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 pinning synchronization of complex networks with stochastic perturbations. (English) Zbl 1198.34090
Summary: The adaptive pinning synchronization is investigated for complex networks with nondelayed and delayed couplings and vector-form stochastic perturbations. Two kinds of adaptive pinning controllers are designed. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are developed to guarantee the synchronization of the proposed complex networks even if partial states of the nodes are coupled. Furthermore, three examples with their numerical simulations are employed to show the effectiveness of the theoretical results.

MSC:
34D06Synchronization
90B10Network models, deterministic (optimization)
34K50Stochastic functional-differential equations
92B20General theory of neural networks (mathematical biology)
WorldCat.org
Full Text: DOI EuDML
References:
[1] M. Chen and D. Zhou, “Synchronization in uncertain complex networks,” Chaos, vol. 16, no. 1, Article ID 013101, 8 pages, 2006. · Zbl 1144.37338 · doi:10.1063/1.2126581
[2] J. Cao, Z. Wang, and Y. Sun, “Synchronization in an array of linearly stochastically coupled networks with time delays,” Physica A, vol. 385, no. 2, pp. 718-728, 2007. · doi:10.1016/j.physa.2007.06.043
[3] J. Zhou, J. Lu, and J. Lü, “Adaptive synchronization of an uncertain complex dynamical network,” IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 652-656, 2006. · doi:10.1109/TAC.2006.872760
[4] J. Lu, D. W. C. Ho, and J. Cao, “Synchronization in arrays of delay-coupled neural networks via adaptive control,” in Proceedings of IEEE International Conference on Control and Automation (ICCA ’08), pp. 438-443, May 2008. · doi:10.1109/ICCA.2007.4376395
[5] C. W. Wu, “On the relationship between pinning control effectiveness and graph topology in complex networks of dynamical systems,” Chaos, vol. 18, no. 3, Article ID 037103, 6 pages, 2008. · Zbl 1309.05169 · doi:10.1063/1.2944235
[6] W. Yu, G. Chen, and J. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429-435, 2009. · Zbl 1158.93308 · doi:10.1016/j.automatica.2008.07.016
[7] T. Chen, X. Liu, and W. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems I, vol. 54, no. 6, pp. 1317-1326, 2007. · doi:10.1109/TCSI.2007.895383
[8] W. Xia and J. Cao, “Pinning synchronization of delayed dynamical networks via periodically intermittent control,” Chaos, vol. 19, no. 1, Article ID 013120, 8 pages, 2009. · Zbl 1311.93061 · doi:10.1063/1.3071933
[9] L. Xiang, Z. Chen, Z. Liu, F. Chen, and Z. Yuan, “Pinning control of complex dynamical networks with heterogeneous delays,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1423-1433, 2008. · Zbl 1155.34353 · doi:10.1016/j.camwa.2008.03.022
[10] J. Zhou, J. Lu, and J. Lü, “Pinning adaptive synchronization of a general complex dynamical network,” Automatica, vol. 44, no. 4, pp. 996-1003, 2008. · Zbl 1283.93032
[11] J. Zhou, X. Wu, W. Yu, M. Small, and J. Lu, “Pinning synchronization of delayed neural networks,” Chaos, vol. 18, no. 4, Article ID 043111, 9 pages, 2008. · Zbl 1309.92018 · doi:10.1063/1.2995852
[12] W. Guo, F. Austin, S. Chen, and W. Sun, “Pinning synchronization of the complex networks with non-delayed and delayed coupling,” Physics Letters A, vol. 373, no. 17, pp. 1565-1572, 2009. · Zbl 1228.05266 · doi:10.1016/j.physleta.2009.03.003
[13] W. Lu, T. Chen, and G. Chen, “Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay,” Physica D, vol. 221, no. 2, pp. 118-134, 2006. · Zbl 1111.34056 · doi:10.1016/j.physd.2006.07.020
[14] J. Liang, Z. Wang, Y. Liu, and X. Liu, “Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 38, no. 4, pp. 1073-1083, 2008. · doi:10.1109/TSMCB.2008.925724
[15] A. Pototsky and N. Janson, “Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling,” Physica D, vol. 238, no. 2, pp. 175-183, 2009. · Zbl 1168.82020 · doi:10.1016/j.physd.2008.09.010
[16] X. Yang and J. Cao, “Stochastic synchronization of coupled neural networks with intermittent control,” Physics Letters A, vol. 373, no. 36, pp. 3259-3272, 2009. · Zbl 1233.34020 · doi:10.1016/j.physleta.2009.07.013
[17] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509-512, 1999. · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[18] J. Zhou, L. Xiang, and Z. Liu, “Synchronization in complex delayed dynamical networks with impulsive effects,” Physica A, vol. 384, no. 2, pp. 684-692, 2007. · doi:10.1016/j.physa.2007.05.060
[19] X. Liu and T. Chen, “Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix,” Physica A, vol. 387, no. 16-17, pp. 4429-4439, 2008. · doi:10.1016/j.physa.2008.03.005
[20] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004
[21] X. Mao, “A note on the LaSalle-type theorems for stochastic differential delay equations,” Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 125-142, 2002. · Zbl 0996.60064 · doi:10.1006/jmaa.2001.7803
[22] Q. Song and J. Cao, “On pinning synchronization of directed and undirected complex dynamical networks,” IEEE Transactions on Circuits and Systems I, vol. 57, no. 3, pp. 672-680, 2010. · doi:10.1109/TCSI.2009.2024971
[23] X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A, vol. 310, no. 3-4, pp. 521-531, 2002. · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[24] W. Ren, “Consensus seeking in multi-vehicle systems with a time-varying reference state,” in Proceedings of the American Control Conference (ACC ’07), pp. 717-722, New York, NY, USA, July 2007. · doi:10.1109/ACC.2007.4282230