Nonlinear Dynamics

, Volume 69, Issue 3, pp 771–779

Complex projective synchronization in coupled chaotic complex dynamical systems

Original Paper

DOI: 10.1007/s11071-011-0303-0

Cite this article as:
Wu, Z., Duan, J. & Fu, X. Nonlinear Dyn (2012) 69: 771. doi:10.1007/s11071-011-0303-0


In previous papers, the projective factors are always chosen as real numbers, real matrices, or even real-valued functions, which means 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 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.


Complex projective synchronization Complex dynamical system Chaotic Adaptive control 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceJiangxi Normal UniversityNanchangChina
  2. 2.Institute for Pure and Applied MathematicsUniversity of CaliforniaLos AngelesUSA
  3. 3.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA
  4. 4.Department of MathematicsShanghai UniversityShanghaiChina

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