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A new chaos synchronization scheme and its application to secure communications. (English) Zbl 1281.34101

Summary: Under the framework of drive-response systems, a new method of complete dislocated general hybrid projective synchronization (CDGHPS) is proposed. In this design, every state variable of drive system does not equal the corresponding state variable of response system, but equal other ones of response system while evolving in time. Especially, complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization can be considered all as the special cases of the proposed method. In addition, this method is applied to secure communication through chaotic masking, the unpredictability of the scaling factor in projective synchronization can additionally enhance the security of communication. In consideration of random white noise, we study the random white noise perturbing for the transmission of an information signal. Finally, eliminate noise using wavelet transform. Numerical simulations are given to show the effectiveness of these methods.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
94A60 Cryptography
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[1] Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990) · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[2] Liu, H., Lu, J.A., Zhang, Q.J.: Projectively lag synchronization and uncertain parameters identification of a new hyperchaotic system. Nonlinear Dyn. 62, 427-435 (2010) · Zbl 1211.93062 · doi:10.1007/s11071-010-9729-z
[3] Chen, D.Y., Zhang, R., Ma, X.Y., Liu, S.: Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dyn. 69, 35-55 (2012) · Zbl 1253.93017 · doi:10.1007/s11071-011-0244-7
[4] Chen, D.Y., Wu, C., Liu, C.F., Ma, X.Y., You, Y.J.: Synchronization and circuit simulation of a new double-wing chaos. Nonlinear Dyn. 67, 1481-1504 (2012) · Zbl 1256.94082 · doi:10.1007/s11071-011-0083-6
[5] Chen, D.Y., Zhang, R., Sprott, J.C.: Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control. Chaos 22, 023130 (2012) · Zbl 1331.34129 · doi:10.1063/1.4721996
[6] Taherion, S., Lai, Y.: Experimental observation of lag synchronization in coupled chaotic systems. Int. J. Bifurc. Chaos 10, 2587-2594 (2000) · Zbl 0968.37506
[7] Feng, C.F.: Projective synchronization between two different time-delayed chaotic systems using active control approach. Nonlinear Dyn. 62, 453-459 (2010) · Zbl 1211.93064 · doi:10.1007/s11071-010-9733-3
[8] Zanette, D.H., Morelli, L.G.: Synchronization of coupled extended dynamical systems: a short review. Int. J. Bifurc. Chaos 13, 781-796 (2003) · Zbl 1056.37015 · doi:10.1142/S0218127403007114
[9] Li, D., Lu, J., Wu, X.: Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems. Chaos Solitons Fractals 23, 79-85 (2005) · Zbl 1063.37030 · doi:10.1016/j.chaos.2004.03.027
[10] Aguilar-Ibañez, C., Hernáadez-Rubio, E., Suárez-Castañón, M.S.: On the parameters estimation of the Duffing system by systems synchronization. Int. J. Bifurc. Chaos 20, 3303-3309 (2010) · Zbl 1204.34017 · doi:10.1142/S0218127410027696
[11] Harb, A. M.; Ahmad, W. M., Chaotic systems synchronization in secure communication systems, Las Vegas
[12] Mascolo, S., Backstepping design for controlling Lorenz chaos, San Diego, CA, USA
[13] Xu, D.L.: Control of projective synchronization in chaotic systems. Phys. Rev. E 63, 027201 (2001) · doi:10.1103/PhysRevE.63.027201
[14] Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63, 239-252 (2011) · Zbl 1215.93127 · doi:10.1007/s11071-010-9800-9
[15] Salarieh, H., Shahrokhi, M.: Multi-synchronization of chaos via linear output feedback strategy. J. Comput. Appl. Math. 213, 842-852 (2009) · Zbl 1156.65103 · doi:10.1016/j.cam.2008.03.002
[16] Rafikov, R.M., Balthazar, B.J.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13, 1246-1255 (2008) · Zbl 1221.93230 · doi:10.1016/j.cnsns.2006.12.011
[17] Hu, M.F., Xu, Z.Q., Zhang, R.: Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems. Commun. Nonlinear Sci. Numer. Simul. 13, 456-546 (2008) · Zbl 1123.37013 · doi:10.1016/j.cnsns.2006.05.003
[18] Hu, M.F., Xu, Z.Q.: Nonlinear feedback mismatch synchronization of Lorenz chaotic systems. J. Syst. Eng. Electron. 29, 1346-1348 (2007) · Zbl 1174.93469
[19] Mianovic, V., Zaghloul, M.E.: Improved masking algorithm chaotic communication systems. Electron. Lett. 1, 11-12 (1996) · doi:10.1049/el:19960004
[20] Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 40, 626-633 (1993) · doi:10.1109/82.246163
[21] Kocarev, L., Halle, K.S., Eckert, K.: Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurc. Chaos 2, 709-713 (1993) · Zbl 0875.94134
[22] Short, K.M.: Steps toward unmasking secure communications. Int. J. Bifurc. Chaos 4, 959-977 (1994) · Zbl 0875.94002 · doi:10.1142/S021812749400068X
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