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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:
34D06 Synchronization of solutions to ordinary differential equations
90B10 Deterministic network models in operations research
34K50 Stochastic functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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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
[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.
[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. · Zbl 1366.93544
[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.
[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
[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
[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. · Zbl 1374.93297
[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
[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
[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
[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
[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
[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.
[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
[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
[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
[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.
[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.
[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
[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.
[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
[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.
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