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Chaotic Behavior And Chaos Control For A Class Of Complex Partial Differential Equations

Author

Listed:
  • G. M. MAHMOUD

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

  • H. A. ABDUSALAM

    (Department of Mathematics, Faculty of Sciences, University of Cairo, Giza, Egypt)

  • A. A. M. FARGHALY

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

Abstract

Systems of complex partial differential equations, which include the famous nonlinear Schrödinger, complex Ginzburg–Landau and Nagumo equations, as examples, are important from a practical point of view. These equations appear in many important fields of physics. The goal of this paper is to concentrate on this class of complex partial differential equations and study the fixed points and their stability analytically, the chaotic behavior and chaos control of their unstable periodic solutions. The presence of chaotic behavior in this class is verified by the existence of positive maximal Lyapunov exponent.The problem of chaos control is treated by applying the method of Pyragas. Some conditions on the parameters of the systems are obtained analytically under which the fixed points are stable (or unstable).

Suggested Citation

  • G. M. Mahmoud & H. A. Abdusalam & A. A. M. Farghaly, 2001. "Chaotic Behavior And Chaos Control For A Class Of Complex Partial Differential Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 889-899.
    • Handle: RePEc:wsi:ijmpcx:v:12:y:2001:i:06:n:s0129183101002073
    DOI: 10.1142/S0129183101002073
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    Cited by:

    1. Xu, Yong & Xu, Wei & Mahmoud, Gamal M., 2008. "On a complex Duffing system with random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 126-132.

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