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Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes

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  • Liu, Tao
  • Zhao, Jun
  • Hill, David J.

Abstract

In this paper, we study the global synchronization of nonlinearly coupled complex delayed dynamical networks with both directed and undirected graphs. Via Lyapunov–Krasovskii stability theory and the network topology, we investigate the global synchronization of such networks. Under the assumption that coupling coefficients are known, a family of delay-independent decentralized nonlinear feedback controllers are designed to globally synchronize the networks. When coupling coefficients are unavailable, an adaptive mechanism is introduced to synthesize a family of delay-independent decentralized adaptive controllers which guarantee the global synchronization of the uncertain networks. Two numerical examples of directed and undirected delayed dynamical network are given, respectively, using the Lorenz system as the nodes of the networks, which demonstrate the effectiveness of proposed results.

Suggested Citation

  • Liu, Tao & Zhao, Jun & Hill, David J., 2009. "Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1506-1519.
  • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1506-1519
    DOI: 10.1016/j.chaos.2007.09.075
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    1. Checco, Paolo & Biey, Mario & Kocarev, Ljupco, 2008. "Synchronization in random networks with given expected degree sequences," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 562-577.
    2. Li, Ping & Yi, Zhang & Zhang, Lei, 2006. "Global synchronization of a class of delayed complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 903-908.
    3. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    4. Wang, Weiwei & Cao, Jinde, 2006. "Synchronization in an array of linearly coupled networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 197-211.
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    6. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    7. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    8. Yu, Yongguang & Zhang, Suochun, 2005. "Global synchronization of three coupled chaotic systems with ring connection," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1233-1242.
    9. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    10. Gu, Ya-Qin & Shao, Chun & Fu, Xin-Chu, 2006. "Complete synchronization and stability of star-shaped complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 480-488.
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