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Zbl 1115.37035
Mahmoud, Gamal M.; Al-Kashif, M.A.; Aly, Shaban A.
Basic properties and chaotic synchronization of complex Lorenz system. (English)
[J] Int. J. Mod. Phys. C 18, No. 2, 253-265 (2007). ISSN 0129-1831

Summary: This paper aims at studying the basic properties and chaotic synchronization of the complex Lorenz system: $$\dot x=\alpha(y-x), \quad\dot y=\gamma x-y-xz,\quad \dot z=-\beta z+\frac 12(\overline xy+x\overline y),\tag *$$ where $\alpha, \gamma,\beta$ are positive (real or complex) parameters, $x$ and $y$ are complex variables, $z$ is 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 (*).

MSC 2000:: *37D45 Strange attractors, chaotic dynamics
93C10 Nonlinear control systems
93D15 Stabilization of systems by feedback

Keywords: chaotic attractor; chaos; active control; error system; equilibria; dissipation

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