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)
Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters. (English) Zbl 1221.93123
Summary: This paper brings attention to hyperchaos anti-synchronization between two identical and different hyperchaotic systems by using adaptive control. The sufficient conditions for achieving the anti-synchronization of two hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the hyperchaotic Chen system is controlled to be the hyperchaotic Lü system. Theoretical analysis and numerical simulations are shown to verify the results.
MSC:
93C40Adaptive control systems
34H10Chaos control (ODE)
34C28Complex behavior, chaotic systems (ODE)
34D06Synchronization
References:
[1]Chen, G.; Dong, X.: From chaos to order, (1998)
[2]Luo, A. C. J.: A theory for synchronization of dynamical systems, Commun nonlinear sci numer simulat 14, No. 5, 1901-1951 (2009) · Zbl 1221.37218 · doi:10.1016/j.cnsns.2008.07.002
[3]Dou, F.; Sun, J.; Duan, W.; Lü, K.: Controlling hyperchaos in the new hyperchaotic system, Commun nonlinear sci numer simulat 14, 552-559 (2009)
[4]Rafikov, M.; Balthazar, J.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun nonlinear sci numer simulat 13, 1246-1255 (2008) · Zbl 1221.93230 · doi:10.1016/j.cnsns.2006.12.011
[5]Ho, M. C.; Hung, Y. C.; Chou, C. H.: Phase and anti-phase synchronization of two chaotic systems by using active control, Phys lett A 296, 43-48 (2002) · Zbl 1098.37529 · doi:10.1016/S0375-9601(02)00074-9
[6]Li, Guo-Hui; Zhou, Shi-Ping: Anti-synchronization in different chaotic systems, Chaos, solitons & fractals 32, 516-520 (2007)
[7]El-Dessoky, M.: Synchronization and anti-synchronization of a hyperchaotic Chen system, Chaos, solitons & fractals (2007) · Zbl 1197.37026 · doi:10.1016/j.chaos.2007.06.053
[8]Wang, Z.: Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters, Commun nonlinear sci numer simulat 14, No. 5, 2366-2372 (2009)
[9]Al-Sawalha, M. M.; Noorani, M. S. M.: Chaos anti-synchronization between two novel different hyperchaotic systems, Chin phys lett 25, No. 8, 2743-2746 (2008)
[10]Al-Sawalha, M. M.; Noorani, M. S. M.: Active anti-synchronization between identical and distinctive hyperchaotic systems, Open syst inform dyn 15, No. 4, 371-382 (2008) · Zbl 1188.70060 · doi:10.1142/S1230161208000250
[11]Al-Sawalha, M. M.; Noorani, M. S. M.: On anti-synchronization of chaotic systems via nonlinear control, Chaos, solitons & fractals (2008) · Zbl 1198.93145 · doi:10.1016/j.chaos.2008.11.011
[12]Al-Sawalha, M. M.; Noorani, M. S. M.: Anti-synchronization of two hyperchaotic systems via nonlinear control, Commun nonlin sci numer simul 14, No. 8, 3402-3411 (2009) · Zbl 1221.37210 · doi:10.1016/j.cnsns.2008.12.021
[13]Li, Ruihong; Xu, Wei; Li, Shuang: Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control, Chaos, solitons & fractals (2007) · Zbl 1197.37138 · doi:10.1016/j.chaos.2007.09.032
[14]Feng, J.; Chen, S.; Wang, C.: Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification, Chaos, solitons & fractals 26, 1163-1169 (2005)
[15]Chen, S.; Hua, J.; Wang, C.; Lü, J.: Adaptive synchronization of uncertain rssler hyperchaotic system based on parameter identification, Phys lett A 321, 50-55 (2004) · Zbl 1118.81326 · doi:10.1016/j.physleta.2003.12.011
[16]Wu, X.; Zhang, H.: Synchronization of two hyperchaotic systems via adaptive control, Chaos, solitons & fractals (2007) · Zbl 1197.37046 · doi:10.1016/j.chaos.2007.06.100
[17]Wua, X.; Guana, Z.; Wua, Z.: Adaptive synchronization between two different hyperchaotic systems, Nonlinear anal 68, 1346-1351 (2008) · Zbl 1151.34041 · doi:10.1016/j.na.2006.12.028
[18]Gao, T.; Chen, Z.; Yuan, Z.; Yu, D.: Adaptive synchronization of a new hyperchaotic system with uncertain parameters, Chaos, solitons & fractals 33, 922-928 (2007)
[19]Wang, B.; Wen, G.: On the synchronization of a hyperchaotic system based on adaptive method, Phys lett A (2008)
[20]Jia, Q.: Adaptive control and synchronization of a new hyperchaotic system with unknown parameters, Phys lett A 362, 424-429 (2007) · Zbl 1197.34107 · doi:10.1016/j.physleta.2006.10.044
[21]Zhang, H.; Huang, W.; Wang, Z.; Chai, T.: Adaptive synchronization between two different chaotic systems with unknown parameters, Phys lett A 350, 363-366 (2006) · Zbl 1195.93121 · doi:10.1016/j.physleta.2005.10.033
[22]Yuxia, L.; Wallace, K.; Chen, G.: Generating hyperchaos via state feedback control, Int J bifurcat chaos 15, 3367-3375 (2005)
[23]Park, J.: Adaptive synchronization of hyperchaotic Chen system with uncertain parameters, Chaos, solitons & fractals 26, 959-964 (2005)
[24]Chen, A.; Lu, J.; Lü, J.; Yu, S.: Generating hyperchaotic Lü attractor via state feedback control, Physica A 364, 103-110 (2006)