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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 513871, 8 pages
Criterion for Unbounded Synchronous Region in Complex Networks
School of Mathematics and Statistics, State Key Lab of Software Engineering, Wuhan University, Wuhan 430072, China
Received 20 August 2013; Accepted 18 September 2013
Academic Editor: Jinde Cao
Copyright © 2013 Jin Zhou. 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.
- A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, “Synchronization reveals topological scales in complex networks,” Physical Review Letters, vol. 96, Article ID 114102, 2006.
- I. Leyva, A. Navas, I. Sendina-Nadal et al., “Explosive transitions to synchronization in networks of phase oscillators,” Scientific Reports, vol. 3, article 1281, 2013.
- R. M. Szmoski, R. F. Pereira, and S. E. de Souza Pinto, “Effective dynamics for chaos synchronization in networks with time-varying topology,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 6, pp. 1491–1498, 2013.
- Y. Wu, C. Li, Y. Wu, and J. Kurths, “Generalized synchronization between two different complex networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 349–355, 2012.
- L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
- 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.
- X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: robustness and fragility,” IEEE Transactions on Circuits and System I, vol. 49, no. 1, pp. 54–62, 2002.
- A. E. Motter, C. Zhou, and J. Kurths, “Network synchronization, diffusion, and the paradox of heterogeneity,” Physical Review E, vol. 71, no. 1, Article ID 016116, 2005.
- J. Cao and F. Ren, “Exponential stability of discrete-time genetic regulatory networks with delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 520–523, 2008.
- T. Nishikawa and A. E. Motter, “Maximum performance at minimum cost in network synchronization,” Physica D, vol. 224, no. 1-2, pp. 77–89, 2006.
- J. Zhou, J.-a. 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.
- Z. Li and G. Chen, “Robust adaptive synchronization of uncertain dynamical networks,” Physics Letters A, vol. 324, no. 2-3, pp. 166–178, 2004.
- J. Zhou, J.-a. Lu, and J. Lü, “Pinning adaptive synchronization of a general complex dynamical network,” Automatica, vol. 44, no. 4, pp. 996–1003, 2008.
- 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.
- 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.
- W. Yu, G. Chen, and J. Lü, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, no. 2, pp. 429–435, 2009.
- W. Yu, G. Chen, J. Lü, and J. Kurths, “Synchronization via pinning control on general complex networks,” SIAM Journal on Control and Optimization, vol. 51, no. 2, pp. 1395–1416, 2013.
- L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Physical Review Letters, vol. 80, no. 10, pp. 2109–2112, 1998.
- M. Barahona and L. M. Pecora, “Synchronization in small-world systems,” Physical Review Letters, vol. 89, no. 5, Article ID 054101, 4 pages, 2002.
- Y. Chen, G. Rangarajan, and M. Ding, “General stability analysis of synchronized dynamics in coupled systems,” Physical Review E, vol. 67, no. 2, Article ID 026209, 4 pages, 2003.
- K. K. Hassan, Nonlinear Systems, Prentice Hall, 3rd edition, 2002.
- A. Isidori, Nonlinear Control Systems II, Electronic Industry Press, 1st edition, 2012 (Chinese).
- C. Godsil and G. Royle, Algebraic Graph Theory, vol. 207, Springer, New York, NY, USA, 2001.
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, NY, USA, 1985.
- R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.
- C. W. Wu, “Synchronization in networks of nonlinear dynamical systems coupled via a directed graph,” Nonlinearity, vol. 18, no. 3, pp. 1057–1064, 2005.
- W. Lu and T. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physica D, vol. 213, no. 2, pp. 214–230, 2006.
- G. R. Chen, X. F. Wang, and X. Li, Introduction to Complex Networks: Models, Structures and Dynamics, Higher Education Press, 1st edition, 2012.
- J. A. Lu, J. Chen, and J. Zhou, “On relations between synchronous state and solution of single node in complex networks,” Acta Automatica Sinica. In press.
- T. Matsumoto, L. O. Chua, and M. Komuro, “The double scroll,” IEEE Transactions on Circuits and Systems, vol. 32, no. 8, pp. 797–818, 1985.
- E. N. Lorenz, “Deterministic non-periodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963.
- J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 3, pp. 659–661, 2002.
- J. Lü, G. Chen, D. Cheng, and S. Celikovsky, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 12, pp. 2917–2926, 2002.