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Synchronization in general complex dynamical networks with coupling delays

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  • Li, Chunguang
  • Chen, Guanrong

Abstract

Complex networks have attracted increasing attention from various fields of science and engineering today. Due to the finite speeds of transmission and spreading as well as traffic congestions, a signal or influence travelling through a complex network often is associated with time delays, and this is very common in biological and physical networks. In this paper, we introduce complex dynamical network models with coupling delays for both continuous- and discrete-time cases and then investigate their synchronization phenomena and criteria. Based on these new complex network models, we derive synchronization conditions for both delay-independent and delay-dependent asymptotical stabilities in terms of linear matrix inequalities (LMI). We finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:343:y:2004:i:c:p:263-278
    DOI: 10.1016/j.physa.2004.05.058
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    References listed on IDEAS

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    1. Li, Chunguang & Xu, Hongbing & Liao, Xiaofeng & Yu, Juebang, 2004. "Synchronization in small-world oscillator networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 359-364.
    2. 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.
    3. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    4. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    5. Li, Chunguang & Chen, Guanrong, 2004. "Phase synchronization in small-world networks of chaotic oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 73-79.
    6. Li, Chunguang & Li, Shaowen & Liao, Xiaofeng & Yu, Juebang, 2004. "Synchronization in coupled map lattices with small-world delayed interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 365-370.
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