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Impulsive Control and Synchronization of Complex Lorenz Systems

Author

Listed:
  • Shaban Aly
  • Ali Al-Qahtani
  • Houari B. Khenous
  • Gamal M. Mahmoud

Abstract

In this paper, we continue our investigations on control and synchronization of the complex Lorenz systems by investigating impulsive control and synchronization. Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems; For example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics and so forth do exhibit impulsive effects. Some new and more comprehensive criteria for global exponential stability and asymptotical stability of impulsively controlled complex Lorenz systems are established with varying impulsive intervals. The effectiveness of the proposed technique is verified through numerical simulations.

Suggested Citation

  • Shaban Aly & Ali Al-Qahtani & Houari B. Khenous & Gamal M. Mahmoud, 2014. "Impulsive Control and Synchronization of Complex Lorenz Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:932327
    DOI: 10.1155/2014/932327
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    References listed on IDEAS

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    1. Ian Stewart, 2000. "The Lorenz attractor exists," Nature, Nature, vol. 406(6799), pages 948-949, August.
    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. 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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