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)
Modified impulsive synchronization of hyperchaotic systems. (English) Zbl 1221.93243
Summary: In an original impulsive synchronization only instantaneous errors are used to determine the impulsive inputs. To improve the synchronization performance, addition of an integral term of the errors is proposed here. In comparison with the original form, the proposed modification increases the impulse distances which leads to reduction in the control cost as the most important characteristic of the impulsive synchronization technique. It can also decrease the error magnitude in the presence of noise. Sufficient conditions are presented through four theorems for different situations (nominal, uncertain, noisy, and noisy uncertain cases) under which stability of the error dynamics is guaranteed. Results from computer based simulations are provided to illustrate feasibility and effectiveness of the modified impulsive synchronization method applied on Rossler hyperchaotic systems.

93D21Adaptive or robust stabilization
34A37Differential equations with impulses
37D45Strange attractors, chaotic dynamics
[1]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys. rev. Lett. 64, 821-824 (1990)
[2]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 · doi:10.1016/S0375-9601(00)00777-5
[3]Bai, E. W.; Lonngren, K. E.: Synchronization of two Lorenz systems using active control, Chaos soliton. Fract. 8, 51-58 (1997) · Zbl 1079.37515 · doi:10.1016/S0960-0779(96)00060-4
[4]Zhang, H.; Ma, X. K.; Liu, W. Z.: Synchronization of chaotic systems with parametric uncertainty using active sliding mode control, Chaos soliton. Fract. 21, 1249-1257 (2004) · Zbl 1061.93514 · doi:10.1016/j.chaos.2003.12.073
[5]Huang, L.; Feng, R.; Wang, M.: Synchronization of chaotic systems via nonlinear control, Phys. lett. A 320, 271-275 (2004) · Zbl 1065.93028 · doi:10.1016/j.physleta.2003.11.027
[6]Wang, C. C.; Su, J. P.: A new adaptive variable structure control for chaotic synchronization and secure communication, Chaos soliton. Fract. 20, 967-977 (2004) · Zbl 1050.93036 · doi:10.1016/j.chaos.2003.10.026
[7]Yau, H. T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos soliton. Fract. 22, 341-347 (2004) · Zbl 1060.93536 · doi:10.1016/j.chaos.2004.02.004
[8]Li, Z. G.; Wen, C. Y.; Soh, Y. C.; Xie, W. X.: The stabilization and synchronization of Chua’s oscillators via impulsive control, IEEE trans. Circuits syst. I 48, No. 11, 1351-1355 (2001) · Zbl 1024.93052 · doi:10.1109/81.964427
[9]Itoh, M.; Yang, T.; Chua, L. O.: Conditions for impulsive synchronization of chaotic and hyperchaotic systems, Int. J. Bifurcat. chaos 11, 551-560 (2001) · Zbl 1090.37520 · doi:10.1142/S0218127401002262
[10]Li, C.; Liao, X.: Impulsive synchronization of nonlinear coupled chaotic systems, Phys. lett. A 328, 47-50 (2004) · Zbl 1134.37367 · doi:10.1016/j.physleta.2004.05.065
[11]Haeri, M.; Dehghani, M.: Impulsive synchronization of Chen’s hyperchaotic system, Phys. lett. A 356, No. 3, 226-230 (2006) · Zbl 1160.94398 · doi:10.1016/j.physleta.2006.03.051
[12]Chen, D.; Sun, J.; Huang, C.: Impulsive control and synchronization of general chaotic system, Chaos soliton. Fract. 28, 213-218 (2006) · Zbl 1091.93023 · doi:10.1016/j.chaos.2005.05.057
[13]Parlitz, U.; Kocarev, L.; Stojanovski, T.; Junge, L.: Chaos synchronization using sporadic driving, Physica D 109, 139-152 (1997) · Zbl 0925.58086 · doi:10.1016/S0167-2789(97)00165-6
[14]Stojanovski, T.; Kocarev, L.; Parlitz, U.; Harris, R.: Sporadic driving of dynamical systems, Phys. rev. E 55, No. 4, 4035-4048 (1997)
[15]Haeri, M.; Dehghani, M.: Robust stability of impulsive synchronization in hyperchaotic systems, Commun. nonlinear sci. Numer. simul. 14, No. 3, 880-891 (2009) · Zbl 1221.93210 · doi:10.1016/j.cnsns.2007.11.019
[16]Haeri, M.; Dehghani, M.: Impulsive synchronization of different hyperchaotic systems, Chaos soliton. Fract. 38, No. 1, 120-131 (2008)
[17]Cafagna, D.; Grassi, G.: Synchronizing hyperchaos using a scalar signal: a unified framework for systems with one or several nonlinearities, Asia-Pacific conf. Circuits syst. APCCAS’02 28 – 31, 575-580 (2002)
[18]Grassi, G.; Miller, D. A.: Experimental realization of observer-based hyperchaos synchronization, IEEE trans. Circuits syst. I 48, No. 3, 366-374 (2001)
[19]Tamasevicius, A.; Cenys, A.; Mykolaitis, G.; Namajunas, A.; Lindberg, E.: Synchronization of hyperchaotic oscillators, Electron lett. 33, 2025-2026 (1997)
[20]Yang, T.: Impulsive control theory, (2001)
[21]Liu, X.: Impulsive stabilization and control of chaotic system, Nonlinear anal. Theory methods appl. 47, No. 2, 1081-1092 (2001) · Zbl 1042.93523 · doi:10.1016/S0362-546X(01)00248-6
[22]Li, C.; Liao, X.: Complete and lag synchronization of chaotic systems via small pulses, Chaos soliton. Fract. 22, 857-867 (2004) · Zbl 1129.93508 · doi:10.1016/j.chaos.2004.03.006
[23]Sun, J.; Zhang, Y.; Qiao, F.; Wu, Q.: Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach, Chaos soliton. Fract. 19, No. 5, 1049-1055 (2004) · Zbl 1069.37029 · doi:10.1016/S0960-0779(03)00264-9
[24]Li, C.; Chen, G.; Liao, X.: Chaos quasi-synchronization induced by impulsive control and parameter mismatches, Chaos 16, No. 2, 023102 (2006) · Zbl 1146.37326 · doi:10.1063/1.2179648
[25]Li, C.; Liao, X.; Yang, X.; Huang, T.: Impulsive stabilization and synchronization of delayed chaotic systems, Chaos 15, No. 4, 043103 (2005) · Zbl 1144.37371 · doi:10.1063/1.2102107
[26]Zhang, Y.; Sun, J.: Controlling chaotic Lu systems using impulsive control, Phys. lett. A 342, No. 3, 256-262 (2005) · Zbl 1222.93193 · doi:10.1016/j.physleta.2005.05.059
[27]Sun, J.; Zhang, Y.; Wu, Q.: Impulsive control for the stabilization and synchronization of Lorenz systems, Phys. lett. A 298, No. 2 – 3, 153-160 (2002) · Zbl 0995.37021 · doi:10.1016/S0375-9601(02)00466-8
[28]Yang, T.; Yang, L. B.; Yang, C. M.: Impulsive control of Lorenz system, Physica D 110, No. 1 – 2, 18-24 (1997) · Zbl 0925.93414 · doi:10.1016/S0167-2789(97)00116-4
[29]Li, C.; Liao, X.; Zhang, X.: Impulsive synchronization of chaotic systems, Chaos 15, No. 2, 023104 (2005) · Zbl 1080.37034 · doi:10.1063/1.1899823