The European Physical Journal Special Topics

, Volume 226, Issue 10, pp 2219–2234

Complexity in synchronized and non-synchronized states: A comparative analysis and application

  • Sanjay K. Palit
  • Nur Aisyah Abdul Fataf
  • Mohd Rushdan Md Said
  • Sayan Mukherjee
  • Santo Banerjee
Regular Article
Part of the following topical collections:
  1. Aspects of Statistical Mechanics and Dynamical Complexity

Abstract

This analysis shows the dynamics of a hyperchaotic system changes from its original state to a synchronized state with nonlinear controller. The decreasing complexity of the coupled systems also quantifies the loss of information from its original state to the synchronized state. We proposed and modified a chaos synchronization based secure communication scheme to implement in case of non synchronization. The scheme is designed and illustrated using examples and simulations. Security analysis of the proposed scheme is also investigated. This analysis gives a new direction on chaos based cryptography in case of the coupled systems completely in non synchronized state.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Lakshmanan, K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization (World Scientific, Singapore, 1996)Google Scholar
  3. 3.
    S.K. Han, C. Kurrer, Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    B. Blasius, A. Huppert, L. Stone, Nature 399, 354 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    L. Zhou, C. Wang, H. He, Y. Lin, Comm. Nonlin. Sci. Num. Simul. 22, 623 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    X. Wua, C. Xuc, J. Fengd, Comm. Nonlin. Sci. Num. Simul. 20, 1004 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    H.U. Voss, Phys. Rev. E 61, 5115 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    Z. Li, C.Z. Han, Chin. Phys. 10, 494 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    Z. Li, C.Z. Han, Chin. Phys. 11, 9 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    S.H. Chen, L.M. Zhao, J. Liu, Chin. Phys. 11, 543 (2002)CrossRefGoogle Scholar
  13. 13.
    J. Mu, C. Tao, G.H. Du, Chin. Phys. 12, 381 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    J.Y. Sang, J. Yang, L.J. Yue, Chin. Phys. B 20, 080507 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    R.X. Zhang, S.P. Yang, Chin. Phys. B 20, 090512 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    O.E. Rössler, Phys. Lett. A 71, 155 (1979)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    U.E. Vincent, R. Guo, Phys. Lett. A 375, 2322 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    C. Zeng-qiang, Y. Yong, Q. Guo-yuan, Y. Zhu-zhi, Phys. Lett. A 360, 696 (2007)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    T. Gao, G. Chen, Z. Chen, S. Cang, Phys. Lett. A 361, 78 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    S. Banerjee, P. Saha, A.R. Chowdhury, Phys. Scrip. 63, 177 (2001)ADSCrossRefGoogle Scholar
  21. 21.
    Z. Wei, P. Yu, W. Zhang, M. Yao, Int. J. Bifurc. Chaos 25, 1550028 (2015)CrossRefGoogle Scholar
  22. 22.
    Z. Wei, P. Yu, W. Zhang, M. Yao, Nonlin. Dyn. 82, 131 (2015)CrossRefGoogle Scholar
  23. 23.
    C. Li, J.C. Sprott, Int. J. Bifurc. Chaos 24, 1450034 (2014)CrossRefGoogle Scholar
  24. 24.
    Y. Chen, Q. Yang, Nonlin. Dyn. 77, 569 (2014)CrossRefGoogle Scholar
  25. 25.
    E. Ott, Chaos in dynamical systems (Cambridge University Press, 1993)Google Scholar
  26. 26.
    K. Briggs, Phys. Lett. A 151, 27 (1990)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    M.T. Rosenstein, J.J. Collins, C.J. De Luca, Physica D 65, 117 (1993)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)CrossRefGoogle Scholar
  30. 30.
    Y.G. Sinai, Dokl. Akad. Nauk. SSSR 124, 768 (1959)MathSciNetGoogle Scholar
  31. 31.
    A. Kolmogorov, Dokl. Akad. Nauk. SSSR 124, 754 (1959)MathSciNetGoogle Scholar
  32. 32.
    S. Pincus, Proc. Natl. Acad. Sci. 88, 2297 (1991)ADSCrossRefGoogle Scholar
  33. 33.
    J. Richman, J. Moorman, Am. J. Physiol. 278, H2039 (2000)Google Scholar
  34. 34.
    N. Packard, J. Crutchfield, D. Farmer, R. Shaw, Phys. Rev. Lett. 45, 712 (1980)ADSCrossRefGoogle Scholar
  35. 35.
    N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Phys. Rev. E 66, 026702 (2002)ADSCrossRefGoogle Scholar
  36. 36.
    H. Rabarimanantsoa, L. Achour, C. Letellier, A. Cuvelier, J.F. Muir, Chaos 17, 0013115 (2007)ADSCrossRefGoogle Scholar
  37. 37.
    J.S. Iwanski, E. Bradley, Chaos 8, 861 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    E. Bradley, R. Mantilla, Chaos 12, 596 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    M. Thiel, M.C. Romano, P.L. Read, J. Kurths, Chaos 14, 234 (2004)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Y. Zou, M. Romano, M. Thiel, J. Kurths, Recurrence Quantification Analysis, Eds. C.L. Webber, Jr. N. Marwan (Springer, 2015), p. 65Google Scholar
  41. 41.
    C. Letellier, H. Rabarimanantsoa, L. Achour, A. Cuvelier, J.F. Muir, Phil. Trans. Royal Soc. London A: Math., Phys. and Engg. Sci. 366, 062163 (2008)Google Scholar
  42. 42.
    D. Eroglu, T.K.D. Peron, N. Marwan, F.A. Rodrigues, L.D.F. Costa, M. Sebek, I.Z. Kiss, J. Kurths, Phys. Rev. E 90, 042919 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    K.M. Cuomo, A.V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993)ADSCrossRefGoogle Scholar
  44. 44.
    G. Álvarez, F. Montoya, M. Romera, G. Pastor, Chaos, Solit. Frac. 23, 1749 (2005)CrossRefMATHGoogle Scholar
  45. 45.
    G. Qi, M.A. Wyk, B.J. Wyk, G. Chen, Phys. Lett. A 372, 124 (2008)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    G. Álvarez, S. Li, Comp. Comm. 27, 1679 (2004)CrossRefGoogle Scholar
  47. 47.
    S. Li, G. Alvarez, G. Chen, Chaos Solit. Frac. 25, 109 (2005)ADSCrossRefGoogle Scholar
  48. 48.
    S. Li, G. Alvarez, G. Chen, X. Mou, Chaos 15, 013703 (2005)ADSCrossRefGoogle Scholar
  49. 49.
    T. Yang, L.B. Yang, C.M. Yang, Phys. Lett. A 247, 105 (1998)ADSCrossRefGoogle Scholar
  50. 50.
    Y.G. Yu, S.C. Zhang, Chaos, Solit. Frac. 27, 1369 (2006)CrossRefGoogle Scholar
  51. 51.
    X. Wu, J. Lü, Chaos, Solit. Frac. 18, 721 (2003)CrossRefGoogle Scholar
  52. 52.
    T. Yang, L.O. Chua, Int. J. Bifurc. Chaos. 9, 215 (1999)CrossRefGoogle Scholar
  53. 53.
    J.H. Park, O.M. Kwon, Chaos Solit. Frac. 17, 709 (2003)CrossRefGoogle Scholar
  54. 54.
    V. Sundarapandian, Int. J. Cont. Th. Comp. Mod. 1, 15 (2011)MathSciNetGoogle Scholar
  55. 55.
    W. Hahn, The Stability of Motion (Springer, New York, 1967)Google Scholar
  56. 56.
    C. Paar, J. Pelzl, Introduction to Public-Key Cryptography (Springer, 2009)Google Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Basic Sciences and Humanities Department, Calcutta Institute of Engineering and ManagementKolkataIndia
  2. 2.School of Foundation Studies National Defence University of MalaysiaKuala LumpurMalaysia
  3. 3.Institute for Mathematical Research, Universiti Putra MalaysiaSerdangMalaysia
  4. 4.Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra MalaysiaSerdangMalaysia
  5. 5.Department of MathematicsSivanath Sastri CollegeKolkataIndia

Personalised recommendations