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