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Effects of small world topology on the critical boundary for Boolean networks

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  • Zhang, Xin
  • Zhao, Qianchuan

Abstract

Due to their complexity, real dynamic systems are widely regarded as operating on the boundary between order and chaos. Therefore it is of great interest to determine analytical expressions for this boundary. For random Boolean networks model, a well known critical value of bias is established as pcrit=12(1+1−2K), where K is the mean connectivity. Recent research shows, however, that this expression may need to be modified. In this paper, we shall focus on the effects of topology deviation from the random network assumption since the topologies of many real networks are neither pure random nor fully regular Boolean networks. A modification of the critical boundary condition is given with parameters of the degree distribution in the setting of more realistic networks modeled with small world features.

Suggested Citation

  • Zhang, Xin & Zhao, Qianchuan, 2009. "Effects of small world topology on the critical boundary for Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3657-3666.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:17:p:3657-3666
    DOI: 10.1016/j.physa.2009.05.035
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    References listed on IDEAS

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    1. Serra, Roberto & Villani, Marco & Agostini, Luca, 2004. "On the dynamics of random Boolean networks with scale-free outgoing connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 665-673.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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