## Complete synchronization of chaotic complex nonlinear systems with uncertain parameters.(English)Zbl 1215.93114

Summary: Our main objective in this work is to investigate complete synchronization (CS) of $$n$$-dimensional chaotic complex systems with uncertain parameters. An adaptive control scheme is designed to study the synchronization of chaotic attractors of these systems. We applied this scheme, as an example, to study complete synchronization of chaotic attractors of two identical complex Lorenz systems. The adaptive control functions and the parameters estimation laws are calculated analytically based on the complex Lyapunov function. We show that the error dynamical systems are globally stable. Numerical simulations are computed to check the analytical expressions of adaptive controllers.

### MSC:

 93C95 Application models in control theory 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 34H10 Chaos control for problems involving ordinary differential equations
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