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Basic Properties And Chaotic Synchronization Of Complex Lorenz System

Author

Listed:
  • GAMAL M. MAHMOUD

    (Department of Mathematics, Assiut University, Assiut 71516, Egypt)

  • M. A. Al-KASHIF

    (Department of Mathematics, Assiut University, Assiut 71516, Egypt)

  • SHABAN A. ALY

    (Department of Mathematics, AL-Azhar University, Assiut 71516, Egypt)

Abstract

This paper aims at studying the basic properties and chaotic synchronization of complex Lorenz system:$$ \dot x =\alpha (y -x)\,,\qquad \dot y =\gamma x -y -xz\,,\qquad \dot z =-\beta z +\frac{1}{2} (\bar x y +x\bar y)\,,\eqno(\star) $$where α, γ, β are positive (real or complex) parameters,xandyare complex variables,zis a real variable, an overbar denotes complex conjugate variable and dots represent derivatives with respect to time. This system arises in many important applications in physics, for example, in laser physics and rotating fluids dynamics.Numerically we show that this system is a chaotic system and exhibits chaotic attractors. The necessary conditions for system (⋆) to generate chaos are obtained. Analytical and numerical calculations are presented to achieve synchronization. Active control technique is used to synchronize chaotic attractors of equations (⋆).

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:02:n:s0129183107010425
    DOI: 10.1142/S0129183107010425
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    Cited by:

    1. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2021. "Exponential synchronization of fractional-order complex chaotic systems and its application," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. 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.
    3. Emad E. Mahmoud & Fatimah S. Abood, 2017. "A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization," Complexity, Hindawi, vol. 2017, pages 1-13, August.
    4. 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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