CHAOTIC BEHAVIOR AND CHAOS CONTROL FOR A CLASS OF COMPLEX PARTIAL DIFFERENTIAL EQUATIONS

G. M. Mahmoud (), H. A. Abdusalam () and A. A. M. Farghaly
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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

International Journal of Modern Physics C (IJMPC), 2001, vol. 12, issue 06, 889-899

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).

Keywords: Chaotic Behavior; Lyapunov Exponent; Chaos Control (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0129183101002073

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