zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Adaptive controller design for modified projective synchronization of Genesio-Tesi chaotic system with uncertain parameters. (English) Zbl 1142.93428
Summary: The paper addresses control problem for the modified projective synchronization of the Genesio-Tesi chaotic systems with three uncertain parameters. An adaptive control law is derived to make the states of two identical Genesio-Tesi systems asymptotically synchronized up to specific ratios. The stability analysis in the paper is proved using a well-known Lyapunov stability theory. A numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

93D21Adaptive or robust stabilization
37D45Strange attractors, chaotic dynamics
Full Text: DOI
[1] Fujisaka, H.; Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Progr theor phys 69, 32-47 (1983) · Zbl 1171.70306
[2] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems. Phys rev lett 64, 821-824 (1990) · Zbl 0938.37019
[3] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos. Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501
[4] Lu, H.; He, Z.: Chaotic behavior in first-order autonomous continuous-time systems with delay. IEEE trans circuit syst 43, 700-702 (1996)
[5] Chen, G.: Chaos on some controllability conditions for chaotic dynamics control. Chaos, solitons & fractals 8, 1461-1470 (1997)
[6] Pyragas, K.: Continuous control of chaos by self-controlling feedback. Phys lett A 170, 421-428 (1992)
[7] Park, J. H.; Kwon, O. M.: LMI optimization approach to stabilization of time-delay chaotic systems. Chaos, solitons & fractals 23, 445-450 (2005) · Zbl 1061.93509
[8] Lu, J.; Wu, X.; Lü, J.: Synchronization of a unified chaotic system and the application in secure communication. Phys lett A 305, 365-370 (2002) · Zbl 1005.37012
[9] Wang, C. C.; Su, J. P.: A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos, solitons & fractals 20, 967-977 (2004) · Zbl 1050.93036
[10] Park, J. H.: Chaos synchronization of between two different chaotic dynamical systems. Chaos, solitons & fractals 27, 549-554 (2006) · Zbl 1102.37304
[11] Park, J. H.: Chaos synchronization of nonlinear Bloch equations. Chaos, solitons & fractals 27, 357-361 (2006) · Zbl 1091.93029
[12] Park, J. H.: Adaptive synchronization of hyperchaotic Chen system with uncertain parameters. Chaos, solitons & fractals 26, 959-964 (2005) · Zbl 1093.93537
[13] Park, J. H.: Adaptive synchronization of Rössler system with uncertain parameters. Chaos, solitons & fractals 25, 333-338 (2005) · Zbl 1125.93470
[14] Park, J. H.: Adaptive synchronization of a four-dimensional chaotic system with uncertain parameters. Int J non sci numer simul 6, 305-310 (2005)
[15] Park, J. H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int J non sci numer simul 6, 201-206 (2005)
[16] Wu, X.; Lu, J.: Parameter identification and backstepping control of uncertain Lü system. Chaos, solitons & fractals 18, 721-729 (2003) · Zbl 1068.93019
[17] Li, D.; Lu, J. A.; Wu, X.: Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems. Chaos, solitons & fractals 23, 79-85 (2005) · Zbl 1063.37030
[18] Lü, J.; Zhou, T.; Zhang, S.: Chaos synchronization between linearly coupled chaotic systems. Chaos, solitons & fractals 14, 529-541 (2002) · Zbl 1067.37043
[19] Park, J. H.: Stability criterion for synchronization of linearly coupled unified chaotic systems. Chaos, solitons & fractals 23, 1319-1325 (2005) · Zbl 1080.37035
[20] Agiza, H. N.; Yassen, M. T.: Synchronization of Rössler and Chen chaotic dynamical systems using active control. Phys lett A 278, 191-197 (2001) · Zbl 0972.37019
[21] Wang, Y.; Guan, Z. H.; Wang, H. O.: Feedback an adaptive control for the synchronization of Chen system via a single variable. Phys lett A 312, 34-40 (2003) · Zbl 1024.37053
[22] Bai, E. W.; Lonngren, K. E.: Sequential synchronization of two Lorenz systems using active control. Chaos, solitons & fractals 11, 1041-1044 (2000) · Zbl 0985.37106
[23] Lu, J.; Wu, X.; Han, X.; Lü, J.: Adaptive feedback synchronization of a unified chaotic system. Phys lett A 329, 327-333 (2004) · Zbl 1209.93119
[24] Yang, X. S.; Chen, G.: Some observer-based criteria for discrete-time generalized chaos synchronization. Chaos, solitons & fractals 13, 1303-1308 (2002) · Zbl 1006.93580
[25] 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, 980-994 (1995)
[26] Wang, Y. W.; Guan, Z. H.: Generalized synchronization of continuous chaotic systems. Chaos, solitons & fractals 27, 97-101 (2006) · Zbl 1083.37515
[27] Li GH. Generalized projective synchronization between Lorenz system and Chen’s system. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.11.073.
[28] Li GH. Modified projective synchronization of chaotic system. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.12.009.
[29] Huang, L.; Feng, R.; Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys lett A 320, 271-275 (2004) · Zbl 1065.93028
[30] Chen, M.; Han, Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control. Chaos, solitons & fractals 17, 709-716 (2003) · Zbl 1044.93026
[31] Genesio, R.; Tesi, A.: A harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28, 531-548 (1992) · Zbl 0765.93030