- About this Journal ·
- Abstracting and Indexing ·
- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 625372, 14 pages
Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations
1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, Hunan Information Science Vocational College, Changsha, Hunan 410151, China
Received 4 January 2013; Accepted 2 February 2013
Academic Editor: Chuangxia Huang
Copyright © 2013 Xinsong Yang et al. 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.
- S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001.
- D. J. Watts and S. H. Strogatz, “Collective dynamics of "small-world" networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998.
- W. Yu, P. DeLellis, G. Chen, M. di Bernardo, and J. Kurths, “Distributed adaptive control of synchronization in complex networks,” Institute of Electrical and Electronics Engineers, vol. 57, no. 8, pp. 2153–2158, 2012.
- X. Yang, J. Cao, and J. Lu, “Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time-varying delays,” International Journal of Robust and Nonlinear Control, 2012.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- P. Zhou and R. Ding, “Modified function projective synchronization between different dimension fractional-order chaotic systems,” Abstract and Applied Analysis, vol. 2012, Article ID 862989, 12 pages, 2012.
- Q. Zhu and J. Cao, “Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays,” Nonlinear Dynamics, vol. 61, no. 3, pp. 517–534, 2010.
- M. Ayati and H. Khaloozadeh, “A stable adaptive synchronization scheme for uncertain chaotic systems via observer,” Chaos, Solitons and Fractals, vol. 42, no. 4, pp. 2473–2483, 2009.
- C. Huang, K. Cheng, and J. Yan, “Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 2784–2792, 2009.
- N. N. Verichev, S. N. Verichev, and M. Wiercigroch, “Asymptotic theory of chaotic synchronization for dissipative-coupled dynamical systems,” Chaos, Solitons and Fractals, vol. 41, no. 2, pp. 752–763, 2009.
- T. M. Hoang and M. Nakagawa, “A secure communication system using projective-lag and/or projective-anticipating synchronizations of coupled multidelay feedback systems,” Chaos, Solitons and Fractals, vol. 38, no. 5, pp. 1423–1438, 2008.
- L. Wang and Q. Wang, “Synchronization in complex networks with switching topology,” Physics Letters A, vol. 375, no. 34, pp. 3070–3074.
- J. Wu and L. Jiao, “Synchronization in complex dynamical networks with nonsymmetric coupling,” Physica D, vol. 237, no. 19, pp. 2487–2498, 2008.
- X. Liu and T. Chen, “Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix,” Physica A, vol. 387, pp. 4429–4439, 2008.
- Z. Duan, G. Chen, and L. Huang, “Complex network synchronizability: analysis and control,” Physical Review E, vol. 76, no. 5, part 2, Article ID 056103.
- W. Lu and T. Chen, “Synchronization of coupled connected neural networks with delays,” IEEE Transactions on Circuits and Systems, vol. 51, no. 12, pp. 2491–2503, 2004.
- G. Chen, J. Zhou, and Z. Liu, “Global synchronization of coupled delayed neural networks and applications to chaotic CNN models,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 7, pp. 2229–2240, 2004.
- W. Yu, J. Cao, and G. Chen, “Local synchronization of a complex network model,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 1, pp. 230–241, 2009.
- Q. Song, “Synchronization analysis of coupled connected neural networks with mixed time delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3907–3914, 2009.
- P. Li, J. Cao, and Z. Wang, “Robust impulsive synchronization of coupled delayed neural networks with uncertainties,” Physica A, vol. 373, pp. 261–272, 2007.
- 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.
- X. Liu and T. Chen, “Boundedness and synchronization of y-coupled Lorenz systems with or without controllers,” Physica D, vol. 237, no. 5, pp. 630–639, 2008.
- J. Zhou, J. Lu, and J. Lü, “Adaptive synchronization of an uncertain complex dynamical network,” Institute of Electrical and Electronics Engineers, vol. 51, no. 4, pp. 652–656, 2006.
- Q. Zhu and J. Cao, “Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2139–2159, 2011.
- M. Chen and D. Zhou, “Synchronization in uncertain complex networks,” Chaos, vol. 16, no. 1, Article ID 013101, 8 pages, 2006.
- 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.
- 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.
- J. Zhou, X. Wu, W. Yu, M. Small, and J.-a. Lu, “Pinning synchronization of delayed neural networks,” Chaos, vol. 18, no. 4, Article ID 043111, 9 pages, 2008.
- 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.
- W. Guo, “Lag synchronization of complex networks via pinning control,” Nonlinear Analysis. Real World Applications, vol. 12, no. 5, pp. 2579–2585, 2011.
- X. Wu and H. Lu, “Outer synchronization of uncertain general complex delayed networks with adaptive coupling,” Neurocomputing, vol. 82, pp. 157–166, 2012.
- Y. Sun, J. Cao, and Z. Wang, “Exponential synchronization of stochastic perturbed chaotic delayed neural networks,” Neurocomputing, vol. 70, no. 13, pp. 2477–2485, 2007.
- Q. Zhu and J. Cao, “pth moment exponential synchronization for stochastic delayed Cohen-Grossberg neural networks with Markovian switching,” Nonlinear Dynamics, vol. 67, no. 1, pp. 829–845, 2012.
- 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 B, vol. 38, no. 4, pp. 1073–1083, 2008.
- W. Yu, G. Chen, and J. Cao, “Adaptive synchronization of uncertain coupled stochastic complex networks,” Asian Journal of Control, vol. 13, no. 3, pp. 418–429, 2011.
- S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1994.
- K. Q. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay System, Birkhauser, Boston, Mass, USA, 2003.
- V. Popov, Hyperstability of Control System, Springer, Berlin, Germany, 1973.
- X. Wang, X. Li, and G. Chen, Complex Network Theory and Its Application, Tsinghua University Press, Beijing, China, 2006.
- W. Yu, G. Chen, and J. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429–435, 2009.
- 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.
- 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.
- Y. Liu, Z. Wang, and X. Liu, “Exponential synchronization of complex networks with Markovian jump and mixed delays,” Physics Letters A, vol. 372, no. 22, pp. 3986–3998, 2008.
- Y. Tang, J. A. Fang, and Q. Miao, “On the exponential synchronization of stochastic jumping chaotic neural networks with mixed delays and sector-bounded non-linearities,” Neurocomputing, vol. 72, no. 7–9, pp. 1694–1701, 2009.