Skip to main content
SpringerLink
Log in

Synchronization of N different coupled chaotic systems with ring and chain connections

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Synchronization of N different coupled chaotic systems with ring and chain connections is investigated. The New system, the Chen system, the Lü system, the Lorenz system, and the Rössler system are used as examples in verifying effectiveness of the method. Based on the Lyapunov stability theory, the form of the controller is designed and the area of the coupling coefficients is determined. Simulations indicate that global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients by using the controller.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pecora L M, Carroll T L. Synchronization in chaotic systems[J]. Phys Rev Lett, 1990, 64(8):821–824.

    Article  MathSciNet  Google Scholar 

  2. Yassen M T. Chaos synchronization between two different chaotic systems using active control[J]. Chaos Solitons and Fractals, 2005, 23(1):131–140.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen H K. Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü[J]. Chaos, Solitons and Fractals, 2005, 25(5):1049–1056.

    Article  MATH  MathSciNet  Google Scholar 

  4. Park J H. Chaos synchronization between two different chaotic dynamical systems[J]. Chaos, Solitons and Fractals, 2006, 27(2):594–554.

    Google Scholar 

  5. Elabbasy E M, Agiza H N, El-Dessoky M M et al. Adaptive synchronization of Lü system with uncertain parameters[J]. Chaos, Solitons and Fractals, 2004, 21(3):657–667.

    Article  MATH  Google Scholar 

  6. Park J H. Adaptive synchronization of Rössler system with uncertain parameters[J]. Chaos, Solitons and Fractals, 2005, 25(2):333–338.

    Article  MATH  Google Scholar 

  7. Park J H. Adaptive synchronization of hyperchaotic Chen system with uncertain parameters[J]. Chaos, Solitons and Fractals, 2005, 26(3):959–964.

    Article  MATH  MathSciNet  Google Scholar 

  8. Yu Y G, Zhang S C. Adaptive backstepping synchronization of uncertain chaotic system[J]. Chaos, Solitons and Fractals, 2004, 21(3):643–649.

    Article  MATH  MathSciNet  Google Scholar 

  9. Yassen M T. Adaptive chaos control and synchronization for uncertain new chaotic dynamical system[J]. Phys Lett A, 2006, 350(1):36–43.

    Article  Google Scholar 

  10. Huang L L, Feng R P, Wang M et al. Synchronization of chaotic systems via nonlinear control[J]. Phys Lett A, 2004, 320(4):271–275.

    Article  MATH  MathSciNet  Google Scholar 

  11. Yue L J, Shen K. Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback[J]. Chin Phys, 2005, 14(9):1760–1765.

    Article  Google Scholar 

  12. Yassen M T. Controlling chaos and synchronization for new chaotic system using linear feedback control[J]. Chaos, Solitons and Fractals, 2005, 26(3):913–920.

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen H K. Global chaos synchronization of new chaotic systems via nonlinear control[J]. Chaos, Solitons and Fractals, 2005, 23(4):1245–1251.

    MATH  Google Scholar 

  14. Park J H. Chaos synchronization of a chaotic system via nonlinear control[J]. Chaos, Solitons and Fractals, 2005, 25(3):579–584.

    Article  MATH  Google Scholar 

  15. Park J H. On synchronization of unified chaotic systems via nonlinear control[J]. Chaos, Solitons and Fractals, 2005, 25(3):699–704.

    Article  MATH  Google Scholar 

  16. Lü J H, Zhou T S, Zhou S C. Chaos synchronization between two different chaotic systems[J]. Chaos, Solitons and Fractals, 2002, 14(4):529–541.

    Article  MATH  MathSciNet  Google Scholar 

  17. Yu Y G, Zhang S. The synchronization of linearly bidirectional coupled chaotic systems[J]. Chaos, Solitons and Fractals, 2002, 22(1):189–197.

    Article  MathSciNet  Google Scholar 

  18. Park J H. Stability criterion for synchronization of linearly coupled unified chaotic systems[J]. Chaos, Solitons and Fractals, 2005, 23(4):1319–1325.

    MATH  Google Scholar 

  19. Ge Z M, Chen Y S. Adaptive synchronization of unidirectional and mutual coupled chaotic systems[J]. Chaos, Solitons and Fractals, 2005, 26(3):881–888.

    Article  MATH  MathSciNet  Google Scholar 

  20. Wang J, Deng B, Tsang K M. Chaotic synchronization of neurons coupled with gap junction under external electrical stimulation[J]. Chaos, Solitons and Fractals, 2004, 22(2):469–476.

    Article  MATH  Google Scholar 

  21. Haken H. Synchronization and pattern recognition in a pulse-coupled neural net[J]. Physica D, 2005, 205(1):1–6.

    Article  MATH  MathSciNet  Google Scholar 

  22. Yue L J, Shen K. Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback[J]. Chin Phys, 2005, 14(9):1760–1765.

    Article  Google Scholar 

  23. Zou Y L, Zhu J, Chen G R et al. Chaotic coupling synchronization of hyperchaotic oscillators[J]. Chin Phys, 2005, 14(4):697–702.

    Article  Google Scholar 

  24. Huang L L, Wang M, Feng R P. Synchronization of generalized Henon map via backstepping design[J]. Chaos, Solitons and Fractals, 2005, 23(2):617–620.

    Article  MATH  Google Scholar 

  25. Liu S T, Chen G R. Nonlinear feedback-controlled generalized synchronization of spatial chaos[J]. Chaos, Solitons and Fractals, 2004, 22(1):35–46.

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang Y W, Guan Z H. Generalized synchronization of continuous chaotic system[J]. Chaos, Solitons and Fractals, 2006, 27(1):97–101.

    Article  MATH  MathSciNet  Google Scholar 

  27. Zou Y L, Zhu J. Controlling projective synchronization in coupled chaotic systems[J]. Chin Phys, 2006, 15(9):1965–1970.

    Article  Google Scholar 

  28. Yan J P, Li C P. Generalized projective synchronization of a unified chaotic system[J]. Chaos, Solitons and Fractals, 2005, 26(4):1119–1124.

    Article  MATH  MathSciNet  Google Scholar 

  29. Wen G L, Xu D L. Nonlinear observer control for full-state projective synchronization in chaotic continuous-time systems[J]. Chaos, Solitons and Fractals, 2005, 26(1):71–77.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Physics and Electronic Technology, Liaoning Normal University, Dalian, 116029, P. R. China

    Yan Liu  (刘艳) & Ling Lü  (吕翎)

Authors
  1. Yan Liu  (刘艳)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ling Lü  (吕翎)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ling Lü  (吕翎).

Additional information

(Communicated by CHEN Li-qun)

Project supported by the Natural Science Foundation of Liaoning Province (No. 20052151) and the Innovative Team Program of Liaoning Educational Committee

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Lü, L. Synchronization of N different coupled chaotic systems with ring and chain connections. Appl. Math. Mech.-Engl. Ed. 29, 1299–1308 (2008). https://doi.org/10.1007/s10483-008-1005-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-1005-y

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation