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.
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VanWiggeren, G.D., Roy, R.: Communication with chaotic lasers. Science 279, 1198–1200 (1998)
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)
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)
Zhao, Q.C., Yin, H.X.: Performance analysis of orthogonal optical chaotic division multiplexing utilizing semiconductor lasers. Optics Laser Technol. 47, 208–213 (2013)
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)
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)
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)
Farmer, J.D.: Chaotic attractors of an infinite-dimensional dynamical system. Phys. D 4(3), 366–393 (1982)
Kouomou, Y.C., Colet, P., Larger, L., Gastaud, N.: Chaotic breathers in delayed electro-optical systems. Phys. Rev. Lett. 95(20), 203903 (2005)
Erneux, T., Larger, L., Lee, M.W., Goedgebuer, J.-P.: Ikeda Hopf bifurcation revisited. Phys. D 194(1–2), 49–64 (2004)
Cohen, A., Ravoori, B., Murphy, T., Roy, R.: Using synchronization for prediction of high-dimensional chaotic dynamics. Phys. Rev. Lett. 101(15), 154102 (2008)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002)
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)
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)
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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.
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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
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DOI: https://doi.org/10.1007/s11071-015-2181-3