- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 275205, 8 pages
-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays
1The Institute of Advanced Computing Technology, Beihang University (BUAA), Beijing 100191, China
2State Key Laboratory of Software Development Environment, Beihang University (BUAA), Beijing 100191, China
Received 25 January 2013; Accepted 14 April 2013
Academic Editor: Jong Hae Kim
Copyright © 2013 Bowen Du and Dianfu Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. J. Watts and S. H. Strogatz, “Collective dynamics of “small world” networks,” Nature, vol. 393, pp. 440–442, 1998.
- A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” American Association for the Advancement of Science, vol. 286, no. 5439, pp. 509–512, 1999.
- J. J. Wu, Z. Y. Gao, and H. J. Sun, “Optimal traffic networks topology: a complex networks perspective,” Physica A, vol. 387, no. 4, pp. 1025–1032, 2008.
- S. Biswas, R. Tatchikou, and F. Dion, “Vehicle-to-vehicle wireless communication protocols for enhancing highway traffic safety,” IEEE Communications Magazine, vol. 44, no. 1, pp. 74–82, 2006.
- S. Chen, W. Huang, C. Cattani, and G. Altieri, “Traffic dynamics on complex networks: a survey,” Mathematical Problems in Engineering, vol. 2012, Article ID 732698, 23 pages, 2012.
- X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: robustness and fragility,” IEEE Transactions on Circuits and Systems I, vol. 49, no. 1, pp. 54–62, 2002.
- X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A, vol. 310, no. 3-4, pp. 521–531, 2002.
- X. Li, X. F. Wang, and G. R. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems I, vol. 51, no. 10, pp. 2074–2087, 2004.
- L. Y. Xiang, Z. X. Liu, Z. Q. Chen, F. Chen, and Z. Z. Yuan, “Pinning control of complex dynamical networks with general topology,” Physica A, vol. 379, no. 1, pp. 298–306, 2007.
- T. P. Chen, X. W. Liu, and W. L. Lu, “Pinning complex networks by a single controller,” IEEE Transactions on Circuits and Systems I, vol. 54, no. 6, pp. 1317–1326, 2007.
- J. Zhou, J.-A. Lu, and J. H. Lü, “Pinning adaptive synchronization of a general complex dynamical network,” Automatica, vol. 44, no. 4, pp. 996–1003, 2008.
- W. W. Yu, G. R. Chen, and J. H. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429–435, 2009.
- C. Li and G. Chen, “Synchronization in general complex dynamical networks with coupling delays,” Physica A, vol. 343, no. 1–4, pp. 263–278, 2004.
- Z. X. Liu, Z. Q. Chen, and Z. Z. Yuan, “Pinning control of weighted general complex dynamical networks with time delay,” Physica A, vol. 375, no. 1, pp. 345–354, 2007.
- L. Y. Xiang, Z. Q. Chen, Z. X. Liu, F. Chen, and Z. Z. Yuan, “Pinning control of complex dynamical networks with heterogeneous delays,” Computers and Mathematics with Applications, vol. 56, no. 5, pp. 1423–1433, 2008.
- J. Yao, Z.-H. Guan, and D. J. Hill, “Passivity-based control and synchronization of general complex dynamical networks,” Automatica, vol. 45, no. 9, pp. 2107–2113, 2009.
- B. Shen, Z. D. Wang, and X. H. Liu, “Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 145–157, 2011.
- S. G. Wang, H. X. Yao, and M. P. Sun, “Cluster synchronization of timevarying delays coupled complex networks with nonidentical dynamical nodes,” Journal of Applied Mathematics, vol. 2012, Article ID 958405, 12 pages, 2012.
- T. B. Wang, W. N. Zhou, D. J. Zhao, and S. W. Zhao, “Exponential synchronization analysis and control for discrete-time uncertain delay complex networks with stochastic effects,” Mathematical Problems in Engineering, vol. 2012, Article ID 261274, 14 pages, 2012.
- X. R. Wang, R. F. Rao, and S. M. Zhong, “LMI approach to stability analysis of Cohen-Grossberg neural networks with p-Laplace diffusion,” Journal of Applied Mathematics, vol. 2012, Article ID 523812, 12 pages, 2012.
- Y. F. Wang and L. S. Wang, “LMI-based approach for exponential robust stability of high-order Hopfield neural networks with time-varying delays,” Journal of Applied Mathematics, vol. 2012, Article ID 182745, 8 pages, 2012.
- C. W. Wu and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Transactions on Circuits and Systems I, vol. 42, no. 8, pp. 430–447, 1995.
- Y.-Y. Hou, T.-L. Liao, and J.-J. Yan, “ synchronization of chaotic systems using output feedback control design,” Physica A, vol. 379, no. 1, pp. 81–89, 2007.
- J. H. Park, D. H. Ji, S. C. Won, and S. M. Lee, “ synchronization of time-delayed chaotic systems,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 170–177, 2008.
- S. M. Lee, D. H. Ji, J. H. Park, and S. C. Won, “ synchronization of chaotic systems via dynamic feedback approach,” Physics Letters A, vol. 372, no. 29, pp. 4905–4912, 2008.
- R. Horn and C. Johnson, Matrix Analysis, Cambridge University, Cambridge, UK, 2005.
- S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994.
- Y. M. Jia, Robust H∞ Control, Science Press, Beijing, China, 2007.
- E. Fridman and U. Shaked, “A descriptor system approach to control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002.
- P. Lin, Y. M. Jia, and L. Li, “Distributed robust consensus control in directed networks of agents with time-delay,” Systems and Control Letters, vol. 57, no. 8, pp. 643–653, 2008.
- C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer, New York, NY, USA, 1982.