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Stability and Stabilizing of Fractional Complex Lorenz Systems

Author

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  • Rabha W. Ibrahim

Abstract

We study the stability and stabilization of complex fractional Lorenz system. The fractional calculus are taken in sense of the Caputo derivatives. The technique is based on stability theory of fractional‐order systems. Numerical solutions are imposed.

Suggested Citation

  • Rabha W. Ibrahim, 2013. "Stability and Stabilizing of Fractional Complex Lorenz Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:127103
    DOI: 10.1155/2013/127103
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    References listed on IDEAS

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    1. A. M. A. El-Sayed & E. Ahmed & H. A. A. El-Saka, 2012. "Dynamic Properties of the Fractional‐Order Logistic Equation of Complex Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    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. A. M. A. El-Sayed & E. Ahmed & H. A. A. El-Saka, 2012. "Dynamic Properties of the Fractional-Order Logistic Equation of Complex Variables," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, August.
    5. Yan, Jianping & Li, Changpin, 2007. "On chaos synchronization of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 725-735.
    6. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
    7. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    8. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
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    Cited by:

    1. Meng Yang & Xinxi Xu & Chen Su, 2013. "A Study on Vibration Characteristics and Stability of the Ambulance Nonlinear Damping System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Pensri Pramukkul & Adam Svenkeson & Paolo Grigolini & Mauro Bologna & Bruce West, 2013. "Complexity and the Fractional Calculus," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).

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