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Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication. (English) Zbl 1059.93118
Summary: The issues of lag synchronization of coupled time-delayed systems with chaos are investigated in detail. Two different systems are considered, namely neural and Mackey-Glass systems. Some sufficient conditions for determining the lag synchronization between the drive and corresponding coupling systems are derived. Moreover, synchronization attributes, such as the relationship among the speed that lag synchronization can achieve, the time delays in the involved systems and the synchronization lag, are analyzed. By using the proposed lag synchronization technique with the chaotic masking strategy, an application to a secure communication scheme is also discussed. The effectiveness of the proposed approach is illustrated by computer simulations.

MSC:
93D20Asymptotic stability of control systems
34K20Stability theory of functional-differential equations
37D45Strange attractors, chaotic dynamics
37N99Applications of dynamical systems
93C23Systems governed by functional-differential equations
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References:
[1] Hayes, S.; Grebogi, C.; Ott, E.: Communicating with chaos. Phys. rev. Lett. 70, 3031 (1993)
[2] Kocarev, L.; Parlitz, U.: General approach for chaotic synchronization with applications to communication. Phys. rev. Lett. 74, 5028 (1995)
[3] G. Chen, X. Dong, From Chaos to Order, World Scientific, Singapore, 1998. · Zbl 0908.93005
[4] Corron, N. J.; Hahs, D. W.: A new approach to communications using chaotic signals. IEEE trans. Circuits syst. I 44, 373-382 (1997) · Zbl 0902.94003
[5] Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE trans. Circuits syst. II 40, 626-633 (1993)
[6] G. Grassi, S. Mascolo, Prentice-Hall, Englewood Cliffs, NJ, 1999.
[7] Wu, C. W.; Chua, L. O.: Int. J. Bifurcat. chaos. 3, 1619-1627 (1993)
[8] Yang, T.; Chua, L. O.: Secure communication via chaotic parameter modulation. IEEE trans. Circuits syst. I 43, 817-819 (1996)
[9] Yang, T.; Wu, C.; Chua, L.: Cryptography based on chaotic systems. IEEE trans. Circuits syst. I 44, 469-472 (1997) · Zbl 0884.94021
[10] Pecora, L. M.; Carroll, T. L.; Systems, Synchronization In Chaotic: Phys. rev. Lett.. 64, 821-824 (1990) · Zbl 0938.37019
[11] Pecora, L. M.; Carroll, T. L.: Driving systems with chaotic signals. Phys. rev. A 44, 2374-2383 (1991)
[12] Colet, P.; Roy, R.: Digital communication with synchronized chaotic lasers. Opt. lett. 19, 2056 (1994)
[13] Jr., K. S. Thornburg; Moller, M.; Roy, R.; Carr, T. W.: Chaos and coherence in coupled lasers. Phys. rev. E 55, 3865 (1997)
[14] Barsella, A.; Lepers, C.: Chaotic lag synchronization and pulse-induced transient chaos in lasers coupled by saturable absorber. Opt. commun. 205, 397-403 (2002)
[15] Wang, X. -J; Rinzel, J.: Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural comput. 4, 84 (1992)
[16] Golomb, D.; Rinzel, J.: Dynamics of globally coupled inhibitory neurons with heterogeneity. Phys. rev. E 48, 4810 (1993)
[17] Bar-Eli, K.: On the stability of coupled chemical oscillators. Physica D 14, 242 (1985)
[18] Han, S. K.; Kurrer, C.; Kuramoto, Y.: Dephasing and bursting in coupled neural oscillators. Phys. rev. Lett. 75, 3190 (1995)
[19] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: Phase synchronization of chaotic oscillators. Phys. rev. Lett. 76, 1804 (1996) · Zbl 0896.60090
[20] Boccaletti, S.: The synchronization of chaotic systems. Phys. rep. 366, 1-101 (2002) · Zbl 0995.37022
[21] Rulkov, N. F.; Sushchik, M. M.; Tsimring, L. S.; Abarbanel, H. D. I: Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. rev. E 51, 980 (1995)
[22] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. rev. Lett. 78, 4193 (1997) · Zbl 0896.60090
[23] Ahlers, V.; Parlitz, U.; Lauterborn, W.: Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers. Phys. rev. E 58, 7208 (1998)
[24] Sivaprakasam, S.; Shore, K. A.: Demonstration of optical synchronization of chaotic external-cavity laser diodes. Opt. lett. 24, 466 (1999)
[25] Fujino, H.; Ohtsubo, J.: Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers. Opt. lett. 25, 625 (2000)
[26] Sivaprakasam, S.; Shahverdiev, E. M.; Shore, K. A.: Experimental verification of the synchronization condition for chaotic external cavity diode lasers. Phys. rev. E 62, 7505 (2000)
[27] Voss, H. U.: Anticipating chaotic synchronization. Phys. rev. E 61, 5115 (2000)
[28] Sivaprakasam, S.; Shahverdiev, E. M.; Spencer, P. S.; Shore, K. A.: Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback. Phys. rev. Lett. 87, 154101 (2001)
[29] Shahverdiev, E. M.: Lag synchronization in time-delayed systems. Phys. lett. A 292, 320-324 (2002) · Zbl 0979.37022
[30] Gopalsamy, K.; Leung, I. K. C; Delays, Convergence Under Dynamical Thresholds With: IEEE neural networks. 8, No. 2, 341-348 (1994)
[31] Liao, X. F.: Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function. Chaos solitons fract. 12, No. 8, 1535-1547 (2001) · Zbl 1012.92005
[32] Peng, J.; Liao, X. F.: Synchronization of a coupled time-delay chaotic system and its application to secure communications. J. comput. Res. dev. 40, No. 2, 263-268 (2003)
[33] Pyragas, K.; Estimations, Synchronization Of Coupled Time-Delayed Systems: Analytical: Phys. rev. E. 58, 3067 (1998)
[34] Masoller, C.: Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback. Phys. rev. Lett. 86, 2782 (2001) · Zbl 0978.37022
[35] Pyragas, K.: Predictable chaos in slightly perturbed unpredictable chaotic systems. Phys. lett. A 181, 203 (1993)
[36] Mensour, B.; Longtin, A.: Synchronization of delay-differential equations with application to private communication. Phys. lett. A 244, 59-70 (1998) · Zbl 0935.34062
[37] J.K. Hale, S.M.V. Lunel, Introduction to the Theory of Functional Differential Equations, vol. 99, Applied Mathematical Sciences, Springer-Verlag, New York, 1991.