Synchronization of Two Chaotic Oscillators Through Threshold Coupling

  • A. Chithra
  • I. Raja Mohamed
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 732)


In this paper, the dynamic modeling of two identical oscillators which are coupled through threshold controller is proposed. Until now, most of the synchronization of chaotic systems found in literature is based on common coupling methods (unidirectional and bidirectional) that attracted the attention of researchers. To strengthen this, the idea illustrated here is to show the effectiveness of a new kind of coupling called threshold controller coupling. Using this, complete and anticipatory synchronization could be achieved. The system used is of second-order non-autonomous type. The coupled system is investigated using MATLAB–Simulink technique. The result shows that based on coupling strength, coupled system is switched among the basic synchronization, viz. lead and complete.


Modeling Synchronization Threshold controller Chaotic MATLAB–Simulink 



This research work is supported by SERB under project No: SR/S2/HEP-042/2012, and authors thank SERB for providing financial support.


  1. 1.
    Pikovsky, A.S., Rosenblum, M.G., Kurths, J.: Synchronization—A Unified Approach to Nonlinear Science. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  2. 2.
    Huygen, C.: The Pendulum Clock. Iowa State University Press, Ames (1986)Google Scholar
  3. 3.
    Fujisaka, H., Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69, 32 (1983)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Pecora, L.M., Carroll, T.L.: Synchronization in Chaotic system. Phy. Rev. Lett. 64, 821 (1990)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Abarbanel, H.D.I., Rulkov, N.F., Sushchik, M.M.: Generalized synchronization of chaos: the auxiliary system approach. Phys. Rev. E 53, 4528–4535 (1996)CrossRefGoogle Scholar
  6. 6.
    Lakshmanan, M., Murali, K.: Chaos in Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996)CrossRefGoogle Scholar
  7. 7.
    Raja Mohamed, I., Srinivasan, K.: Lag and anticipating synchronization in one way coupled Chua’s circuit. In: 2nd International Conference on Devices, Circuits and Systems, (2014)Google Scholar
  8. 8.
    Pikovsky, A.S., Rosenblum, M.G., Osipov, G.V., Kurths, J.: Phase synchronization of chaotic oscillators by external driving. Phys. D 104(3–4), 219–238 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chen, H.: Global chaos synchronization of new chaotic systems via nonlinear control. Solitons Fractals 23, 1245–1251 (2005)CrossRefGoogle Scholar
  10. 10.
    Srinivasan, K., Senthilkumar, D.V., Raja Mohamed, I., Murali, K., Lakshmanan, M., Kurths, J.: Anticipating, complete and lag synchronization in Rc-phase-shift network based coupled Chua’s circuits without delay. Chaos: An Interdisc. J. Nonlinear Sci. 22 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Pecora, L.M., Carroll, T.L., Johnson, G.A., Mar D.J.: Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: Am. Inst. phys. 4 (1997)Google Scholar
  12. 12.
    Murali, K., Lakshmanan. M.: Synchronization through compound chaotic signal in Chua’s circuit and Murali- Lakshmanan- Chua circuit. Int. J. Bifurcat. chaos 7, 415 (1997)CrossRefGoogle Scholar
  13. 13.
    Senthilkumar, D.V., Lakshmanan, M.: Transition from anticipatory to lag synchronization via complete synchronization in time–delay systems. Phys. Rev. E. 71 (2005)Google Scholar
  14. 14.
    Raja Mohamed, I., Murali, k., Sinha. S., Lindberg, E.: Design of threshold Controller based chaotic circuits. Int. J. Bifurcat. Chaos 20, 2185 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Suresh, R., Srinivasan, K., Senthilkumar., V, Murali, K., Lakshmanan, M., Kurths, J.: Dynamic Environment coupling induced synchronized states in coupled time-delayed electronic circuits. Int. J. Bifurcat. Chaos 24 (2014)CrossRefGoogle Scholar
  16. 16.
    Heagy, J.F., Carroll, T.L., Pecora, L.M.: Synchronous chaos in coupled oscillator systems. Phys. Rev. E 50, 1874 (1994)CrossRefGoogle Scholar
  17. 17.
    Cumo, K.M, Oppenheim, V., Stogatz, SH.: Synchronization of Lorenz-based Chaotic circuits with applications to communications IEEE Trans. Circ. Sys.-11: Analog Digit. Sig. Process. 40(10) (1993)Google Scholar
  18. 18.
    Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N.: Synchronization of two mutually coupled duffing—type circuits. Int. J Circ. Sys. Sig. Process. 1, 274 (2007)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of PhysicsB. S. Abdur Rahman UniversityChennaiIndia

Personalised recommendations