- About this Journal
- Abstracting and Indexing
- Aims and Scope
- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 959368, 11 pages
Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix
College of Mathematics and Computational Sciences, Shenzhen University, Shenzhen 518060, China
Received 15 September 2012; Accepted 18 November 2012
Academic Editor: M. De la Sen
Copyright © 2013 Jianwen Feng 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.
- D. J. Watts and S. H. Strogatz, “Collective dynamics of 'small-world9 networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998.
- S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, no. 6825, pp. 268–276, 2001.
- M. E. J. Newman, “The structure and function of complex networks,” SIAM Review, vol. 45, no. 2, pp. 167–256, 2003.
- X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: robustness and fragility,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 49, no. 1, pp. 54–62, 2002.
- A. Zheleznyak and L. O. Chua, “Coexistence of low- and high-dimensional spatiotemporal chaos in a chain of dissipativelycoupled. Chuas circuits,” International Journal of Bifurcation and Chaos, vol. 4, pp. 639–672, 1994.
- V. Perez-Munuzuri, V. Perez-Villar, and L. O. Chua, “Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 3, pp. 174–181, 1993.
- C. W. Wu and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 42, no. 8, pp. 430–447, 1995.
- J. Cao, P. Li, and W. Wang, “Global synchronization in arrays of delayed neural networks with constant and delayed coupling,” Physics Letters A, vol. 353, no. 4, pp. 318–325, 2006.
- W. Yu, J. Cao, and J. Lü, “Global synchronization of linearly hybrid coupled networks with time-varying delay,” SIAM Journal on Applied Dynamical Systems, vol. 7, no. 1, pp. 108–133, 2008.
- J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005.
- T. Chen, W. Wu, and W. Zhou, “Global μ-synchronization of linearly coupled unbounded time-varying delayed neural networks with unbounded delayed coupling,” IEEE Transactions on Neural Networks, vol. 19, no. 10, pp. 1809–1816, 2008.
- Y. Wang, Z. Wang, and J. Liang, “Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances,” Journal of Physics A, vol. 42, no. 13, Article ID 135101, 2009.
- K. Wang, X. Fu, and K. Li, “Cluster synchronization in community networks with nonidentical nodes,” Chaos. An Interdisciplinary Journal of Nonlinear Science, vol. 19, no. 2, Article ID 023106, p. 10, 2009.
- J. Wang, J. Feng, C. Xu, and Y. Zhao, “Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix,” Nonlinear Dynamics, vol. 67, pp. 1635–1646, 2012.
- V. Afraimovich, A. Cordonet, and N. F. Rulkov, “Generalized synchronization of chaos in noninvertible maps,” Physical Review E, vol. 66, no. 1, Article ID 016208, 6 pages, 2002.
- S. Taherion and Y. C. Lai, “Observability of lag synchronization of coupled chaotic oscillators,” Physical Review E, vol. 59, no. 6, pp. R6247–R6250, 1999.
- Q. Zhang and J. Zhao, “Projective and lag synchronization between general complex networks via impulsive control,” Nonlinear Dynamics, vol. 67, pp. 2519–2525, 2011.
- M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Physical Review Letters, vol. 76, no. 11, pp. 1804–1807, 1996.
- R. Brown and L. Kocarev, “A unifying definition of synchronization for dynamical systems,” Chaos, vol. 10, no. 2, pp. 344–349, 2000.
- D. Miller, K. Kowalski, and A. Lozowski, “Synchronization and anti-synchronization of Chua’s oscillators via a piecewise linearcoupling circuit,” Chaos, vol. 5, pp. 458–462, 1999.
- I. Wedekind and U. Parlitz, “Experimental observation of synchronization and anti-synchronization of chaotic low-frequency-fluctuations in external cavity semiconductor lasers,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 11, no. 4, pp. 1141–1147, 2001.
- J. Hu, S. Chen, and L. Chen, “Adaptive control for anti-synchronization of Chua's chaotic system,” Physics Letters A, vol. 339, no. 6, pp. 455–460, 2005.
- L. Hui, “Synchronization and anti-synchronization of Colpitts oscillators using active control,” Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 87–93, 2005.
- W. L. Li, X. Q. Chen, and Z. P. Shen, “Anti-synchronization of two different chaotic systems,” Physica A, vol. 387, no. 14, pp. 3747–3750, 2008.
- C. Li and X. Liao, “Anti-synchronization of a class of coupled chaotic systems via linear feedback control,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 16, no. 4, pp. 1041–1047, 2006.
- J. Meng and X. Wang, “Robust anti-synchronization of a class of delayed chaotic neural networks,” Chaos. An Interdisciplinary Journal of Nonlinear Science, vol. 17, no. 2, Article ID 023113, p. 6, 2007.
- H. Zhu and B. T. Cui, “The antisynchronization of a class of chaotic delayed neural networks,” Chaos, vol. 17, no. 4, Article ID 043122, p. 7, 2007.
- H. Rui and A. Li, “A special full-state hybrid projective synchronization in symmetrical chaotic systems,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 321–329, 2008.
- H.-T. Yau, “Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs,” Nonlinear Analysis. Real World Applications, vol. 9, no. 5, pp. 2253–2261, 2008.
- J. H. Chen, H. K. Chen, and Y. K. Lin, “Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems,” Chaos, Solitons and Fractals, vol. 39, no. 2, pp. 707–716, 2009.
- C. Grabow, S. Grosskinsky, and M. Timme, “Small-world network spectra in mean-field theory,” Physical Review Letters, vol. 108, Article ID 218701, 2012.
- W. Sun, Z. Chen, Y. Lü, and S. Chen, “An intriguing hybrid synchronization phenomenon of two coupled complex networks,” Applied Mathematics and Computation, vol. 216, no. 8, pp. 2301–2309, 2010.
- J. Lu and D. W. C. Ho, “Stabilization of complex dynamical networks with noise disturbance under performance constraint,” Nonlinear Analysis. Real World Applications, vol. 12, no. 4, pp. 1974–1984, 2011.
- J. Feng, J. Wang, C. Xu, and F. Austin, “Cluster synchronization of nonlinearly coupled complex networks via pinning control,” Discrete Dynamics in Nature and Society, Article ID 262349, 23 pages, 2011.
- J. Lu, J. Kurths, J. Cao, N. Mahdavi, and C. Huang, “Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, pp. 285–291, 2012.
- 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.
- X. Liu and T. Chen, “Synchronization of identical neural networks and other systems with an adaptive coupling strength,” International Journal of Circuit Theory and Applications, vol. 38, no. 6, pp. 631–648, 2010.
- W. Wu and T. Chen, “Global synchronization criteria of linearly coupled neural network systems with time-varying coupling,” IEEE Transactions on Neural Networks, vol. 19, no. 2, pp. 319–332, 2008.