUD & M. A. Al-KASHIF & SHABAN A. ALY, 2007. "Basic Properties And Chaotic Synchronization Of Complex Lorenz System," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 253-265.
    3. Gamal M. Mahmoud & Mansour E. Ahmed & Emad E. Mahmoud, 2008. "Analysis Of Hyperchaotic Complex Lorenz Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(10), pages 1477-1494.
    4. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
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    Cited by:

    1. Mahmoud, Emad E. & AL-Harthi, Bushra H., 2020. "A hyperchaotic detuned laser model with an infinite number of equilibria existing on a plane and its modified complex phase synchronization with time lag," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Li Xiong & Zhenlai Liu & Xinguo Zhang, 2017. "Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System," Complexity, Hindawi, vol. 2017, pages 1-23, November.
    3. 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.
    4. Nguyen, Le Hoa & Hong, Keum-Shik, 2011. "Synchronization of coupled chaotic FitzHugh–Nagumo neurons via Lyapunov functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 590-603.
    5. Chen, Yuming & Yang, Qigui, 2015. "A new Lorenz-type hyperchaotic system with a curve of equilibria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 40-55.
    6. Cuimei Jiang & Shutang Liu, 2017. "Synchronization and Antisynchronization of -Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection," Complexity, Hindawi, vol. 2017, pages 1-15, January.

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