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The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 35–44 | Cite as

Phase synchronization in unidirectionally coupled Ikeda time-delay systems

  • D.V. SenthilkumarEmail author
  • M. Lakshmanan
  • J. Kurths
Article

Abstract

Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled systems phase synchronization (PS)does exist in a range of the coupling strength which is preceded by a transition regime (approximate PS)and a nonsynchronous regime. However, exact generalized synchronization does not seem to occur in the coupled Ikeda systems (for the range of parameters we have studied)even for large coupling strength, in contrast to our earlier studies in coupled piecewise-linear and Mackey-Glass systems [27,28]. The above transitions are characterized in terms of recurrence based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence (CPR), joint probability of recurrence (JPR)and similarity of probability of recurrence (SPR). The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets.

Keywords

Lyapunov Exponent Coupling Strength European Physical Journal Special Topic Chaotic Attractor Phase Synchronization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. H. Fujisaka, T. Yamada, Prog. Theor. Phys. 69, 32 (1983); Prog. Theor. Phys. 70, 1240 (1983) Google Scholar
  2. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990) Google Scholar
  3. See for example, Chaos 7, (1997); Special Focus Issue on Chaotic Synchronization, edited by L. Pecora Google Scholar
  4. A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization - A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001)Google Scholar
  5. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)Google Scholar
  6. See for example, Int. J. Bifurc. Chaos 10 (2000); Special Focus Issue on Phase Synchronization, edited by J. KurthsGoogle Scholar
  7. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 76, 1804 (1996) Google Scholar
  8. A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, J. Kurths, Physica D 104, 219 (1997) Google Scholar
  9. A.S. Pikovsky, G.V. Osipov, M.G. Rosenblum, M. Zaks, J. Kurths, Phys. Rev. Lett. 79, 47 (1997) Google Scholar
  10. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997) Google Scholar
  11. U. Parlitz, L. Junge, W. Lauterborn, L. Kocarev, Phys. Rev. E 54, 2115 (1996) Google Scholar
  12. M. Zhan, G.W. Wei, C.H. Lai, Phys. Rev. E 65, 036202 (2002) Google Scholar
  13. G.V. Osipov, M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. E 55, 2353 (1997) Google Scholar
  14. M. Zhan, Z.G. Zheng, G. Hu, X.H. Peng, Phys. Rev. E 62, 3552 (2000) Google Scholar
  15. E. Rosa, C.M. Ticos, W.B. Pardo, J.A. Walkenstein, M. Monti, J. Kurths, Phys. Rev. E 68, 025202(R)(2003) Google Scholar
  16. S. Guan, C.H. Lai, G.W. Wei, Phys. Rev. E 72, 016205 (2005) Google Scholar
  17. A. Pujol-Peré, O. Calvo, M.A. Matias, J. Kurths, Chaos 13, 319 (2003) Google Scholar
  18. M.S. Baptista, T.P. Silva, J.C. Sartorelli, I.L. Caldas, E. Rosa, Phys. Rev. E 67, 056212 (2003)Google Scholar
  19. S.K. Dana, B. Blasius, J. Kurths, Chaos 16, 023111 (2006)Google Scholar
  20. K.V. Volodehenko, V.N. Ivanov, S.H. Gong, M. Choi, Y.J. Park, C.M. Kim, Opt. Lett. 26, 1406 (2001)Google Scholar
  21. D.J. DeShazer, R. Breban, E. Ott, R. Roy, Phys. Rev. Lett. 87, 0444101 (2001)Google Scholar
  22. D. Maza, A. Vallone, H. Mancini, S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2000) Google Scholar
  23. P. Tass, M.G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, H.J. Freund, Phys. Rev. Lett. 81, 3291 (1998)Google Scholar
  24. R.C. Elson, A.I. Selverston, R. Huerta, N.F. Rulkov, M.I. Rabinovich, H.D.I. Abarbanel, Phys. Rev. Lett. 81, 5692 (1998) Google Scholar
  25. D. Maraun, J. Kurths, Geophys. Res. Lett. 32, L15709 (2005) Google Scholar
  26. D.V. Senthilkumar, Chaotic Synchronizations and their Transitions in Nonlinear Time-delay Systems, Ph.D. thesis, Bharathidasan University, 2008 Google Scholar
  27. D.V. Senthilkumar, M. Lakshmanan, J. Kurths, Phys. Rev. E 74, 035205(R) (2006) Google Scholar
  28. D.V. Senthilkumar, M. Lakshmanan, J. Kurths, Chaos 18, 023118 (2008) Google Scholar
  29. K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980) Google Scholar
  30. G.V. Osipov, B. Hu, C. Zhou, M.V. Ivanchenko, J. Kurths, Phys. Rev. Lett. 91, 024101 (2003) Google Scholar
  31. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007) Google Scholar
  32. K. Ikeda, K. Matsumoto, Physica D 29, 223 (1987) Google Scholar
  33. C. Masoller, D.H. Zanette, Physica A 300, 359 (2001) Google Scholar
  34. M. Le Berre, E. Ressayre, A. Tallet, H.M. Gibbs, D.L. Kaplan, M.H. Rose, Phys. Rev. A 35, 3020 (1987) Google Scholar
  35. H.U. Voss, Phys. Rev. E 61, 5115 (2000) Google Scholar
  36. E.M. Shahverdiev, S. Sivaprakasam, K.A. Shore, Phys. Rev. E 66, 017204 (2002) Google Scholar
  37. E.M. Shahverdiev, S. Sivaprakasam, K.A. Shore, Phys. Lett. A 292, 320 (2002) Google Scholar
  38. E.M. Shahverdiev, K.A. Shore, Phys. Rev. E 71, 016201 (2005) Google Scholar
  39. M.C. Romano, M. Thiel, J. Kurths, I.Z. Kiss, J.L. Hudson, Europhys. Lett. 71, 466 (2005) Google Scholar
  40. T. Pereira, M.S. Baptista, J. Kurths, Phys. Rev. E 75, 026216 (2007) Google Scholar

Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  1. 1.Centre for Nonlinear Dynamics, Department of PhysicsBharathidasan UniversityTiruchirapalliIndia
  2. 2.Interdisciplinary Centre for Dynamics of Complex Systems, University of PotsdamPotsdamGermany
  3. 3.Humboldt University, Berlin and Potsdam Institute for Climate Impact ResearchPotsdamGermany

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