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Scaling behaviors and self-organized criticality of two-dimensional small-world neural networks

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Listed:
  • Zeng, Hong-Li
  • Zhu, Chen-Ping
  • Wang, Shu-Xuan
  • Guo, Yan-Dong
  • Gu, Zhi-Ming
  • Hu, Chin-Kun

Abstract

It is widely believed that the brains of human beings work at or near the state of self-organized criticality (SOC). In the present work, we investigate two-dimensional small-world neural networks (2D SWNN) with Bak–Sneppen (BS)-type neurons as their nodes. By taking threshold firing and refractory period as the key features of neurons in the simulations, a few power laws are obtained for suitable range of parameters. The SOC characterized by the power-law distribution of avalanche sizes as well as 1∕f noise emerges in the present model. Moreover, a set of scaling relations are found to exhibit criticality. The exponent for the power spectrum of all return time is α=0.71, which is comparable with what were found in medical experiments.

Suggested Citation

  • Zeng, Hong-Li & Zhu, Chen-Ping & Wang, Shu-Xuan & Guo, Yan-Dong & Gu, Zhi-Ming & Hu, Chin-Kun, 2020. "Scaling behaviors and self-organized criticality of two-dimensional small-world neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317947
    DOI: 10.1016/j.physa.2019.123191
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    References listed on IDEAS

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    1. Chang, Hui & Xu, Xiu-Lian & Hu, Chin-Kun & Fu, Chunhua & Feng, Ai-xia & He, Da-Ren, 2014. "A manipulator game model of urban public traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 378-385.
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    3. K. E. Lee & J. W. Lee, 2006. "Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 271-275, March.
    4. Yang, Albert C.-C & Peng, C.-K & Yien, H.-W & Goldberger, Ary L, 2003. "Information categorization approach to literary authorship disputes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(3), pages 473-483.
    5. Chi, Ting-Ting & Wang, Shih-Chieh & Hu, Chin-Kun, 2015. "Word population analysis and other evidences indicate that Shiji was amended by Liu Xiang," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 408-417.
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