Adaptive synchronization of the complex dynamical network with double non-delayed and double delayed coupling

Yuhua Xu1, Wuneng Zhou2, Jian-an Fang2
1College of Department of Mathematics and Finance, Yunyang Teachers’ College, Hubei, Shiyan, P. R. China
2College of Information Science and Technology, Donghua University, Shanghai, P.R. China

Tóm tắt

To simulate more realistic networks, we introduce a complex dynamical network model with double non-delayed and double delayed coupling and further investigate its synchronization phenomenon in this paper. Based on Lyapunov stability theory, adaptive synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, the complex dynamical network with double non-delayed and double delayed coupling can asymptotically synchronize to a given trajectory. What is more, the coupling matrix is not assumed to be symmetric or irreducible. Finally, simulation results show the method is effective.

Tài liệu tham khảo

X. Li and G. Chen, “Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint,” IEEE Trans. on Circuits and Systems I, vol. 50, no. 11, pp. 1381–1390, 2003. J. Lü and G. Chen, “A time-varying complex dynamical network models and its controlled synchronization criteria,” IEEE Trans. on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005. J. Lü, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical networks,” Physica A, vol. 334, no. 1–2, pp. 281–302, 2004. J. Zhou, T. Chen, and L. Xiang, “Adaptive synchronization of coupled chaotic systems based on parameters identification and its applications,” International Journal of Bifurcation and Chaos, vol. 16, no. 3, pp. 2923–2933, 2006. J. Zhou, L. Xiang, and Z. Liu, “Global synchronization in general complex delayed dynamical networks and its applications,” Physica A, vol. 385, no. 2, pp. 729–742, 2007. Z. Ma, Z. Liu, and G. Zhang, “A new method to realize cluster synchronization in connected chaotic networks,” Chaos, vol. 16, no. 2, pp. 023103, 2006. H. Tang, L. Chen, J. Lu, and C. Tse, “Adaptive synchronization between two complex networks with nonidentical topological structures,” Physica A, vol. 387, no. 22, pp. 5623–5630, 2008. Y. Tang and J. Fang, “Synchronization of Ncoupled fractional-order chaotic systems with ring connection,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, pp. 401–412, 2010. J. Zhou, J. Lu, and J. Lü, “Adaptive synchronization of an uncertain complex dynamical network,” IEEE Trans. on Automatic Control, vol. 51, no. 4, pp. 652–656, 2006. 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. Lü, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical networks,” Physica A, vol. 34, no. 1–2, pp. 281–302, 2004. D. Yu, M. Righero, and L. Kocarev, “Estimating topology of network,” Physical Review Letters, vol. 97, no. 18, 188701, 2006. J. Zhou and J. Lu, “Topology identification of weighted complex dynamical networks,” Physica A, vol. 386, no. 1, pp. 481–491, 2007. W. Yu and J. Cao, “Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks,” Chaos, vol. 16, no. 2, pp. 023119, 2006. Z. Wu, K. Li, and X. Fu, “Parameter identification of dynamical networks with community structure and multiple coupling delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 1, pp. 3587–3592, 2010. W. Sun, S. Chen, and W. Guo, “Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling,” Physics Letters A, vol. 372, no. 42, pp. 6340–6346, 2008. H. Liu, J. Lu, and J. Lü, “Structure identification of uncertain general complex dynamical networks with time delay,” Automatica, vol. 45, no. 8, pp. 1799–1807, 2009. X. Wu, “Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay,” Physica A, vol. 387, no. 4, pp. 997–1008, 2008. Q. Zhang, J. Lu, J. Lü, and C. Tse, “Adaptive feedback synchronization of a general complex dynamical network with delayed nodes,” IEEE Trans. on Circuits and Systems II, vol. 55, no. 2, pp. 183–187, 2008. H. R. Karimi, “A sliding mode approach to H∞ synchronization of master-slave time-delays systems with Markovian jumping parameters and nonlinear uncertainties,” J. of the Franklin Institute, doi: 10.1016/j.jfranklin.2011.09.015, 2011. H. R. Karimi, “Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations,” Int. J. Control, Automation, and Systems, vol. 9, no. 4, pp. 671–680, 2011. H. R. Karimi and H. Gao, “LMI-based H∞ synchronization of second-order neutral master-slave systems using delayed output feedback control,” Int. J. Control, Automation, and Systems, vol. 7, no. 3, pp. 371–380, 2009. H. R. Karimi, “Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks,” Journal of Chaos, Solitons & Fractals, vol. 41, pp. 1125–1135, 2009. D. Yue and H. Li, “Synchronization stability of continuous/discrete complex dynamical networks with interval time varying delays,” Neuro-computing, vol. 73, no. 2, pp. 809–819, 2010. J. Yao, H. O. Wang, Z. Guan, and W. Xu, “Passive stability and synchronization of complex spatiotemporal switching networks with time delays,” Automatica, vol. 45, no. 3, pp. 1721–1728, 2009. H. R. Karimi and H. Gao, “New delay-dependent exponential H∞ synchronization for uncertain neural networks with mixed time-delays,” IEEE Trans. on Systems, Man and Cybernetics, Part B, vol. 40, no. 1, pp. 173–185, 2010. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnana, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994. J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos, vol. 12, no. 3, pp. 659–661, 2002. 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.