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Keywords:
partial generalized synchronization; differential system; discrete system
partial generalized synchronization; differential system; discrete system
Summary:
This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.
References:
[1] Afraimovich V. S., Verichev N. N., Rabinovich M. I.: Stochastically synchronized oscillation in dissipative systems. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29 (1986), 1050–1060 MR 0877439
[2] Agiza H. N., Yassen M. T.: Synchronization of Rossler and Chen chaotic dynamiacal systems using active control. Phys. Lett. A 278 (2000), 191–197 DOI 10.1016/S0375-9601(00)00777-5 | MR 1827067
[3] Blekman I. I., Fradkov A. I., Nijmeijer, H., Pogromsky A. Y.: On self-synchron- ization and controlled synchronization. Systems Control Lett. 31 (1997), 299–305 DOI 10.1016/S0167-6911(97)00047-9 | MR 1482331
[4] Celikovský S., Chen G.: Secure Synchronization of a class of chaotic systems from a nonlinear observer approach. IEEE Trans. Automat. Control 50 (2005), 76–82 DOI 10.1109/TAC.2004.841135 | MR 2110810
[5] Chen G., Dong X.: From Chaos to Order: Methodologies, Perspectives, and Applications. World Scientific, Singapore 1998 MR 1642791 | Zbl 0908.93005
[6] Chen G., Mao, Y., Chui C.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solitons and Fractals 21 (2004), 749–761 DOI 10.1016/j.chaos.2003.12.022 | MR 2043749 | Zbl 1049.94009
[8] Grassi G., Mascolo S.: Synchronization of highorder oscillators by observer design with application to hyperchaos-based cryptography. Internat. J. Circuit Theory Appl. 27 (1999), 543–553 DOI 10.1002/(SICI)1097-007X(199911/12)27:6<543::AID-CTA81>3.0.CO;2-4
[9] Hunt B. R., Ott, E., York J. A.: Differentiable generalized synchronization of chaos. Phys. Rev. E 55 (1997), 4029–4034 DOI 10.1103/PhysRevE.55.4029 | MR 1449377
[10] Itoh M., Chua L. O.: Reconstruction and synchronization of hyperchaotic circuit via one state variable. Internat. J. Bifurcation Chaos 12 (2002), 2069–2085 DOI 10.1142/S0218127402005704 | MR 1941272
[11] Jing J., Min L.: Partial generalized synchronization theorem of discrete system with application in encryption scheme. In: Proc. Internat. Conference on Communications, Circuit and Systems, Kokura, Fukuoka 2007, Vol. I, pp. 51–55
[12] Kocarev L., Parlitz U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 76 (1996), 1816–1819 DOI 10.1103/PhysRevLett.76.1816
[13] Lau F. C. M., Tse C. K.: Chaos-Based Digital Communication Systems. Springer, Berlin 2003 Zbl 1054.94504
[14] Liu J. M., Tang S.: Chaotic optical communications using synchronized semiconductor lasers with optoelectronic feedback. Comptes Rendus Physique 5 (2004), 654–668
[15] Min L., Chen, G., al. X. Zhang et: Approach to generalized synchronization with application to chaos-based secure communication. Commun. Theory Physics 41 (2004), 632–640 MR 2088885 | Zbl 1167.37393
[16] Murali K., Laskshmanan M.: Secure communication using a compound signal from generalized synchronizable systems. Phys. Lett. 241 (1998), 303–310 DOI 10.1016/S0375-9601(98)00159-5
[17] Pecora L. M., Carroll T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821–824 DOI 10.1103/PhysRevLett.64.821 | MR 1038263 | Zbl 0938.37019
[18] Pogromsky A., Santoboni, G., Nijmeijer H.: Partial synchronization: from symmetry toward stability. Physica D 172 (2002), 65–87 DOI 10.1016/S0167-2789(02)00654-1 | MR 1942999
[19] Rucklidge A. M.: Chaos in models of double convection. J. Fluid Mechanics 237 (1992), 209–229 DOI 10.1017/S0022112092003392 | MR 1161996 | Zbl 0747.76089
[20] Santoboni G., Pogromsky, A., Nijmeijer H.: An observer for phase synchronization of chaos. Phys. Lett. A 291 (2001), 265–273 DOI 10.1016/S0375-9601(01)00652-1 | Zbl 0977.37047
[21] Santoboni G., Pogromsky, A., Nijmeijer H.: Partial observer and partial synchronization. Internat. J. Bifurcation and Chaos 13 (2003), 453–458 DOI 10.1142/S0218127403006698 | MR 1972160
[22] Santoboni G., Pogromsky, A., Nijmeijer H.: An observer for phase synchronization of chaos. Chaos 13 (2003), 356–363 MR 1964977 | Zbl 0977.37047
[23] Sprott J. C.: Simplest dissipative chaotic flow. Phys. Lett. A 228 (1997), 271–274 DOI 10.1016/S0375-9601(97)00088-1 | MR 1442639 | Zbl 1043.37504
[24] Wu C. W., Chua L. O.: Transmission of digital signals by chaotic synchronization. Internat. J. Bifurcation and Chaos 3 (1993), 1619–1627
[25] Yang T., Chua L. O.: Channe-independent chaotic secure communication. Internat. J. Bifurcation and Chaos 6 (1996), 2653–2660 DOI 10.1142/S0218127496001727
[26] Yang T., Chua L. O.: Generalized synchronization of chaos via linear transformations. Internat. J. Bifurcation Chaos 9 (1999), 215–219 DOI 10.1142/S0218127499000092 | MR 1689607 | Zbl 0937.37019
[27] Zhang X., Min L.: A Generalized chaos synchronization based encryption algorithm for sound. Circuits Systems Signal Process. 24 (2005), 535–548 MR 2187037 | Zbl 1103.94020
[28] Zang H., Min, L., Zhao G.: A generalized synchronization theorem for discrete-time chaos system with application in data encryption scheme. In: Proc. Internat. Conference on Communications, Circuit and Systems, Fukuoka 2007, Vol. II, pp. 1325–1329
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