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)
Passive and impulsive synchronization of a new four-dimensional chaotic system. (English) Zbl 1216.34048
Two control methods are investigated for the synchronization of two identical four-dimensional chaotic Qi systems interacting according to the drive-response coupling scheme. It is shown that the driving signal can be constructed in such a way that the corresponding system for the synchronization error becomes passive with respect to the input. This proves the asymptotic stability of the trivial equilibrium of the synchronization error system and, thus, the onset of synchronization between the drive and response chaotic Qi systems. The second considered method is based on the impulsive control technique of synchronization. Sufficient conditions for the global asymptotic stability of the chaotic synchronization are derived. The analytical results are illustrated by numerical simulations.
34H05ODE in connection with control problems
34C28Complex behavior, chaotic systems (ODE)
34D20Stability of ODE
34H10Chaos control (ODE)
34A37Differential equations with impulses
[1]Sparrow, C.: The Lorenz equation: bifurcations, chaos and strange attractors, (1982)
[2]Rössler, O. E.: An equation for continuous chaos, Physics letters A 57, No. 5, 397-398 (1976)
[3]Chen, G.; Ueta, T.: Yet another chaotic attractor, International journal of bifurcation and chaos 9, No. 7, 1465-1466 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[4]Lü, J.; Chen, G.: A new chaotic attractor coined, International journal of bifurcation and chaos 12, No. 3, 659-661 (2002) · Zbl 1063.34510 · doi:10.1142/S0218127402004620
[5]Lü, J.; Chen, G.; Cheng, D.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, International journal of bifurcation and chaos 12, No. 12, 2917-2926 (2003) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[6]Wu, W.; Chen, Z.; Yuan, Z.: The evolution of a novel four-dimensional autonomous system: among 3-torus, limit cycle, 2-torus, chaos and hyperchaos, Chaos, solitons and fractals (2007)
[7]Sun, J.: Impulsive control of a new chaotic system, Mathematics and computers in simulation 64, 669-677 (2004) · Zbl 1076.65119 · doi:10.1016/j.matcom.2003.11.018
[8]Qi, G.; Du, S.; Chen, G.; Chen, Z.; Yuan, Z.: On a four-dimensional chaotic system, Chaos, solitons and fractals 23, 1671-1682 (2005) · Zbl 1071.37025 · doi:10.1016/j.chaos.2004.06.054
[9]Qi, G.; Chen, G.: Analysis and circuit implementation of a new 4D chaotic system, Physics letters A 352, No. 4–5, 386-397 (2006) · Zbl 1187.37050 · doi:10.1016/j.physleta.2005.12.030
[10]Vincent, U. E.: Synchronization of identical and non-identical 4-D chaotic systems using active control, Chaos, solitons and fractals 37, No. 4, 1065-1075 (2008) · Zbl 1153.37359 · doi:10.1016/j.chaos.2006.10.005
[11]Lai, Y. C.; Grebogi, C.: Synchronization of chaotic trajectories using active control, Physical review E 47, No. 4, 2357-2359 (1993)
[12]Han, X.; Lu, J. A.; Wu, X.: Adaptive feedback synchronization of Lü system, Chaos, solitons and fractals 22, No. 1, 221-227 (2004) · Zbl 1060.93524 · doi:10.1016/j.chaos.2003.12.103
[13]Liao, T. L.: Adaptive synchronization of two Lorenz systems, Chaos, solitons and fractals 9, No. 9, 1555-1561 (1998) · Zbl 1047.37502 · doi:10.1016/S0960-0779(97)00161-6
[14]Tan, X. H.; Zhang, J. Y.; Yang, Y. R.: Synchronization chaotic systems using backstepping design, Chaos, solitons and fractals 16, No. 1, 37-45 (2003) · Zbl 1035.34025 · doi:10.1016/S0960-0779(02)00153-4
[15]Shimizu, Y.; Miyazaki, M.; Lee, H. H.: Chaos synchronization based on fuzzy model using sliding mode control, International journal of innovative computing information and control 1, No. 3, 563-579 (2005)
[16]Liu, L.; J.; Lu, J. N.; Y., Shi: Different type of synchronization phenomena in unidirectional coupled unified chaotic systems, International journal of innovative computing information and control 3, No. 3, 697-708 (2007)
[17]Yu, W.: Passive equivalence of chaos in Lorenz system, IEEE transaction on circuits and systems-1: fundamental theory and applications 46, No. 7, 876-878 (1999)
[18]Kemih, K.: Synchronization of Chen system based on passivity technique for CDMA underwater communication, International journal of innovative computing, information and control 3, No. 5, 1301-1308 (2007)
[19]Zhang, Q.; Lu, J.: Impulsive control and synchronization, of a critical chaotic system, Wuhan university journal of natural sciences 12, No. 3, 426-430 (2007) · Zbl 1174.93547 · doi:10.1007/s11859-006-0056-7