Previous |  Up |  Next

Article

Title: Partial generalized synchronization theorems of differential and discrete systems (English)
Author: Jing, Jianyi
Author: Min, Lequan
Author: Zhao, Geng
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 44
Issue: 4
Year: 2008
Pages: 511-521
Summary lang: English
.
Category: math
.
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. (English)
Keyword: partial generalized synchronization
Keyword: differential system
Keyword: discrete system
MSC: 34K23
MSC: 34K99
idZBL: Zbl 1234.34037
idMR: MR2459069
.
Date available: 2009-09-24T20:37:30Z
Last updated: 2013-09-21
Stable URL: http://hdl.handle.net/10338.dmlcz/135870
.
Reference: [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
Reference: [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 MR 1827067, 10.1016/S0375-9601(00)00777-5
Reference: [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 MR 1482331, 10.1016/S0167-6911(97)00047-9
Reference: [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 MR 2110810, 10.1109/TAC.2004.841135
Reference: [5] Chen G., Dong X.: From Chaos to Order: Methodologies, Perspectives, and Applications.World Scientific, Singapore 1998 Zbl 0908.93005, MR 1642791
Reference: [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 Zbl 1049.94009, MR 2043749, 10.1016/j.chaos.2003.12.022
Reference: [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 10.1002/(SICI)1097-007X(199911/12)27:6<543::AID-CTA81>3.0.CO;2-4
Reference: [9] Hunt B. R., Ott, E., York J. A.: Differentiable generalized synchronization of chaos.Phys. Rev. E 55 (1997), 4029–4034 MR 1449377, 10.1103/PhysRevE.55.4029
Reference: [10] Itoh M., Chua L. O.: Reconstruction and synchronization of hyperchaotic circuit via one state variable.Internat. J. Bifurcation Chaos 12 (2002), 2069–2085 MR 1941272, 10.1142/S0218127402005704
Reference: [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
Reference: [12] Kocarev L., Parlitz U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems.Phys. Rev. Lett. 76 (1996), 1816–1819 10.1103/PhysRevLett.76.1816
Reference: [13] Lau F. C. M., Tse C. K.: Chaos-Based Digital Communication Systems.Springer, Berlin 2003 Zbl 1054.94504
Reference: [14] Liu J. M., Tang S.: Chaotic optical communications using synchronized semiconductor lasers with optoelectronic feedback.Comptes Rendus Physique 5 (2004), 654–668
Reference: [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 Zbl 1167.37393, MR 2088885
Reference: [16] Murali K., Laskshmanan M.: Secure communication using a compound signal from generalized synchronizable systems.Phys. Lett. 241 (1998), 303–310 10.1016/S0375-9601(98)00159-5
Reference: [17] Pecora L. M., Carroll T. L.: Synchronization in chaotic systems.Phys. Rev. Lett. 64 (1990), 821–824 Zbl 0938.37019, MR 1038263, 10.1103/PhysRevLett.64.821
Reference: [18] Pogromsky A., Santoboni, G., Nijmeijer H.: Partial synchronization: from symmetry toward stability.Physica D 172 (2002), 65–87 MR 1942999, 10.1016/S0167-2789(02)00654-1
Reference: [19] Rucklidge A. M.: Chaos in models of double convection.J. Fluid Mechanics 237 (1992), 209–229 Zbl 0747.76089, MR 1161996, 10.1017/S0022112092003392
Reference: [20] Santoboni G., Pogromsky, A., Nijmeijer H.: An observer for phase synchronization of chaos.Phys. Lett. A 291 (2001), 265–273 Zbl 0977.37047, 10.1016/S0375-9601(01)00652-1
Reference: [21] Santoboni G., Pogromsky, A., Nijmeijer H.: Partial observer and partial synchronization.Internat. J. Bifurcation and Chaos 13 (2003), 453–458 MR 1972160, 10.1142/S0218127403006698
Reference: [22] Santoboni G., Pogromsky, A., Nijmeijer H.: An observer for phase synchronization of chaos.Chaos 13 (2003), 356–363 Zbl 0977.37047, MR 1964977
Reference: [23] Sprott J. C.: Simplest dissipative chaotic flow.Phys. Lett. A 228 (1997), 271–274 Zbl 1043.37504, MR 1442639, 10.1016/S0375-9601(97)00088-1
Reference: [24] Wu C. W., Chua L. O.: Transmission of digital signals by chaotic synchronization.Internat. J. Bifurcation and Chaos 3 (1993), 1619–1627
Reference: [25] Yang T., Chua L. O.: Channe-independent chaotic secure communication.Internat. J. Bifurcation and Chaos 6 (1996), 2653–2660 10.1142/S0218127496001727
Reference: [26] Yang T., Chua L. O.: Generalized synchronization of chaos via linear transformations.Internat. J. Bifurcation Chaos 9 (1999), 215–219 Zbl 0937.37019, MR 1689607, 10.1142/S0218127499000092
Reference: [27] Zhang X., Min L.: A Generalized chaos synchronization based encryption algorithm for sound.Circuits Systems Signal Process. 24 (2005), 535–548 Zbl 1103.94020, MR 2187037
Reference: [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
.

Files

Files Size Format View
Kybernetika_44-2008-4_7.pdf 932.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo