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)
Projective synchronization of a class of delayed chaotic systems via impulsive control. (English) Zbl 1233.34017
Summary: The authors study the projective synchronization of a class of delayed chaotic systems. The drive-response system can be synchronized to within a desired scaling factor via impulsive control. Some sufficient conditions are derived by the stability analysis of the impulsive functional differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.
MSC:
34D06Synchronization
34C28Complex behavior, chaotic systems (ODE)
37B25Lyapunov functions and stability; attractors, repellers
34H10Chaos control (ODE)
49N25Impulsive optimal control problems
References:
[1]Boccaletti, S.; Kurths, J.; Osipov, G.; Valladares, D. L.; Zhou, C. S.: Phys. rep., Phys. rep. 366, 1 (2002)
[2]Pecora, L. M.; Carroll, T. L.: Phys. rev. Lett., Phys. rev. Lett. 64, 821 (1990)
[3]Carroll, T. L.; Heagy, J. F.; Pecora, L. M.: Phys. rev. E, Phys. rev. E 54, 4676 (1996)
[4]Rosenblum, M.; Pikovsky, A.; Kurtz, J.: Phys. rev. Lett., Phys. rev. Lett. 76, 1804 (1996)
[5]Pikovsky, A. S.; Rosenblum, M. G.; Osipov, G. V.; Kurths, J.: Physica D, Physica D 104, 219 (1997)
[6]Rosenblum, M.; Pikovsky, A.; Kurtz, J.: Phys. rev. Lett., Phys. rev. Lett. 78, 4193 (1997)
[7]Morgul, O.; Solak, E.: Phys. rev. E, Phys. rev. E 54, 4803 (1996)
[8]Morgul, O.; Solak, E.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 7, 1307 (1997)
[9]Mainieri, R.; Rehacek, J.: Phys. rev. Lett., Phys. rev. Lett. 82, 3042 (1999)
[10]Xu, D.: Phys. rev. E, Phys. rev. E 63, 027201 (2001)
[11]Xu, D.; Liu, Z.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 12, 1395 (2002)
[12]Xu, D.; Ong, W. L.; Li, Z.: Phys. lett. A, Phys. lett. A 305, 167 (2002)
[13]Wang, B.; Bu, S.: Int. J. Modern phys. B, Int. J. Modern phys. B 16, 2415 (2004)
[14]Yu, H.; Peng, J.; Liu, Y.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 16, 1049 (2006)
[15]Hu, M.; Xu, Z.; Zhang, R.; Hu, A.: Phys. lett. A, Phys. lett. A 365, 315 (2007)
[16]Hu, M.; Yang, Y.; Xu, Z.: Phys. lett. A, Phys. lett. A 372, 3228 (2008)
[17]Park, J. H.: J. comput. Appl. math., J. comput. Appl. math. 213, 288 (2008)
[18]Tang, Y.; Fang, J.: Phys. lett. A, Phys. lett. A 372, 1816 (2008)
[19]Chen, H.; Liu, J.: IEEE J. Quantum electron., IEEE J. Quantum electron. 36, 27 (2000)
[20]Choi, M. Y.; Kim, H. J.; Kim, D.; Hong, H.: Phys. rev. E, Phys. rev. E 61, 371 (2000)
[21]Yalcin, M. E.; Suykens, J. A. K.; Vandewalle, J.: Int. J. Bifur. chaos, Int. J. Bifur. chaos 11, 1707 (2001)
[22]Cao, J.; Lu, J.: Chaos, Chaos 16, 013133 (2006)
[23]Zhou, S.; Li, H.; Wu, Z.: Phys. rev. E, Phys. rev. E 75, 037203 (2007)
[24]Chen, G.; Yu, X.: IEEE trans. Circ. syst.-I, IEEE trans. Circ. syst.-I 46, 767 (1999)
[25]Cao, J.; Li, H. X.; Ho, D. W. C.: Chaos solitons fractals, Chaos solitons fractals 23, 1285 (2005)
[26]Stojanovski, T.; Kocarev, L.; Parlitz, U.: Phys. rev. E, Phys. rev. E 43, 782 (1996)
[27]Sun, J.; Zhang, Y.; Wu, Q.: Phys. lett. A, Phys. lett. A 298, 153 (2002)
[28]Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H.: IEEE trans. Circ. syst.-II, IEEE trans. Circ. syst.-II 40, 626 (1993)
[29]Li, C.; Liao, X.; Yang, X.: Chaos, Chaos 15, 043103 (2005)
[30]Khadra, A.; Liu, X.; Shen, X.: Automatica, Automatica 41, 1491 (2005)
[31]Yang, T.; Chua, L. O.: IEEE trans. Circ. syst.-I, IEEE trans. Circ. syst.-I 44, 976 (1997)
[32]Yang, Y.; Cao, J.: Physica A, Physica A 386, 492 (2007)
[33]Luo, R.: Chinese phys. Lett. A, Chinese phys. Lett. A 372, 648 (2008)
[34]Tang, Y.; Wang, Z.; Fang, J.: Chaos, Chaos 19, 013112 (2009)
[35]Hu, M.; Yang, Y.; Xu, Z.; Zhang, R.; Guo, L.: Physica A, Physica A 381, 457 (2007)
[36]Zhao, Y.; Yang, Y.: Phys. lett. A, Phys. lett. A 372, 7165 (2008)
[37]Yang, T.: Impulsive control theory, (2001)
[38]Feng, C.; Zhang, Y.; Wang, Y.: Chin. phys. Lett., Chin. phys. Lett. 23, 1418 (2006)
[39]Feng, C.; Zhang, Y.; Sun, J.; Wang, Y.: Chaos solitons fractals, Chaos solitons fractals 38, 743 (2008)
[40]Lu, W.; Chen, T.: Physica D, Physica D 221, 118 (2006)