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Emergence of the small-world architecture in neural networks by activity dependent growth

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  • Gafarov, F.M.

Abstract

In this paper, we propose a model describing the growth and development of neural networks based on the latest achievements of experimental neuroscience. The model is based on two evolutionary equations. The first equation is for the evolution of the neurons state and the second is for the growth of axon tips. By using the model, we demonstrated the neuronal growth process from disconnected neurons to fully connected three-dimensional networks. For the analysis of the network’s connections structure, we used the random graphs theory methods. It is shown that the growth in neural networks results in the formation of a well-known “small-world” network model. The analysis of the connectivity distribution shows the presence of a strictly non-Gaussian but no scale-free degree distribution for the in-degree node distribution. In terms of the graphs theory, this study developed a new model of dynamic graph.

Suggested Citation

  • Gafarov, F.M., 2016. "Emergence of the small-world architecture in neural networks by activity dependent growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 409-418.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:409-418
    DOI: 10.1016/j.physa.2016.06.016
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    References listed on IDEAS

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    1. Perotti, Juan I. & Tamarit, Francisco A. & Cannas, Sergio A., 2006. "A scale-free neural network for modelling neurogenesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 71-75.
    2. Martín-Hernández, J. & Wang, H. & Van Mieghem, P. & D’Agostino, G., 2014. "Algebraic connectivity of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 92-105.
    3. Colman, E.R. & Rodgers, G.J., 2013. "Complex scale-free networks with tunable power-law exponent and clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5501-5510.
    4. Zhang, Zhongzhi & Zhou, Shuigeng & Shen, Zhen & Guan, Jihong, 2007. "From regular to growing small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 765-772.
    5. Weaver, Iain S., 2015. "Preferential attachment in randomly grown networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 85-92.
    6. Park, Chang-hyun & Kim, Soo Yong & Kim, Yun-Hee & Kim, Kyungsik, 2008. "Comparison of the small-world topology between anatomical and functional connectivity in the human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5958-5962.
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