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The emergence of chaos in complex dynamical networks

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  • Zhang, Hai-Feng
  • Wu, Rui-Xin
  • Fu, Xin-Chu

Abstract

The emergence of chaos is an important issue in the study of coupled dynamical networks. In this paper, we suppose that all nodes are non-chaotic before they are coupled together, however, the chaotic state will emerge without changing each node’s parameter if these nodes are connected through a certain type of network. First we give a sufficient condition for the emergence of chaotic state, then such mergence in several types of networks are discussed. Moreover, we extend our results to a general case. Finally, we illustrate our results by some numerical examples.

Suggested Citation

  • Zhang, Hai-Feng & Wu, Rui-Xin & Fu, Xin-Chu, 2006. "The emergence of chaos in complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 472-479.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:472-479
    DOI: 10.1016/j.chaos.2005.07.001
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    References listed on IDEAS

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    1. Li, Xiang & Chen, Guanrong & Ko, King-Tim, 2004. "Transition to chaos in complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 367-378.
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    Cited by:

    1. Guan, Zhi-Hong & Zhang, Hao, 2008. "Stabilization of complex network with hybrid impulsive and switching control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1372-1382.
    2. Posadas-Castillo, C. & Cruz-Hernández, C. & López-Gutiérrez, R.M., 2009. "Experimental realization of synchronization in complex networks with Chua’s circuits like nodes," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1963-1975.
    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. Yuan, Wu-Jie & Luo, Xiao-Shu & Jiang, Pin-Qun & Wang, Bing-Hong & Fang, Jin-Qing, 2008. "Transition to chaos in small-world dynamical network," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 799-806.
    5. Marjan Sedighi Anaraki & Fangyan Dong & Hajime Nobuhara & Kaoru Hirota, 2006. "Visualization of Complex Networks Based on Dyadic Curvelet Transform," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 4(1), pages 51-62.

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