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Dynamics and synchronization of new hyperchaotic complex Lorenz system. (English) Zbl 1255.93102

Summary: The aim of this paper is to introduce a new hyperchaotic complex Lorenz system. This hyperchaotic complex system is constructed by adding a linear controller to the second equation of the chaotic complex Lorenz system. The new system is a 7-dimensional continuous real autonomous hyperchaotic system. This system has hyperchaotic attractors and quasi-periodic solutions with three zero Lyapunov exponents, while the chaotic attractors exist for all the parameters values of this system with two zero Lyapunov exponents. The fractional Lyapunov dimension of the hyperchaotic attractors of this system is calculated. Bifurcation diagrams are used to demonstrate chaotic and hyperchaotic behaviors of new system. The active control method based on Lyapunov stability analysis is used to study synchronization of this system. Numerical simulations are implemented to verify the results of these investigations.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34D06 Synchronization of solutions to ordinary differential equations
37N35 Dynamical systems in control
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