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On chaos synchronization of a complex two coupled dynamos system

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  • Mahmoud, Gamal M.
  • Aly, Shaban A.
  • Farghaly, Ahmed A.

Abstract

The main objective of this work is to investigate the chaotic behavior and chaos synchronization of a complex two coupled dynamos system subject to different initial conditions. This system exhibits a chaotic attractor which is found numerically. The global synchronization and active control techniques are used in this investigation. The feedback gain matrix and Lyapunov function are calculated and used to show that the linear error dynamical system is asymptotically stable. The analytical results are tested numerically and excellent agreement is found.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:178-187
    DOI: 10.1016/j.chaos.2006.01.036
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    1. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    2. Lei, Youming & Xu, Wei & Shen, Jianwei & Fang, Tong, 2006. "Global synchronization of two parametrically excited systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 428-436.
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    4. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    5. H. N. Agiza, 2004. "Chaos Synchronization Of Two Coupled Dynamos Systems With Unknown System Parameters," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 873-883.
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    Cited by:

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    2. Zhou, Qian & Chen, Zeng-qiang & Yuan, Zhu-zhi, 2009. "Blowout bifurcation and chaos–hyperchaos transition in five-dimensional continuous autonomous systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1012-1020.
    3. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    4. Shang, Li-Jen & Shyu, Kuo-Kai, 2009. "A method for extracting chaotic signal from noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1120-1125.
    5. 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.

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