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Transition to chaos in complex dynamical networks

Author

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  • Li, Xiang
  • Chen, Guanrong
  • Ko, King-Tim

Abstract

The transition from a non-chaotic state to a chaotic state is a commonly concerned issue in the study of coupled dynamical networks. In this work, we consider a network consisting of nodes that are in non-chaotic states with parameters in non-chaotic regions before they are coupled together. We show that if these non-chaotic nodes are linked together through a suitable structural topology, positive Lyapunov exponents of the coupled network can be generated by choosing a certain uniform coupling strength, and the threshold for this coupling strength is determined by the complexity of the network topology. Moreover, we show that topological effects of scale-free and random networks, which are two basic types of complex network models, can be visualized based on their topological sensitivity to random failures and intentional attacks. Our simulation results on a 1000-node scale-free network and a 1000-node random network of the Logistic maps have verified that, during the transition from non-chaotic to chaotic states, if the topology is more heterogenous then the coupling strength required to achieve the transition can be decreased.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:338:y:2004:i:3:p:367-378
    DOI: 10.1016/j.physa.2004.02.010
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    Cited by:

    1. Nicolò Pecora & Alessandro Spelta, 2014. "Shareholding Network in the Euro Area Banking Market," DISCE - Working Papers del Dipartimento di Economia e Finanza def014, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    2. Li, Lixiang & Li, Weiwei & Kurths, Jürgen & Luo, Qun & Yang, Yixian & Li, Shudong, 2015. "Pinning adaptive synchronization of a class of uncertain complex dynamical networks with multi-link against network deterioration," Chaos, Solitons & Fractals, Elsevier, vol. 72(C), pages 20-34.
    3. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    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. repec:ctc:serie1:def14 is not listed on IDEAS
    6. 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.

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