## Complex projective synchronization in coupled chaotic complex dynamical systems.(English)Zbl 1253.93060

Summary: In previous papers, the projective factors are always chosen as real numbers, real matrices, or even real-valued functions, which means that the coupled systems evolve in the same or inverse direction simultaneously. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, the projective synchronization with respect to a complex factor, called Complex Projective Synchronization (CPS), should be taken into consideration. In this paper, based on Lyapunov’s stability theory, three typical chaotic complex dynamical systems are considered and the corresponding controllers are designed to achieve the complex projective synchronization. Further, an adaptive control method is adopted to design a universal controller for partially linear systems. Numerical examples are provided to show the effectiveness of the proposed method.

### MSC:

 93C15 Control/observation systems governed by ordinary differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C40 Adaptive control/observation systems 34D06 Synchronization of solutions to ordinary differential equations 34H10 Chaos control for problems involving ordinary differential equations
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