Skip to main content
SpringerLink
Log in

Experimental realization of mixed-synchronization in counter-rotating coupled oscillators

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Recently, a novel mixed synchronization phenomenon is observed in counter-rotating nonlinear coupled oscillators (Prasad in Chaos Solitons Fractals 43:42–46, 2010). In mixed synchronization state: some variables are synchronized in-phase, while others are out-of-phase. We have experimentally verified the occurrence of mixed synchronization states in coupled counter-rotating chaotic piecewise Rössler oscillator. Analytical discussion on approximate stability analysis and numerical confirmation on the experimentally observed behavior is also given.

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. Prasad, A.: Universal occurrence of mixed synchronization in counter-rotating nonlinear coupled oscillators. Chaos Solitons Fractals 43, 42–46 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Huygens, C.: C. Horoloqium Oscilatorium. Apud F. Muquet, Parisiis (1973); English translation: The Pendulum Clock. Iowa State University Press, Ames

    Google Scholar 

  3. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  4. Pikovsky, A.S., Rosenblum, M.G., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge Nonlinear Science Series. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  5. Fujisaka, H., Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Prog. Theor. Phys. 69, 32–47 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Afraimovich, V.S., Verichev, N.N., Rabinovich, M.I. (Izvestiya Vysshikh Uchebnykh Zavedenii Radiofizika): Stochastic synchronization of oscillations in dissipative systems. Biom. J. 29, 1050 (1986)

    Google Scholar 

  7. Mahmoud, G.M., Aly, S.A., Al-Kashif, M.A.: Dynamical properties of chaos synchronization of a new chaotic complex nonlinear system. Nonlinear Dyn. 51, 171–181 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76, 1804–1807 (1996)

    Article  Google Scholar 

  9. Rosa, E.R., Ott, E., Hess, M.H.: Transition to phase synchronization of chaos. Phys. Rev. Lett. 80, 1642–1645 (1998)

    Article  Google Scholar 

  10. Liu, J., Ye, C., Zhang, S., Song, W.: Anti-phase synchronization in coupled map lattices. Phys. Lett. A 274, 27–29 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, Z.-L., Shi, X.-R.: Anti-synchronization of Liu system and Lorenz system with known or unknown parameters. Nonlinear Dyn. 57, 425–430 (2009)

    Article  MATH  Google Scholar 

  12. Rosenblum, M.G., Pikovsky, A.S., Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78, 4193–4196 (1997)

    Article  Google Scholar 

  13. Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Abarbanel, H.D.I.: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51, 980–994 (1995)

    Article  Google Scholar 

  14. Kocarev, L., Parlitz, U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 76, 1816–1819 (1996)

    Article  Google Scholar 

  15. Boccaletti, S., Valladares, D.L.: Characterization of intermittent lag synchronization. Phys. Rev. E 62, 7497–7500 (2000)

    Article  Google Scholar 

  16. Zaks, M.A., Park, E.H., Rosenblum, M.G., Kurths, J.: Alternating locking ratios in imperfect phase synchronization. Phys. Rev. Lett. 82, 4228–4231 (1999)

    Article  Google Scholar 

  17. Sivaprakasam, S., Pierce, I., Rees, P., Spencer, P.S., Shore, K.A., Valle, A.: Inverse synchronization in semiconductor laser diodes. Phys. Rev. A 64, 013805 (2001)

    Article  Google Scholar 

  18. Kim, C.M., Rim, S., Kye, W.H., Ryu, J.W., Park, Y.J.: Anti-synchronization of chaotic oscillators. Phys. Rev. A 320, 39–46 (2003)

    MathSciNet  MATH  Google Scholar 

  19. Zhu, H., Cui, B.: The antisynchronization of a class of chaotic delayed neural networks. Chaos 17, 043122 (2007)

    Article  MathSciNet  Google Scholar 

  20. Aronson, D.G., Ermentrout, G.B., Kopell, N.: Amplitude response of coupled oscillators. Physica D 41, 403–449 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  21. Karnatak, R., Ramaswamy, R., Prasad, A.: Amplitude death in the absence of time delays in identical coupled oscillators. Phys. Rev. E 76, 035201 (2007)

    Article  Google Scholar 

  22. Karnatak, R., Ramaswamy, R., Prasad, A.: Synchronization regimes in conjugate coupled chaotic oscillators. Chaos 19, 033143 (2009)

    Article  Google Scholar 

  23. Sharma, A., Shrimali, M.D., Prasad, A., Ramaswamy, R., Feudel, U.: Phase-flip transition in relay-coupled nonlinear oscillators. Phys. Rev. E 84, 016226 (2011)

    Article  Google Scholar 

  24. Ramana Reddy, D.V., Sen, A., Johnston, G.L.: Time delay induced death in coupled limit cycle oscillators. Phys. Rev. Lett. 80, 5109–5112 (1998)

    Article  Google Scholar 

  25. Prasad, A., Dhamala, M., Adhikari, B.M., Ramaswamy, R.: Amplitude death in nonlinear oscillators with nonlinear coupling. Phys. Rev. E 81, 027201 (2010)

    Article  Google Scholar 

  26. Prasad, A., Dhamala, M., Adhikari, B.M., Ramaswamy, R.: Targeted control of amplitude dynamics in coupled nonlinear oscillators. Phys. Rev. E 82, 027201 (2010)

    Article  Google Scholar 

  27. Resmi, V., Ambika, G., Amritkar, R.E.: Synchronized states in chaotic systems coupled indirectly through a dynamic environment. Phys. Rev. E 81, 046216 (2010)

    Article  Google Scholar 

  28. Sharma, A., Shrimali, M.D.: Pramana. Phys. Rev. 77, 881 (2011)

    Google Scholar 

  29. Grosu, I., Banerjee, R., Roy, P.K., Dana, S.K.: Design of coupling for synchronization of chaotic oscillators. Phys. Rev. E 76, 035201 (2007)

    Article  Google Scholar 

  30. Dana, S.K., Padmanaban, E., Banerjee, R., Roy, P.K., Grosu, I.: In: International Symposium on Signals, Circuits and Systems (2009)

    Google Scholar 

  31. Heagy, J.F., Corroll, T.L., Pecora, L.M.: Synchronous chaos in coupled oscillator systems. Phys. Rev. E 50, 1874–1885 (1994)

    Article  Google Scholar 

  32. Taherion, S., Lai, Y.C.: Observability of lag synchronization of coupled chaotic oscillators. Phys. Rev. E 59, R6247–R6250 (1999)

    Article  Google Scholar 

  33. Sprott, J.C.: A new class of chaotic circuit. Phys. Lett. A 266, 19–23 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The LNM Institute of Information Technology, Jaipur, 302 031, India

    Amit Sharma

  2. Indian Institute of Technology Rajasthan, Jodhpur, 342 011, India

    Manish Dev Shrimali

Authors
  1. Amit Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manish Dev Shrimali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manish Dev Shrimali.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, A., Dev Shrimali, M. Experimental realization of mixed-synchronization in counter-rotating coupled oscillators. Nonlinear Dyn 69, 371–377 (2012). https://doi.org/10.1007/s11071-011-0270-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0270-5

Keywords

Search

Navigation