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)
Finite-time stochastic synchronization of complex networks. (English) Zbl 1201.37118
Summary: We study the finite-time stochastic synchronization problem for complex networks with stochastic noise perturbations. By using finite-time stability theorem, inequality techniques, the properties of Wiener process and adding suitable controllers, sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks. The effects of control parameters on synchronization speed and time are also analyzed. The results of this paper are applicable to both directed and undirected weighted networks while do not need to know any information about eigenvalues of coupling matrix. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, the results of this paper are important. A numerical example shows the effectiveness of our new results.

37N35Dynamical systems in control
60G35Signal detection and filtering (stochastic processes)
90B15Network models, stochastic (optimization)
Full Text: DOI
[1] Strogatz, S. H.: Exploring complex networks, Nature 410, 268-276 (2001)
[2] Newman, M. E. J.: The structure and function of complex networks, SIAM rev. 45, 167-256 (2003) · Zbl 1029.68010 · doi:10.1137/S003614450342480
[3] Watts, D. J.; Strogatz, S. H.: Collective dynamics of ’small-world’ networks, Nature 393, 440-442 (1998)
[4] Wang, X. F.; Chen, G.: Complex networks: small-world, scale-free and beyond, IEEE circuits syst. Mag. 3, No. 1, 6-20 (2003)
[5] Park, K.; Lai, Y. C.; Gupte, S.; Kim, J. W.: Synchronization in complex networks with a modular structure, Chaos 16, 015105 (2006) · Zbl 1144.37396 · doi:10.1063/1.2154881
[6] Perez-Munuzuri, V.; Perez-Villar, V.; Chua, L. O.: Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths, IEEE trans. Circuits syst. I 40, No. 3, 174-181 (1993) · Zbl 0800.92038 · doi:10.1109/81.222798
[7] Lu, J.; Yu, X.; Chen, G.: Chaos synchronization of general complex dynamical networks, Physica A 334, 281-302 (2004)
[8] Strogatz, S.; Stewart, D.: Coupled oscillators and biological synchronization, Sci. am. 269, 102-109 (1993)
[9] Y. Zhang, Z. He, A secure communication scheme based on cellular neural networks, in: Proceedings of IEEE International Conference on Intelligent Processing Systems 1, 1997, pp. 521 -- 524.
[10] Chen, G.; Duan, Z.: Network synchronizability analysis: a graph-theoretic approach, Chaos 18, 037102 (2008) · Zbl 1309.05166
[11] Wu, C.; Chua, L.: Synchronization in an array of linearly coupled dynamical systems, IEEE trans. Circuit syst. I 42, No. 8, 430-447 (1995) · Zbl 0867.93042 · doi:10.1109/81.404047
[12] Lu, W.; Chen, T.: New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D 213, 214-230 (2006) · Zbl 1105.34031 · doi:10.1016/j.physd.2005.11.009
[13] Wu, J.; Jiao, L.: Global synchronization and state tuning in asymmetric complex dynamical networks, IEEE trans. Circuits syst.-II: express briefs 55, No. 9, 392-396 (2008)
[14] Li, Z.; Lee, J.: New eigenvalue based approach to synchronization in asymmetrically coupled networks, Chaos 17, 043117 (2007) · Zbl 1163.37347 · doi:10.1063/1.2804525
[15] Ott, E.; Grebogi, C.; Yorke, J. A.: Control. chaos, Phys. rev. Lett. 64, No. 11, 1196-1199 (1990) · Zbl 0964.37501
[16] Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys. rev. Lett. 64, No. 8, 821-824 (1990) · Zbl 0938.37019
[17] Luo, R.: Impulsive control and synchronization of a new chaotic system, Phys. lett. A 372, 648-653 (2008) · Zbl 1217.37033 · doi:10.1016/j.physleta.2007.08.010
[18] Yang, Y.; Cao, J.: Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects, Phys. A 386, 492-502 (2007)
[19] Huang, X.; Cao, J.: Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme, Nonlinearity 19, No. 12, 2797-2811 (2006) · Zbl 1111.37022 · doi:10.1088/0951-7715/19/12/004
[20] Cao, J.; Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay, Chaos 16, 013133 (2006) · Zbl 1144.37331 · doi:10.1063/1.2178448
[21] Yu, W.; Cao, J.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Phys. A 375, 467-482 (2007)
[22] Xiang, L.; Liu, Z.; Chen, Z.; Chen, F.; Yuan, Z.: Pinning control of complex dynamical networks with general topology, Phys. A 379, 298-306 (2007)
[23] Li, S.; Tian, Y.: Finite time synchronization of chaotic systems, Chaos solit. Fract. 15, 303-310 (2003) · Zbl 1038.37504 · doi:10.1016/S0960-0779(02)00100-5
[24] Wang, H.; Han, Z.; Xie, Q.; Zhang, W.: Finite-time chaos control via nonsingular terminal sliding mode control, Commun. nonlinear sci. Numer. simulat. 14, No. 6, 2728-2733 (2009) · Zbl 1221.37225 · doi:10.1016/j.cnsns.2008.08.013
[25] Bowong, S.; Kakmeni, M.; Koina, R.: Chaos synchronization and duration time of a class of uncertain chaotic systems, Math. comput. Simulat. 71, 212-228 (2006) · Zbl 1161.37317 · doi:10.1016/j.matcom.2006.01.006
[26] Haimo, Vt.: Finite time controllers, SIAM J. Control optim. 24, 760-770 (1986) · Zbl 0603.93005 · doi:10.1137/0324047
[27] Bowong, S.; Kakmeni, F.: Chaos control and duration time of a class of uncertain chaotic systems, Phys. lett. A 316, 206-217 (2003) · Zbl 1031.37071 · doi:10.1016/S0375-9601(03)01152-6
[28] S. Bhat, D. Bernstein, Finite-time stability of homogeneous systems, in: Proceedings of ACC, Albuquerque, NM, 1997, pp. 2513 -- 2514.
[29] Hong, Y.; Wang, J.; Cheng, D.: Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE trans. Auto. cont. 51, No. 5, 858-862 (2006)
[30] Y. Feng, L. Sun, X. Yu, Finite time synchronization of chaotic systems with unmatched uncertainties, The 30th Annual Conference of the IEEE Industrial Electronics Society, Busan Korea, 2004, pp. 2911 -- 2916.
[31] Hassan, Sa.; Aria, Al.: Adaptive synchronization of two chaotic systems with stochastic unknown parameters, Commun. nonlinear sci. Numer. simulat. 14, 508-519 (2009) · Zbl 1221.93246 · doi:10.1016/j.cnsns.2007.09.002
[32] Yu, W.; Cao, J.: Synchronization control of stochastic delayed neural networks, Phys. A 373, 252-260 (2006)
[33] Sun, Y.; Cao, J.; Wang, Z.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing 70, 2465-2477 (2007)
[34] Cao, J.; Wang, Z.; Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays, Phys. A 385, 718-728 (2007)
[35] Yang, X.; Cao, J.: Stochastic synchronization of coupled neural networks with intermittent control, Phys. lett. A 373, 3259-3272 (2009) · Zbl 1233.34020 · doi:10.1016/j.physleta.2009.07.013
[36] Liu, B.; Liu, X.; Chen, G.; Wang, H.: Robust impulsive synchronization of uncertain dynamical networks, IEEE trans. Circuit syst. I: regular 52, No. 7, 1431-1441 (2005)
[37] J. Lü, Daniel W.C. Ho, J. Cao, Synchronization in arrays of delay-coupled neural networks via adaptive control, 2007 IEEE International Conference on Control and Automation, pp. 438 -- 443.
[38] Zhou, J.; Lu, J.; Lü, J.: Adaptive synchronization of an uncertain complex dynamical network, IEEE trans. Auto. cont. 51, No. 4, 652-656 (2006)
[39] Xu, L.; Wang, X.: Mathematical analysis methods and examples, (1983)