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A New Complex Hyper-chaotic System and Chaotic Synchronization of Error Feedback with Disturbance

  • Weidong Guan
  • Dengwei Yan
  • Lidan WangEmail author
  • Shukai Duan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11554)

Abstract

In this paper, a new complex hyper-chaotic system is proposed. Through the separation of real and imaginary parts, the basic dynamics such as symmetry, dissipation, equilibrium stability, Lyapunov exponent spectrum and power spectrum are studied. Then, according to the Lyapunov stability theory, using the error feedback synchronization method, we design a complex feedback controller to realize the chaotic synchronization of the proposed chaotic system with both parameters and external disturbances. Theoretical analysis shows that the controller can make the synchronization error gradually towards zero point. In addition, the numerical simulation of the complex chaotic synchronization system is carried out. The simulation results further verify the effectiveness of the proposed method.

Keywords

Complex hyper-chaotic system Parameter perturbation External disturbance Feedback synchronization 

References

  1. 1.
    Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196–1199 (1990)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Pecora, L.M., Caeeoll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 8210–8224 (1990)MathSciNetGoogle Scholar
  3. 3.
    Yang, X.S.: On the existence of generalized synchronizer in unidirectionally coupled systems. Appl. Math. Comput. 122(1), 71–79 (2001)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Elabbasv, E.M., Agiza, H.N.: Synchronization of modified Chen system. Int. J. Bifurcat. Chaos 14(11), 3969–3979 (2004)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Mahmound, G.M., Bountis, T.: Active control and global synchronization of the complex Chen system and Lu system. Int. J. Bifurcat. Chaos 17(12), 4295–4308 (2007)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Mahmound, G.M.: Modified projective lag synchronization of two nonidentical hyperchaotic complex nonlinear systems. Int. J. Bifurcat. Chaos 21(8), 2369–2379 (2011)zbMATHGoogle Scholar
  7. 7.
    Gamal, M.M., Mansour, E.A., Nabil, S.: On autonomous and nonautonomous modified hyperchaotic complex Lu systems. Int. J. Bifurcat. Chaos 21(7), 1913–1936 (2011)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Mahmoud, G.M., Bountis, T.: The dynamics of systems of complex nonlinear oscillators: a review. Int. J. Bifurcat. Chaos 14(11), 3821–3846 (2004)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Zhu, H.L., Zhang, X.B.: Dynamical analysis of a new complex chaotic system and its synchronization. J. Dyn. Control 6(4), 307–311 (2008)Google Scholar
  10. 10.
    Mahmoud, G.M., Bountis, T., AbdEl-Latif, G.M., Mahmoud, E.E.: Chaos synchronization of two different chaotic complex Chen and Lii systems. Nonlinear Dyn. 55(1–2), 43–53 (2009)zbMATHGoogle Scholar
  11. 11.
    Zhang, X.B., Zhao, H.G.: Modified function projective synchronization of different chaotic systems. J. Chongqing Normal Univ. 30(2), 65–68 (2013)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Skardal, P.S., Taylor, D., Sun, J.: Optimal synchronization of complex networks. Phys. Rev. Lett. 113(14), 144101 (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Weidong Guan
    • 1
    • 2
    • 3
  • Dengwei Yan
    • 1
    • 2
    • 3
  • Lidan Wang
    • 1
    • 2
    • 3
    Email author
  • Shukai Duan
    • 1
    • 2
    • 3
  1. 1.Southwest UniversityChongqingChina
  2. 2.Chongqing Key Laboratory of Brain Inspired Computing and Intelligent ControlChongqingChina
  3. 3.National and Local Joint Engineering Laboratory of Intelligent Transmission and Control TechnologyChongqingChina

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