Geodesic
Dynamics of stability regions of discrete models of neural networks of small world type when the numeric characteristics of the network graph change
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 7 (2018) no. 2, pp. 22-31

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The article gives the description of the discrete models of neural networks with constraints of the type of small world with probability redirecting connections within the network p varying from 0 to 1. At the value p = 0 we obtain a model of a regular neural network. A regular neural network is a ring neural network, in which each neuron interacts with several neighbors along the ring. At p = 1, we obtain a model, the neurons of which are randomly connected to other neurons of the network without formation of isolated neurons. The neural networks are widely used in modeling various neural structures in living organisms, for example, mammalian brain hypocampus. The paper studies the dynamics of the stability regions of the neural networks in case of changes in the probability of redirecting links, clustering coefficient and the length of the shortest path in the average for the graph of neural network. In a series of numerical experiments, the regions of stability of the studied neural network models for various network parameters were constructed, and the conclusion about increasing the stability region while reducing the length of the shortest path on average and the clustering coefficient of the network graph was drawn.
Keywords: Watts-Strogatz discrete models, small world, stability. 
@article{VYURV_2018_7_2_a1,
     author = {S. A. Ivanov and M. M. Kipnis},
     title = {Dynamics of stability regions of discrete models of neural networks of small world type when the numeric characteristics of the network graph change},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {22--31},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2018_7_2_a1/}
}
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S. A. Ivanov; M. M. Kipnis. Dynamics of stability regions of discrete models of neural networks of small world type when the numeric characteristics of the network graph change. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 7 (2018) no. 2, pp. 22-31. http://geodesic.mathdoc.fr/item/VYURV_2018_7_2_a1/