zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An adaptive chaos synchronization scheme applied to secure communication. (English) Zbl 1048.93508
Summary: This paper deals with the problem of synchronization of a class of continuous-time chaotic systems using the drive-response concept. An adaptive observer-based response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to unknown parameters. Using the Lyapunov stability theory an adaptation law is derived to estimate the unknown parameters. We show that synchronization is achieved asymptotically. The approach is next applied to chaos-based secure communication. To demonstrate the efficiency of the proposed scheme numerical simulations are presented.

MSC:
93C95Applications of control theory
37N35Dynamical systems in control
WorldCat.org
Full Text: DOI
References:
[1] Pecora, L. M.; Carroll, T. L.: Driving systems with chaotic signals. Phys. rev. A 44, No. 4, 2374-2383 (1991)
[2] Ogorzalek, M.: Taming chaos----part-I: synchronization. IEEE trans. Circ. syst. I 40, No. 10, 693-699 (1993) · Zbl 0850.93353
[3] Morgül, Ö.; Feki, M.: On the synchronization of chaotic systems by using occasional coupling. Phys. rev. E 55, No. 5, 5004-5009 (1997)
[4] Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D.; Zhou, C.: The synchronization of chaotic systems. Phys. rep. 366, 1-101 (2002) · Zbl 0995.37022
[5] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems. Phys. rev. Lett. 64, No. 8, 821-824 (1990) · Zbl 0938.37019
[6] Chua, L.; Itoh, M.; Kocarev, L.; Eckert, K.: Chaos synchronization in Chua’s circuit. J. circ. Syst. comput. 3, No. 1, 93-108 (1993) · Zbl 0875.94133
[7] Hasler M. Synchronization principles and applications. In: IEEE Int. Symp. Circuits and Systems, New York, 1994. p. 314--27 [Chapter 6.2]
[8] Feldmann U, Hasler M, Schwarz W. Communication by chaotic signals: the inverse system approach. In: IEEE Int Symp Circuits and Systems, Vol. 1. Seattle, 1995. p. 3--6 · Zbl 0902.94005
[9] Morgül, Ö.; Solak, E.: Observer based synchronization of chaotic signals. Phys. rev. E 54, No. 5, 4803-4811 (1996)
[10] Morgül, Ö.; Solak, E.: On the synchronization of chaotic systems by using state observers. Int. J. Bifurcat. chaos 7, No. 6, 1307-1322 (1997) · Zbl 0967.93509
[11] Nijmeijer, H.; Mareels, I. M.: An observer looks at synchronization. IEEE trans. Circ. syst. I 44, No. 10, 882-890 (1997)
[12] Feng, L.; Yong, R.; Shan, X.; Qiu, Z.: A linear feedback synchronization theorem for a class of chaotic systems. Chaos, solitons & fractals 13, No. 4, 723-730 (2002) · Zbl 1032.34045
[13] Feki, M.; Robert, B.: Observer-based chaotic synchronization in the presence of unknown inputs. Chaos, solitons & fractals 15, 831-840 (2003) · Zbl 1035.34024
[14] Feki M. Observer-based exact synchronization of ideal and mismatched chaotic systems. Phys Lett A, submitted for publication · Zbl 1010.37016
[15] Liao, T. -L.; Tsai, S. -H.: Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, solitons & fractals 11, No. 9, 1387-1396 (2000) · Zbl 0967.93059
[16] Andrievsky, B.: Adaptive synchronization methods for signal transmission on chaotic carrier. Math. comput. Simul. 58, 285-293 (2002) · Zbl 0995.65133
[17] Marino, R.; Tomei, P.: Nonlinear control design----geometric, adaptive, robust. (1995) · Zbl 0833.93003
[18] Khalil, H. K.: Nonlinear systems. (1992) · Zbl 0969.34001
[19] Besançon, G.: Remarks on nonlinear adaptive observer design. Syst. control lett. 41, 271-280 (2000) · Zbl 0980.93009
[20] Kennedy, M. P.: Bifurcation and chaos. The circuits and filters handbook, 1089-1163 (1995)
[21] Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H.: Synchronization of lorenzed-based chaotic circuits with applications to communications. IEEE trans. Circ. syst. II 40, No. 10, 626-633 (1993)
[22] Dedieu, H.; Kennedy, M. P.; Hasler, M.: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuit. IEEE trans. Circ. syst. II 40, No. 10, 634-642 (1993)
[23] Morgül, Ö.; Feki, M.: A chaotic masking scheme by using synchronized chaotic systems. Phys. lett. A 251, No. 3, 169-176 (1999)