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Suppression of dynamics and frequency synchronization in coupled slow and fast dynamical systems

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Abstract

We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in amplitude. If the mismatch is small, the systems settle to a frequency synchronized state with constant phase difference. But as mismatch in time scale increases, the systems have to compromise to a state of no oscillations. We illustrate this for standard nonlinear systems and identify the regions of quenched dynamics in the parameter plane. The transition curves to this state are studied analytically and confirmed by direct numerical simulations. As an important special case, we revisit the well-known model of coupled ocean-atmosphere system used in climate studies for the interactive dynamics of a fast oscillating atmosphere and slowly changing ocean. Our study in this context indicates occurrence of multi stable periodic states and steady states of convection coexisting in the system, with a complex basin structure.

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References

  1. A.T. Winfree, Geometry of Biological Time (Springer, New York, 1980)

  2. P. Johnson, A. Sutin, J. Acoust. Soc. Am. 117, 124 (2005)

    Article  ADS  Google Scholar 

  3. M.R. Hansen, X. Feng, V. Macho, K. Müllen, H.W. Spiess, G. Floudas, Phys. Rev. Lett. 107, 257801 (2011)

    Article  ADS  Google Scholar 

  4. K.A. Henzler-Wildman, M. Lei, V. Thai, S.J. Kerns, M. Karplus, D. Kern, Nature 450, 913 (2007)

    Article  ADS  Google Scholar 

  5. S.J. Kiebel, J. Daunizeau, K.J. Friston, PLoS Comput. Biol. 4, e1000209 (2008)

    Article  ADS  Google Scholar 

  6. M. Breakspear, C.J. Stam, Phil. Trans. R. Soc. B 360, 1051 (2005)

    Article  Google Scholar 

  7. A.-S. Crépin, J. Norberg, K.-G. Mäler, Ecological Economics 70, 1448 (2011)

    Article  Google Scholar 

  8. D. Das, D.S. Ray, Eur. Phys. J. Special Topics 222, 785 (2013)

    Article  ADS  Google Scholar 

  9. M.C. Soriano, L. Zunino, O.A. Rosso, I. Fischer, C.R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011)

    Article  ADS  Google Scholar 

  10. G.D. Mitsis, R. Zhang, B.D. Levine, V.Z. Marmarelis, Ann. Biomed. Eng. 30, 555 (2002)

    Article  Google Scholar 

  11. L.M. Kay, Chaos 13, 1057 (2003)

    Article  ADS  Google Scholar 

  12. J. David Neelin, J. Atmos. Sci. 48, 584 (1991)

    Article  ADS  Google Scholar 

  13. B.R. Lintner, J.D. Neelin, J. Climate 21, 2187 (2008)

    Article  ADS  Google Scholar 

  14. M. Peña, E. Kalnay, Nonlin. Process. Geophys. 11, 319 (2004)

    Article  ADS  Google Scholar 

  15. Z. Artstein, in Proceedings of DINCON’10, 9th Brazilian conference on dynamics, Control and their application, 2010, p. 1254

  16. J.A. Sanders, F. Verhulst, J. Murdock, Averaging Methods in Nonlinear Dynamical Systems (Springer, New York, 1985)

  17. H. Aoki, K. Kaneko, Phys. Rev. Lett. 111, 144102 (2013)

    Article  ADS  Google Scholar 

  18. M. Krupa, N. Popović, N. Kopell, H.G. Rotstein, Chaos 18, 015106 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  19. A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  20. A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rep. 521, 205 (2012)

    Article  ADS  Google Scholar 

  22. D.L. Valladares, S. Boccaletti, F. Feudel, J. Kurths, Phys. Rev. E 65, 055208(R) (2002)

    Article  ADS  Google Scholar 

  23. P.S. Landa, P.V.E. McClintock, Phys. Rep. 532, 1 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  24. H. Sakaguchi, Prog. Theor. Phys. 80, 743 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  25. G.B. Ermentrout, N. Kopell, SIAM J. Appl. Math. 50, 125 (1990)

    Article  MathSciNet  Google Scholar 

  26. K. Konishi, Phys. Rev. E 68, 067202 (2003)

    Article  ADS  Google Scholar 

  27. D.V. Ramana Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109 (1998)

    Article  ADS  Google Scholar 

  28. A. Prasad, M. Dhamala, B.M. Adhikari, R. Ramaswamy, Phys. Rev. E 81, 027201 (2010)

    Article  ADS  Google Scholar 

  29. Y. Yamaguchi, H. Shimizu, Physica D 11, 212 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  30. M. Shiino, M. Frankowicz, Phys. Lett. A 136, 103 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  31. R.E. Mirollo, S.H. Strogatz, J. Stat. Phys. 60, 245 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  32. R. Karnatak, R. Ramaswamy, A. Prasad, Phys. Rev. E. 76, 035201(R) (2007)

    Article  ADS  Google Scholar 

  33. V. Resmi, G. Ambika, R.E. Amritkar, Phys. Rev. E. 84, 046212 (2011)

    Article  ADS  Google Scholar 

  34. S.M. Shekatkar, G. Ambika, Commun. Nonlinear Sci. Numer. Simul. 25, 50 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  35. S. De Monte, F. d′Ovidio, E. Mosekilde, Phys. Rev. Lett. 90, 054102 (2003)

    Article  ADS  Google Scholar 

  36. K. Fujimoto, K. Kaneko, Physica D 180, 1 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  37. M. Lakshmanan, Nonlinear Dynamics: Integrability, Chaos and Patterns (Springer, India, 2003)

  38. D.V. Ramana Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 85, 16 (2000)

    Article  Google Scholar 

  39. E. Niebur, H.G. Schuster, D.M. Kammen, Phys. Rev. Lett. 67, 20 (1991)

    Article  Google Scholar 

  40. S. Acharya, R.E. Amritkar, Eur. Phys. J. Special Topics 222, 939 (2013)

    Article  ADS  Google Scholar 

  41. L. Siqueira, B. Kirtman, Nonlin. Process. Geophys. 19, 273 (2012)

    Article  ADS  Google Scholar 

  42. S. Soldatenko, D. Chichkine, Wseas Trans. Syst. 13, 2224 (2014)

    Google Scholar 

  43. J.A. Freund, L. Schimansky-Geier, P. Hänggi, Chaos 13, 225 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  44. L. Callenbach, P. Hänggi, S.J. Linz, J.A. Freund, L. Schimansky-Geier, Phys. Rev. E 65, 051110 (2002)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Indian Institute of Science Education and Research, 411008, Pune, India

    Kajari Gupta & G. Ambika

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  1. Kajari Gupta
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  2. G. Ambika
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Correspondence to G. Ambika.

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Gupta, K., Ambika, G. Suppression of dynamics and frequency synchronization in coupled slow and fast dynamical systems. Eur. Phys. J. B 89, 147 (2016). https://doi.org/10.1140/epjb/e2016-70068-8

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