BASIC PROPERTIES AND CHAOTIC SYNCHRONIZATION OF COMPLEX LORENZ SYSTEM

Gamal M. Mahmoud (), M. A. Al-KASHIF () and Shaban A. Aly ()
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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

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 02, 253-265

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 (⋆).

Keywords: Basic properties; chaotic attractor; chaos; synchronization; active control; error system; complex; equilibria; dissipation (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0129183107010425

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