Basic properties and chaotic synchronization of complex Lorenz system
This paper aims at studying the basic properties and chaotic synchronization of complex Lorenz system: x = alpha(y - x), y = gamma x - y - xz, z = -beta z + 1/2 ((x) over bar y + x (y) over bar), (*) 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 (*).
basic properties chaos synchronization complex chaotic attractor active control error system equilibria dissipation