Skip to main content
Log in

A novel chaotic system with suppressed time-delay signature based on multiple electro-optic nonlinear loops

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

Abstract

We present a novel time-delay chaotic system by adopting multiple electro-optic nonlinear loops. The dynamic characteristics of the proposed chaotic system are investigated by means of the bifurcation diagram and the permutation entropy. The security performance of the system is analyzed in detail by using autocorrelation function, delayed mutual information, and the permutation information approach. The simulation results show that the time-delay signature is suppressed under certain simple conditions. Moreover, a synchronization scheme on basis of the proposed system is analyzed. Both the security and the feasibility are verified. The proposed chaotic system can be used in secure communications and also has potential applications in random number generation or chaos computing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. VanWiggeren, G.D., Roy, R.: Communication with chaotic lasers. Science 279, 1198–1200 (1998)

    Article  Google Scholar 

  2. Kim, C.M., Kye, W.H., Rim, S., Lee, S.Y.: Communication key using delay times in time-delayed chaos synchronization. Phys. Lett. A 333(3–4), 235–240 (2004)

    Article  MATH  Google Scholar 

  3. Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia-Ojalvo, J., Mirasso, C.R., Pesquera, L., Shore, K.A.: Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438(7066), 343–346 (2005)

    Article  Google Scholar 

  4. Zhao, Q.C., Yin, H.X.: Performance analysis of orthogonal optical chaotic division multiplexing utilizing semiconductor lasers. Optics Laser Technol. 47, 208–213 (2013)

    Article  Google Scholar 

  5. Sun, J.W., Shen, Y., Yin, Q., Xu, C.J.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos 23(1), 013140 (2013)

    Article  MathSciNet  Google Scholar 

  6. Li, N.Q., Pan, W., Luo, B., Yan, L.S., Zou, X.H., Xu, M.F., Jiang, N., Xiang, S.Y., Mu, P.H.: Numerical characterization of time delay signature in chaotic vertical-cavity surface-emitting lasers with optical feedback. Optics Commun. 285(18), 3837–3848 (2012)

    Article  Google Scholar 

  7. Vicente, R., Daudén, J., Colet, P., Toral, R.: Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop. IEEE J. Quantum Electron. 41(4), 541–548 (2005)

    Article  Google Scholar 

  8. Farmer, J.D.: Chaotic attractors of an infinite-dimensional dynamical system. Phys. D 4(3), 366–393 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kouomou, Y.C., Colet, P., Larger, L., Gastaud, N.: Chaotic breathers in delayed electro-optical systems. Phys. Rev. Lett. 95(20), 203903 (2005)

    Article  Google Scholar 

  10. Erneux, T., Larger, L., Lee, M.W., Goedgebuer, J.-P.: Ikeda Hopf bifurcation revisited. Phys. D 194(1–2), 49–64 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cohen, A., Ravoori, B., Murphy, T., Roy, R.: Using synchronization for prediction of high-dimensional chaotic dynamics. Phys. Rev. Lett. 101(15), 154102 (2008)

    Article  Google Scholar 

  12. Udaltsov, V.S., Goedgebuer, J.-P., Larger, L., Cuenot, J.-B., Levy, P., Rhodes, W.T.: Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations. Phys. Lett. A 308(1), 54–60 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wu, X.M., Sun, Z.Y., Liang, F., Yu, C.B.: Online estimation of unknown delays and parameters in uncertain time delayed dynamical complex networks via adaptive observer. Nonlinear Dyn. 73(3), 1753–1768 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sudheer, K.S., Sabir, M.: Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system. Phys. Lett. A 375(8), 1176–1178 (2011)

    Article  MATH  Google Scholar 

  15. Hizanidis, J., Deligiannidis, S., Bogris, A., Syvridis, D.: Enhancement of chaos encryption potential by combining all-optical and electro-optical chaos generators. IEEE J. Quantum Electron. 46(11), 1642–1649 (2010)

    Article  Google Scholar 

  16. Nguimdo, R.M., Verschaffelt, G., Danckaert, J., Van der Sande, G.: Loss of time-delay signature in chaotic semiconductor ring lasers. Opt. Lett. 37(13), 2541–2543 (2012)

    Article  Google Scholar 

  17. Nguimdo, R.M., Colet, P., Larger, L., Pesquera, L.: Digital key for chaos communication performing time delay concealment. Phys. Rev. Lett. 107(3), 034103 (2011)

    Article  Google Scholar 

  18. Bogris, A., Rizomiliotis, P., Chlouverakis, K.E., Argyris, A., Syvridis, D.: Feedback phase in optically generated chaos: a secret key for cryptographic applications. IEEE J. Quantum Electron. 44(2), 119–124 (2008)

    Article  Google Scholar 

  19. Nguimdo, R.M., Colet, P.: Electro-optic phase chaos systems with an internal variable and a digital key. Opt. Express 20(23), 25333–25344 (2012)

  20. Cheng, M., Deng, L., Li, H., Liu, D.: Enhanced secure strategy for electro-optic chaotic systems with delayed dynamics by using fractional Fourier transformation. Opt. Express 22(5), 5241–5251 (2014)

    Article  Google Scholar 

  21. Kye, W.H., Choi, M., Kim, M.W., Lee, S.Y., Rim, S., Kim, C.M.: Synchronization of delayed systems in the presence of delay time modulation. Phys. Lett. A 322(5–6), 338–343 (2004)

    Article  MATH  Google Scholar 

  22. Robilliard, C., Huntington, E.H., Webb, J.G.: Enhancing the security of delayed differential chaotic systems with programmable feedback. IEEE Trans. Circuits Syst. II 53(8), 722–726 (2006)

    Article  Google Scholar 

  23. Kye, W.H.: Information transfer via implicit encoding with delay time modulation in a time-delay system. Phys. Lett. A 376(40–41), 2663–2667 (2012)

    Article  Google Scholar 

  24. Soriano, M.C., Zunino, L., Rosso, O.A., Fischer, I., Mirasso, C.R.: Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis. IEEE J. Quantum Electron. 47(2), 252–261 (2011)

    Article  Google Scholar 

  25. Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002)

  26. Toomey, J.P., Kane, D.M.: Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy. Opt. Express 22(2), 1713–1725 (2014)

    Article  Google Scholar 

  27. Ravoori, B., Cohen, A.B., Setty, A.V., Sorrentino, F., Murphy, T.E., Ott, E., Roy, R.: Adaptive synchronization of coupled chaotic oscillators. Phys. Rev. E 80(5), 056205 (2009)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the National “863” Program of China (no. 2015AA016904) and the National Nature Science Foundation of China (NSFC) under grant no. 61307091 and 61331010.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Cheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gao, X., Cheng, M., Deng, L. et al. A novel chaotic system with suppressed time-delay signature based on multiple electro-optic nonlinear loops. Nonlinear Dyn 82, 611–617 (2015). https://doi.org/10.1007/s11071-015-2181-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2181-3

Keywords

Navigation